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Dynamic Link Library Solver User`s Guide

1. WRITE 200 200 FORMAT Example NLP problem iC Re initialize the values of the rhs sense and lb arrays rhs 0 1 0 rhs 1 0 0 sense EG 1b 0 INFBOUND 1lb 1 INFBOUND Cc Initialize the values of the variables x 0 0 25 x 1 0 25 C Set up the NLP problem lp loadnlp PROBNAME 2 2 1 obj rhs sense NullL NullL NullL matval x lb ub NullD 4 funcevall jacobian1 C Set up the callback function to display iteration and objective ret setlpcallbackfunc lp lpcallback Solve the nonlinear problem ret optimize lp C Obtain and write out the solution ret solution lp stat objval x NullD NullD NullD WRITE 110 stat objval WRITE 120 x 0 x 1 SENDIF END The Microsoft compilers also support various extensions to FORTRAN that you can use to add Windows user interface features to your FORTRAN application Consult the Microsoft FORTRAN PowerStation or FORTRAN 5 1 manuals for details 108 e Calling the Solver DLL from FORTRAN Dynamic Link Library Solver User s Guide Solver API Reference Overview In this section we present the detailed arguments and return values of each of the Solver DLL s callable routines The declaration syntax used is that of C you will find prototypes and symbolic constants for all of the callable routines in the C C header file frontmip h To see the corresponding declaration syntax in Visual Basic Delphi Pascal and FORTRAN examine
2. Sub Adjust detail Sub End rows rows rows FormforExamp FormforExamp FormforExampl FormforExamp amp constraints PROB NLP cols amp Trim Str cols amp constraints PROB NSP cols amp Trim Str cols amp constraints le2 le3 e4 le5 FormforExample omitted Sub Adjust detail omit End Sub EXAMP2 FRM FormforExamplel ted amp rows amp amp rows amp amp Trim Str in ints variables Trim Str in ints variables Trim Str in ts amp ts amp Private Sub Commandl1_Click ts amp integers integers integers Dim Dim obj 0 To 1 rhs 0 To 1 Dim Dim As Double As Double Dim Dim Dim se ma ma Dim Dim ma ma nse 0 To 1 tbeg 0 To 1 tent 0 To 1 tind 0 To 3 tval 0 To 3 Dim Dim Dim if As Byte l As Long As Long l As Long As Double obj 0 To number_of_variables 1 rhs 0 To number of constraints 1 sense 0 To number _of constraints 1 matbeg 0 To number of variables 1 matcnt 0 To number of variables 1 The size of the arrays of matind and matval depends on the t T For nonlinear problems number of nonzero elements in the LP matrix for linear problems it is easiest to take the number of constraints times t
3. Dynamic Link Library Solver User s Guide Solver API Reference 109 TOAT RATA AA es Ee ahs ce Ok ees ees fate cunes Sahat eluate cate see Mieke oat nates 109 Atsument Types 2acccosccscueeaviecwsghvcuneestectes e E E EE E OA E EENS 110 NULL Values for AfrayS encen iii E R R a 110 Problem Definition Routines ss sssseeeesseseessesersreseeressesessesttstestesesststeseesesstetesseseseserseseeneso 111 LO ACI Peers s E e Rie 111 loadquiad eni a E aie eae eae Oe a E E 113 loadct ype cor rrr iR E RA E E E ee E E eee oie 114 oreka tati o AEE AA EAEE AE E TAA O E E A A T OTS 114 NO ACMI YG 2 5 Aes E cue Beers feet eet E SE OEIS EIE OE ESET 116 testnltypes en teats eae eee A ee ee 117 unloadpro Dieiis EE ee 118 SOM Oty ROWINES EE A E EE 118 OPUIMNIZE 2 56 2s AE AA EE ETE AE a tie ek WR es A et 119 IMIPOP tM Ze oaie st es i AR Rees RR Bi AS eee RN at 119 SOLUHON 2 esi2es ieee aih he oot eeenea sa eR nee R 119 OD SB Accel set res ets E E E chit sade nels E a Ube tls Ak ad AE 121 PSSA sels e eae ama ae hh aah haath eh aa Gta ats 121 Varsta l eooo aia e charg i EEE E E E EEE EE AOA EE N 122 CONSTA be e nE E E E laced GE ERO A EO REER 122 Diagnostic e oE a en EAE A E ee 123 PNAN S ni a a a sh ede ene ae ts ten hee teeter 123 Bets seis hie ete ee sal te ante eee dis fas eae A RE 124 TIS WIIG 225s rebecca be r sec handed E R AE E 124 NP WMG seca dt esas esate EEE acs sh aces Roane hac gE E ae oe 125 UPTO EN EE Yes Souter vec sak E E NEN E SIE E ET 1
4. because the two constraints conflict and getiis to help isolate the source rhs 0 1 rhs 1 0 sense 0 Asc E sense 1 Asc E 1b 0 INFBOUND 1lb 1 INFBOUND ub 0 INFBOUND ub 1 INFBOUND x 0 0 25 x 1 0 25 setintparam 0 PARAM ARGCK 1 lp loadnlp PROBNAME 2 2 1 obj rhs sense _ NullL NullL NullL matval x lb ub NullD 4 AddressOf funceval3 0 If lp 0 Then Exit Sub optimize lp solution lp stat objval x piout slack dj Form2 Text3 Status amp stat Form2 Text4 Objective amp objval If stat PSTAT INFEASIBLE Then setlpcallbackfunc lp 0 findiis lp iisrows iiscols MsgBox Findiis iisrows amp Trim Str iisrows amp iiscols amp Trim Str iiscols ets Form2 Textl iisrows amp Trim Str iisrows Form2 Text2 iiscols amp Trim Str iiscols ReDim rowbdstat iisrows 1 As Long ReDim rowind iisrows 1 As Long getiis lp stat rowind rowbdstat iisrows NullL Null iiscols Form2 TextS5 rowindl amp rowind 0 Form2 Text6 rowbdstatl amp rowbdstat 0 Form2 Text7 rowindl amp rowind 1 Form2 Text8 rowbdstatl amp rowbdstat 1 End If call unloadprob unloadprob lp 90 e Calling the Solver DLL from Visual Basic to release memory Dynamic Link Library Solver User s Guide Case 4 Example program calling the nonlinear Solver DLL for a series of problems which
5. Dynamic Link Library e Version 3 5 Solver User s Guide By Frontline Systems Inc include frontmip h include frontkey h include lt stdio h gt INTARG _CC FuncEval LPREALARG objval HPROBLEM lp INTARG numcols LPREALARG rhs LPREALARG var INTARG numrows INTARG varone INTARG vartwo objval 0 lhs 0 lhs 1 return 0 var 0 var 0 var 1 var 0 var 1 var 0 var 1 var 1 objective constraint left hand side 1 0 constraint left hand side gt 0 0 int main Solve example constrained nonlinear optimization problem double obj i double rhs 2 char sense 2 double 1b double ub long stat double x 2 double objval HPROBLEM 1p 1 double matval 4 1 0 0 0 n EG x INFBOUND INFBOUND INFBOUND INFBOUND ie 0 0 0 2 slack 2 0 piout 2 printf Example NLP problem n loadnlp NULL 1p NULL PROBNAME Bi ae matval 1 X obj rhs sense lb ub NULL 4 NULL FuncEval NULL optimize lp solution lp printf Status printf Final values x 0 i gs Yy printf slack 1d slack i for i 0 iy return 0 amp stat amp objval x piout ld Objective g n 7g x 1 slack NULL stat objval s7g n x 0 x 1 i 7g dual value 1d i piout i 79 n Copyright Sof
6. a complete project with supporting files is included These projects create simple forms that display the results of solving the two optimization problems when a button is pressed The example programs for C C and Visual Basic provide a total of eleven examples of using the Solver DLL The first set source code file vcexamp1 c or VB project vbexamp1 vbp includes five examples 1 A simple two variable LP problem 2 A simple MIP mixed integer linear programming problem 3 An example illustrating the Solver DLL features for diagnosing infeasibility 4 A simple quadratic programming problem which uses the classic Markowitz method to find an efficient portfolio of five securities and 5 An example using the pread function to read and solve a problem defined in algebraic notation in an external text file The second set source code file vcexamp2 c or VB project vbexamp2 vbp includes four examples of nonlinear problems plus two examples of nonsmooth problems 1 A simple two variable NLP problem 2 The same NLP problem with an optional user written routine for computing partial derivatives 3 An example illustrating the diagnosis of infeasibility for nonlinear problems 4 An example showing how you can solve a series of linear and nonlinear problems testing them for linearity and switching between the NLP and LP Solver engines 5 An example where the Evolutionary Solver finds the global minimum of a function with several l
7. repeatedly perturbing one variable at a time and resetting the previously perturbed variable On these calls usually about half of all funceval calls varone and vartwo are the indices 0 to numcols 1 of the only variables whose values have changed since the last call Your funceval routine must still compute values for objval and all elements of the hs array but you may be able to do less work based on knowledge of which variables have changed INTARG jacobian lp numcols numrows nzspace objval obj matbeg matcnt matind matval var objtype matvaltype HPROBLEM lp INTARG numcols numrows nzspace LPREALARG objval obj LPINTARG matbeg matcnt HPINTARG matind HPREALARG matval LPREALARG var LPBYTEARG objtype matvaltype The jacobian routine if supplied is called in preference to funceval but only by the nonlinear GRG Solver engine to compute the objective gradient and the Jacobian matrix of partial derivatives of the problem functions at a specific trial point found by the Solver Each row of the Jacobian is the gradient of the corresponding constraint function Note that if jacobian is supplied funceval will still be called but its varone and vartwo arguments will always be 1 The jacobian routine should compute the value and gradient of the objective and the Jacobian at the trial point represented by the values in the var argument The numcols numrows and nzspace val
8. szVar2 TextOut hDC nDrawX nDrawY szResults strlen szResults nDrawY nSpacing wsprintf szText Status ld Objective s 66 e Native Windows Applications Dynamic Link Library Solver User s Guide stat LPSTR szObj TextOut hDC nDrawX nDrawY szText strlen szText nDrawY nSpacing wsprintf szText xl s x2 s LPSTR szVarl LPSTR szVar2 TextOut hDC nDrawX nDrawY szText strlen szText nDrawY 2 nSpacing EndPaint hWnd amp ps break case WM DESTROY PostQuitMessage 0 break default return DefWindowProc hWnd message wParam 1Param return 0 PBYTE FPSTR double value PBYTE lpstr PBYTE buf lpstr int length 0 DWORD dwFraction if value lt 0 00 buf length value value length wsprintf amp buf length lu DWORD value dwFraction DWORD 1 00E 04 value DWORD value length wsprintf amp buf length 4 4lu dwFraction return lpstr Define a callback function which displays the iteration and current objective value in the window title bar and checks for the ESC key long _CC pivot HPROBLEM lpinfo long wherefrom long NumPivot double Objective char PivotMsg 64 ObjStr 12 MSG msg HWND hWnd getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT amp NumPivot getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ amp Objective FPSTR Objective ObjStr
9. x 0 x 1 for i 0 i lt 1 i printf slack ld 7g piout ld i slack i i piout i printf n setlpcallbackfunc setintparam lp unloadprob amp lp 1p NULL PARAM_DERIV 0 Example C program calling the Attempts to solve the problem Minimize X 2 Y 2 Subject to X Y 1 X Y 0 This problem is infeasible We will call findiis and getiis of the infeasibility INTARG numcols LPREALARG var INTARG _CC funceval3 LPREALARG objval INTARG vartwo HPROBLEM lp LPREALARG lhs Dynamic Link Library Solver User s Guide 7g n nonlinear Solver DLL because the two constraints conflict to help isolate the source INTARG numrows INTARG varone Calling the Solver DLL from C C e 45 objval 0 var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side return 0 void example3 void double obj 2 double rhs 2 1 0 0 0 char sense 2 EE double matval 4 double 1lb INFBOUND INFBOUND double ub INFBOUND INFBOUND long i stat iisrows iiscols double objval long rowind 2 rowbdstat 2 colind 2 colbdstat 2 double x 2 0 25 0 25 double piout 2 slack 2 dj 2 HPROBLEM lp NULL printf nExample NLP problem 3 n setintparam lp PARAM ARGCK 1 lp loadn
10. 1 5x The steps involved in using other 16 bit C C compilers will be very similar 1 Create a Project Start Visual C 1 5x Select Project New In the New Project dialog click the Browse button and navigate to the vcexamp1 subdirectory this is c frontmip examples vcexamp1 in the default directory structure In the File name edit box type vcexamp1 mak then click OK Again in the New Project dialog select Quick Win Application EXE in the Project Type dropdown list ensure that Use Microsoft Foundation Classes is not checked and click OK 2 Add Files The Project Edit dialog is immediately displayed Navigate if necessary to the proper directory select the file veexampl1 c and click on Add In Visual C 1 5x the Project Edit dialog remains open at this point Open the List Files of Type dropdown list and select Library lib Navigate to the directory containing the 16 bit version of the import library frontmip lib in the default directory structure move two levels up and then down to Win16 Select frontmip lib and click on Add Then click on Close If you want to examine the C source code select File Open navigate to the appropriate directory if necessary select vcexamp1 c and click OK 3 Build and Run the Application To compile and link vcexamp1 c and produce vcexamp1 exe select Project Rebuild All VCEXAMP1 EXE Then select Project Execute VCEXAMP1 EXE to run the program This QuickWin application displ
11. It recognizes a specific 16 character license key string which you provide as the probname argument to the oadIp or loadnIp function Without this license key string the Solver DLL will not function all Solver DLL routines will return without doing anything It is important that you keep your license key string confidential and use it only in your application programs Frontline Systems will treat you as responsible for the use of any copies of the Solver DLL that recognize your specific license key string Registry Entries for Use Based Licensing If you have chosen use based licensing you ll receive a version of the Solver DLL that is designed to count the number of uses i e calls to the Joadlp or loadnlp functions or calls to the optimize or mipoptimize functions over time and report this information both to you and to Frontline Systems To maintain the counts across different executions of your application the Solver DLL uses several entries under a single key in the system Registry To use the Solver DLL on a given PC e g your development system or a production server you must first run a supplied program CreateUseKey exe to create the Registry key and associated entries To do this simply select Start Run and type the path of this program normally C Frontmip CreateUseKey exe Assuming that it successfully creates the Registry entries this program displays a confirming MessageBox If run more than once o
12. NULL NULL NULL NULL NULL NULL x lb ub NULL 0O funceval NULL if lp return 1 setintparam lp PARAM NOIMP 1 1 second printf Calling loadnltype n loadnitype lp NULL NULL optimize lp solution lp amp stat amp objval x NULL NULL NULL printf nStatus ld Objective g n stat objval printf Final values x1 g x2 g x3 g n x 0 x 1 x 2 unloadprob amp lp return 0 int main char buf 80 printf NONLINEAR TEST CASES FOR FRONTMIP DLL n n getlimits gets buf examplel1 gets buf example2 gets buf example3 gets buf Ex1 Nonlin example4 gets buf Ex1 Linear example4 gets buf example5 gets buf example return 0 Solver Memory Usage When you pass array arguments to the oadlp loadnIp loadquad and loadctype routines the Solver DLL stores pointers to these arrays it does not make copies of the data When you call optimize or mipoptimize to solve a problem these arrays are used and additional storage is allocated internally by the Solver DLL Some of the additional storage is maintained after optimize or mipoptimize returns so that you can retrieve solution and sensitivity data by calling routines such as solution objsa and rhssa This remaining storage is freed when you call unloadprob 50 e Calling the Solver DLL from C C Dynamic Link Library
13. PARAM ARRAY This parameter affects all of the Solver DLL routines which take arrays as arguments If this parameter is 0 the default all array arguments supplied to the Solver and all array arguments of callback functions i e funceval and jacobian are C style arrays The actual arguments are pointers to the base of the block of memory holding array values If this parameter is 1 all array arguments are Visual Basic or OLE style SAFEARRAYs The actual arguments are pointers to pointers to SAFEARRAY descriptors which contain pointers to the base of the block of memory holding array values PARAM USERP This parameter controls the reporting of use information in certain licensed versions of the Solver DLL The default setting is 0 which means that the Solver DLL operates in Evaluation Test mode It will not keep track of the number of uses or store anything in the Registry but once every 10 minutes it will display a MessageBox on the system console Once the DLL is placed into service this parameter should be set to 1 or 2 In this case the Solver DLL will count uses calls to optimize or mipoptimize and will store this information in the Registry When PARAM _USERP is 1 the DLL will automatically send an updated report of the cumulative number of uses by email to Frontline Systems info frontsys com each time it is run in a new calendar month When PARAM _USERP is 2 the DLL will not send any reports automatically but
14. Solver API Reference The most convenient such value to use in Delphi Pascal is a variable of the appropriate type Longint or Double initialized to 1 You cannot pass the constant 1 because the corresponding parameters have the var attribute In loadnIp setlpcallbackfunc and setmipcallbackfunc you pass procedure pointers as actual arguments There are types defined for these arguments FUNCEVAL and JACOBIAN for loadnlp and CCPROC for setlpcallbackfunc and setmipcallbackfunc in the header file frontmip pas As long as your procedures have signatures that match these types Delphi will allow you to pass the procedure name as the actual argument To pass a NULL or empty pointer for a procedure argument e g to omit a jacobian function in loadnlp or to reset the callback function in set pcallbackfunc use the special constant Nil Building a 32 Bit Delphi Pascal Program You can run the compiled version of the Delphi example psexamp exe using Start Run You can edit compile and test the source code of this example as follows 1 Start the Delphi programming system Select File Open Project navigate to the Delphi example subdirectory c frontmip examples psexamp select psexamp dpr and click OK 2 The Delphi system will load the project s form and related code found in psunit pas Select View Units or View Forms View Project Source in earlier versions of Delphi to examine and if desired
15. We highly recommend that you use the 32 bit versions of the Solver DLL and develop your application for 32 bit platforms such as Windows 95 98 and Windows NT What s New in Version 3 5 10 e Introduction Version 3 5 of the Solver DLL product line introduces a number of new features including the Evolutionary Solver reentrant versions of the Solver DLL for multi threaded applications routines to support use based licensing for Web server and similar applications and the ability to read in and solve a linear quadratic or mixed integer problem written in algebraic notation from a external text file Evolutionary Solver The new Evolutionary Solver engine included with the nonlinear GRG Solver in Version 3 5 of the Solver DLL is designed to find good though not provably optimal solutions for problems where the classical gradient methods in the GRG Solver are not sufficient The GRG Solver assumes that the problem functions objective and constraints are smooth functions of the variables i e the gradients of these functions are everywhere continuous its guaranteed ability to converge to a local optimum depends on this assumption In problems with nonsmooth or even discontinuous functions the GRG Solver often has difficulty reaching a solution In such problems the Evolutionary Solver which makes no assumptions about the problem functions can often find a good solution Even in smooth nonlinear problems t
16. X3 44 x5 lt 2 Minimize portfolio variance xi Q xi Subj to allocations Sum xi 1 and portfolio return Sum Ri xi gt 0 085 The efficient portfolio is the QP solution approx x1 0 462 x25 0 ux3 0 313 x4 0 x5 90 225 The objective approx 0 00014 minimum variance Both the constraint matrix and the Q matrix are passed using the full set of arguments for sparse matrices void example4 void double obj 0 0 0 0 0 0 0 0 0 0 double rhs 1 0 0 085 char sense EG long matbeg 0 2 4 6 8 long matcnt 2 2 2 2 2 long matind 0 1 0 1 0 1 0 1 0 1 double matval 1 0 0 086 1 0 0 071 1 0 0 095 1 0 0 107 1 0 0 069 double 1b 0 0 0 0 0 0 0 0 0 0 double ub 1 0 1 0 1 0 1 0 1 0 long qmatbeg 0 5 10 15 20 long qmatcnt 5 5 5 5 5 long qmatind 07 Le 2 Sn 05 de 2 385 Ae OS Dg 2 35 4G Oy E E S Ae 05 Ly Dy 239g Be he The Q matrix specifies the covariance between each pair of assets double qmatval 0 000204 0 000424 0 000170 0 000448 0 000014 0 000424 0 012329 0 001785 0 001633 0 000539 0 000170 0 001785 0 000365 0 000425 0 000075 0 000448 0 001633 0 000425 0 005141 0 000237 0 000014 0 000539 0 000075 0 000237 0 000509 long stat double objval double x 5 HPROBLEM lp NULL printf nExample QP problem Po
17. addition to bounds on the variables The Small Scale Solver DLL is an enhanced version of the linear mixed integer and nonlinear programming engine used in the Microsoft Excel Solver which was developed by Frontline Systems for Microsoft This Solver has been proven in use over nine years in tens of millions of copies of Microsoft Excel Microsoft selected Frontline Systems technology over several alternatives because it offered the best combination of robust solution methods performance and ease of use The Small Scale Solver DLL is also a well behaved Microsoft Windows Dynamic Link Library It respects Windows conventions for loading and sharing program code Under Windows NT 2000 or Windows 95 98 the Solver DLL runs in 32 bit protected mode and supports preemptive multitasking When used under Windows 3 1 the Solver DLL shares the processor with other applications through Windows non preemptive multitasking It also solves the problems of 16 bit Windows memory management through use of a two level storage allocator which draws upon Windows global memory resources in an efficient manner The algorithmic methods used in the Small Scale Solver DLL include e Simplex method with bounds on the variables for linear programming problems e Very fast exact quadratic method for solving QP problems such as portfolio optimization models e Generalized Reduced Gradient method for solving smooth nonlinear program ming probl
18. and example source code files discussed later in this User Guide The name of the executable file reflects the configuration of the Solver DLL you ordered from Frontline Systems SolvLP exe Linear Simplex Solver only SolvNp exe Nonlinear GRG plus Nonsmooth Evolutionary Solvers only SolvNpLp exe Both Linear Simplex Solver and Nonlinear GRG plus Nonsmooth Evolutionary Solvers SolvLpQp exe Linear Simplex Solver plus Quadratic and MIP enhancements SolvNpLpQp exe Both Linear Simplex Solver plus Quadratic and MIP enhancements and Nonlinear GRG plus Nonsmooth Evolutionary Solvers Simply run this executable program to install the Solver DLL files into the directory structure outlined in the next section for manual installation The installation program will prompt you for two pieces of information e An installation password e A 16 character license key string specific to your application s Both pieces of information are included in the physical package you received from Frontline Systems or they may be provided to you by phone fax or email Carefully enter the license key string exactly as given to you use uppercase for any letters If you have any questions please contact Frontline Systems as shown on the inside title page of this User Guide Copying Disk Files Manually The Solver DLL files can be provided in uncompressed form on floppy disk so they may be copied to a convenient directo
19. conlow 2 Form2 Text23 conupp 2 varupp 0 conupp 0 remove the callback function setlpcallbackfunc lp 0 call unloadprob unloadprob lp Dynamic Link Library Solver User s Guide to release memory Calling the Solver DLL from Visual Basic e 79 Case Example 2 lp loadlp PROBNAME 2 3 1 obj 0 rhs 0 sense 0 _ matbeg 0 matcnt 0 matind 0 matval 0 1b 0 ub 0 1 2 3 6 If lp 0 Then Exit Sub loadctype lp ctype 0 lpwrite can be called anytime after the problem is defined and before unloadprob is called It will write out the following text in file vbexampl1 Maximize LP MIP obj 2 0 x1 3 0 x2 Subject To lon lne 9 0 x1 6 0 x2 lt 54 0 Cae 6 0 x1 7 0 x2 lt 42 0 c3 5 0 x1 10 0 x2 lt 50 0 Bounds 0 0 lt xl lt infinity 0 0 lt x2 lt infinity Integers x1 x2 End lpwrite lp vbexamp1 T i T T T T i T T solve the problem mipoptimize lp obtain the solution display objective and variables solution lp stat objval x 0 1 1 1 Form2 Text3 LPStatus amp Trim Str stat Form2 Text4 Objective amp Trim Str objval Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 call unloadprob to release memory unloadprob lp Case Example 3 80 e Calling the Solver DLL from Visual Basic Dim iisrows As Long Dim iiscols As Long lp loadlp PROBNAME 2
20. double obj 2 double rhs 2 1 0 0 0 char sense 2 EG double matval 4 double 1lb INFBOUND INFBOUND double ub INFBOUND INFBOUND long i stat double objval double x 2 0 0 0 0 double piout 2 slack 2 dj 2 HPROBLEM lp NULL printf nExample NLP problem 1 n setintparam lp PARAM ARGCK 1 lp loadnlp PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval x lb ub NULL 4 funcevall NULL if lp return setlpcallbackfunc lp showiterl1 optimize lp solution lp amp stat amp objval x piout slack dj printf nStatus d Objective g n stat objval printf Final values x1 g x2 g n x 0 x 1 for i 0 i lt 1 i printf slack ld 7g piout ld 7g n i slack i i piout i printf n unloadprob amp lp Example C program calling the nonlinear Solver DLL Solves the problem Minimize X 2 Y 2 Subject to X Y 1 X Y gt 0 Solution is X Y 0 5 Objective 0 5 Here we define the function jacobian as well as funceval to help speed up the evaluation of first partial derivatives at trial points We re use the functions funcevall and showiterl from Example 1 INTARG _CC jacobianl HPROBLEM lp INTARG numcols INTARG numrows INTARG nzspace LPREALARG objval LPREALARG obj LPINTARG matbeg LPINTARG matcnt HPINTARG matind HPREALARG matval LPREALARG var
21. int LRESULT CALLBACK MainWndProc HWND UINT WPARAM LPARAM BOOL InitApplication HINSTANCE BOOL InitInstance HINSTANCE HWND char long long long long Threads are not available in Winl6 ifdef WIN32 DWORD WINAPI RunThread LPVOID endif PBYTE FPSTR double value PBYTE lpstr long _CC pivot HPROBLEM lpinfo long wherefrom typedef long RunSolver HWND hWnd long pstat double pobj double x RunSolver RunLPSolver RunNLPSolver Global data HANDLE hiInst current instance HWND hWnd1 hWnd2 window handles HPROBLEM lp1 1p2 problem handles DWORD dwID1 dwID2 thread IDs in Win32 char szWinTitlel FRONTMIP Example 1 char szWinTitle2 FRONTMIP Example 2 char szClassName FRONTMIP Class long Calls 0 counts calls to RunLPSolver RunNLPSolver int WINAPI WinMain HINSTANCE hiInstance HINSTANCE hPrevinstance LPSTR lpCmdLine int nCmdShow MSG msg if hPrevinstance if InitApplication hInstance return FALSE if InitInstance hInstance amp hWndl szWinTitlel 10 10 300 300 64 e Native Windows Applications Dynamic Link Library Solver User s Guide return FALSE if InitInstance return FALSE ifdef WIN32 srand GetTickCount CreateThread NULL 0 RunThread CreateThread NULL 0 RunThread endif while GetMessage amp msg 0 0 0 TranslateMessage amp msg DispatchMessage amp ms
22. lib Navigate to the Win32 subdirectory that contains the 32 bit version of the import library frontmip lib Select frontmip lib and click OK If you now select the FileView pane in the Project Workspace window and open Vcexamp 1 Files the vcexamp1 c and frontmip lib files should be listed You can double click on vcexamp1 c to see the C source code 3 Build and Run the Application To compile and link vcexamp1 c and produce vcexamp1 exe select Build Rebuild All Then use Build Execute vcexamp1 exe to run the program An output window like the one on the next page should appear Press the ENTER key to continue running the program and produce more output 32 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide 4 D DLLExamp ycexamp1 Release ycexamp1 exe TEST CASES FOR FRONTMIP DLL Example LP problem Iteration 1 Obj 15 Iteration 2 Obj 16 4 LPstatus Objective 1 xi 2 8 x2 3 slack 7 2 piout 6 slack i O piout il 8 2 slack 2 O piout 2 6 16 Obj coefficient 2 Lower 1 5 Upper 2 57143 Obj coefficient 3 Lower 2 33333 Upper 4 Constraint RHS 54 Lower 46 8 Upper ie 030 Constraint RHS 42 Lower 35 Upper 45 Constraint RHS 56 Lower 43 3333 Upper 66 Example MIP problem LPstatus 161 Objective 16 xi 2 x2 4 Building a 16 Bit C C Program A 16 bit version of the example Solver DLL application VCEXAMP1 EXE which runs under Windows 3 x may be built using Microsoft Visual C
23. nDrawY LPtitle strlen LPtitle nDrawY nSpacing wsprintf szText LPstatus ld Objective s LPstat LPSTR szObj TextOut hDC nDrawX nDrawY szText strlen szText nDrawY nSpacing wsprintf szText xl s x2 s LPSTR szVarl LPSTR szVar2 TextOut hDC nDrawX nDrawY szText strlen szText nDrawY 2 nSpacing FPSTR NLPobj szObj Dynamic Link Library Solver User s Guide FPSTR NLPx 0 szVarl1 FPSTR NLPx 1 szVar2 TextOut hDC nDrawX nDrawY NLPtitle strlen NLPtitle nDrawY nSpacing wsprintf szText LPstatus ld Objective s NLPstat LPSTR szObj TextOut hDC nDrawX nDrawY szText strlen szText nDrawY nSpacing wsprintf szText xl s x2 s LPSTR szVarl LPSTR szVar2 TextOut hDC nDrawX nDrawY szText strlen szText nDrawY 2 nSpacing EndPaint hWnd amp ps break case WM DESTROY PostQuitMessage 0 break default return DefWindowProc hWnd message wParam 1Param return 0 PBYTE FPSTR double value PBYTE lpstr PBYTE buf lpstr int length 0 DWORD dwFraction if value lt 0 00 buf length value value length wsprintf amp buf length lu DWORD value dwFraction DWORD 1 00E 04 value DWORD value length wsprintf amp buf length 4 4lu dwFraction return lpstr Define a callback function which display
24. repdate _p reportuse 128 e Solver API Reference problem sizes By calling getproblimits you can find out at runtime which Solver engines are available and how many decision variables constraints and integer variables you can specify in calls to each engine INTARG getuse lp loadprob_p optimize p verify p repload_p repopt_p repdate _ p HPROBLEM lp LPINTARG loadprob_p optimize p verify p LPINTARG repload_p repopt_p repdate_p This function returns information to your application about the number of uses calls to loadlp or loadnIp and calls to optimize or mipoptimize since the Solver DLL was placed in service The p argument is ignored and may be NULL You may also pass NULL for any of the other arguments if you do not need the corresponding information A pointer to a variable of type Long where getuse will store the cumulative number of calls to JoadIp or loadnIp to date A pointer to a variable of type Long where getuse will store the cumulative number of calls to optimize or mipoptimize to date A pointer to a variable of type Long where getuse will store an encrypted form of the cumulative number of uses to date A pointer to a variable of type long where getuse will store the number of calls to loadlp or loadnIp previously reported to Frontline Systems via an earlier call to reportuse or automatically as determined by the PARAM _USERP setting A pointer
25. s Application Program Interface API routines It covers many details besides those features illustrated in the various example applications You ll want to consult this chapter as you develop your own application Included with the Solver DLL are source code header files defining the Solver DLL callable routines and source code for example programs in four languages C C Visual Basic Delphi Pascal and FORTRAN Dynamic Link Library Solver User s Guide Introduction e 11 12 e Introduction Example File Header File C C vcexamp c frontmip h vcexamp2 c Visual Basic vbexamp vbp frontmip bas vbexamp2 vbp ert bas Delphi Pascal psexamp dpr Tinos pas FORTRAN For all four languages the example programs define and solve two optimization problems a simple LP linear programming problem and a simple NLP nonlinear programming problem Note If your version of the Solver DLL includes only the LP or only the NLP Solver engine you will be able to solve only one of these two problems the other will display an error message dialog For C C and Visual Basic more extensive examples are included as outlined below For C C and FORTRAN the example files are text files containing source code the instructions in the appropriate chapters explain how to create a project that will compile link and run the sample programs For Visual Basic and Delphi Pascal which are designed to create forms oriented applications
26. var 0 var 1 var 1 lhs 0 var 0 var 1 lhs 1 var 0 var 1 funcevall 0 END FUNCTION Define a callback function that computes the objective gradient and Jacobian of the constraints for any supplied values of the variables INTEGER 4 FUNCTION jacobian1l STDCALL lp numcols numrows nzspace objval obj matbeg matcnt matind matval var objtype matvaltype INTEGER 4 lIp VALUE numcols VALUE numrows VALUE INTEGER 4 nzspace VALUE REAL 8 objval REFERENCE obj 0 1 INTEGER 4 matbeg 0 1 matcnt 0 1 matind 0 1 REAL 8 matval 0 1 var 0 1 CHARACTER 2 objtype REFERENCE CHARACTER 2 matvaltype REFERENCE WRITE 20 var 0 var 1 FORMAT Jacobian evaluated at x1 F7 2 x2 F7 2 Value of the objective function objval var 0 var 0 var 1 var 1 Partial derivatives of the objective obj 0 2 0 var 0 obj 1 2 0 var 1 Partial derivatives of X Y constant matval 0 1 0 matval 2 1 0 Partial derivatives of X Y variable matval 1 var 1 matval 3 var 0 jacobianl 0 END FUNCTION NCLUDE frontmip for ou must initialize PROBNAME with your own license key string NCLUDE frontkey for OT DEFINED WIN32 NTEGER 4 setintparam loadlp loadctype optimize solution NTEGER 4 lpwrite HHZHKH zal XTERNAL lpcallback funcevall jacobianl INTEGER 4 lpcallback funcevall jacobianl REAL 8 obj 0 1 2 0 3
27. wsprintf PivotMsg Pivot ld Obj s NumPivot LPSTR ObjStr hWnd lpinfo lpl hWnd1l hWnd2 SetWindowText hWnd PivotMsg if PeekMessage MSG FAR amp msg hWnd WM_KEYDOWN WM_KEYDOWN PM NOREMOVE if msg wParam VK_ESCAPE return PSTAT_USER_ABORT return PSTAT CONTINUE Define and solve the example MIP problem long RunLPSolver HWND hWnd long pstat double pobj double x double obj 2 0 3 0 double rhs 54 0 42 0 50 0 char sense LLL long matbeg 0 3 long matcnt 3 3 long matind 0 dy 2 O 1 2 double matval 9 0 6 0 5 0 6 0 7 0 10 0 Dynamic Link Library Solver User s Guide Native Windows Applications e 67 double lb 0 0 0 0 double ub INFBOUND INFBOUND char ctype II HPROBLEM lp NULL _CCPROC lpPivot setintparam lp PARAM ARGCK 1 lp loadlp PROBNAME 2 3 1 obj rhs sense matbeg matcnt matind matval lb ub NULL 2 3 6 if lp return 0 if hWnd hWnd1 lpl lp else lp2 lp loadctype lp ctype lpPivot _CCPROC MakeProcInstance FARPROC pivot hInst setlpcallbackfunc lp lpPivot optimize lp solution lp pstat pobj x NULL NULL NULL unloadprob amp lp return Calls Define a callback function which computes the objective and constraint left hand sides for any supplied values of the decision variables I
28. x 0 Form2 Text2 x2 amp x 1 If nlstat Then Exit Sub Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 91 unloadprob lp Re solve the problem using the LP Solver Form2 Label6 First solution via loadnlp Form2 Label6 Visible True second via loadlp loadlp PROBNAME 2 2 1 obj rhs sense _ NullL NullL NullL matval lb ub NullD 2 2 4 optimize lp lp solution lp stat objval x piout slack dj Form2 Text5 Status amp stat Form2 Text6 Obj amp objval Form2 Text7 xl amp x 0 Form2 Text8 x2 amp x 1 call unloadprob unloadprob lp to release memory Case 5 Example program calling the Evolutionary Solver DLL Minimize the Branin function terml1 X PI 5 1 X PI 4 term2 Y term1l 6 2 term3 10 1 1 PI 8 5 cos X 10 objective term2 term3 1S5 ta Xp Ye 10 3 local optima Dim mid 0O To 1 Dim disp 0 To 1 As 1 global optimum approx 0 3978 As Double Double Dim lower 0 To 1 As Double Dim upper 0 To 1 As Double 1b 0 5 lb 1 5 ub 0 10 ub 1 10 x 0 1 x 1 1 setintparam 0 PARAM ARGCK 1 lp loadnlp PROBNAME 2 0 1 obj NullD NullB _ NullL NullL NullL NullD x 1b ub NullD 0O AddressOf funceval5 0 If lp 0 Then Exit Sub loadnitype lp setintparam lp setlpcallbackfunc lp optimize lp NullB NullB PARA
29. 10 objval term2 term3 funceval5 0 End Function Function funceval6 lp As Long ByVal numcols As Integer ByVal numrows As Integer ByRef objval As Double ByRef lhs As Double ByRef var As Double _ ByVal varone As Integer ByVal vartwo As Integer As Long Err 0 On Error Resume Next If var 0 gt 10 Then objval var 1 var 2 Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 85 Else objval var 1 var 2 End If funceval6 0 End Function Function jacobianl lp As Long ByVal numcols As Integer ByVal numrows As Integer ByVal nzspace As Integer ByRef objval As Double ByRef obj As Double _ ByRef matbeg As Long ByRef matcnt As Long _ ByRef matind As Long ByRef matval As Double ByRef var As Double ByRef objtype As Byte ByRef matvaltype As Byte As Long Err 0 On Error Resume Next MsgBox jacobian evaluated at xl amp var 0 amp x2 amp var 1 Value of the objective function objval var 0 var 0 var 1 var 1 Partial derivatives of the objective obj 0 2 var 0 obj 1 2 var 1 Partial derivatives of X Y constant matval 0 1 matval 2 1 Partial derivatives of X Y variable matval 1 var 1 matval 3 var 0 jacobianl 0 End Function Function jacobian3 lp As Long ByVal numcols As Integer ByVal numrows As Integer ByVal nzspace As Integer ByRef objval As Double
30. 775 831 0300 Fax 775 831 0314 Email info frontsys com kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk kkkkkkkkk kkkkkkkkkkkk Problem 1 Solve the MIP model Maximize 2 x1 3 x2 Subj to 9 x1 6 x2 lt 54 6 xl 7 x2 lt 42 5 x1 10 x2 lt 50 xl x2 non negative integer MIP solution xl 2 x2 4 Objective 16 0 Problem 2 Solve the NLP model Minimize X 2 Y 2 Subject to X Y oe 1 X Y gt 0 xl x2 non negative Solution is X Y 0 5 Objective 0 5 This is a native Windows application It includes two examples of callback routines One to compute the objective and constraints for the nonlinear Solver and another which displays the iteration and current objective value amp quits if the user presses the ESC key If your copy of the Solver DLL does not include the LP or NLP Solver engine a MessageBox will appear and the results will show all zeroes for the solution status objective and final variable values include lt windows h gt 58 e Native Windows Applications Dynamic Link Library Solver User s Guide include lt string h gt include frontmip h include frontkey h Prototyp BOOL InitApplication HINSTANCE BOOL InitInstance HINSTANCE int LRESULT CALLBACK MainWndProc HWND UINT PBYTE FPSTR double value PBYTE lpstr the procedures to follow int WINAPI WinMain HINSTANCE HINSTANCE LPSTR int WPARAM LPARAM lo
31. IR E E 24 Solution Properties of Quadratic Problems ss eesseeeseeseesseeesseseesseserssseesessesresseseesreseesessrene 25 Passing Dense and Sparse Array Arguments sssseseseesereeesteresstsrtsresttsessteressesesstenessrseessesets 26 Arrays and Callback Functions in Visual Basic cccsccesccsseseeceeeceeeeeeesecaeeeneeeeeeneeeeeeeerenseens 28 Using the Solver DLL in Multi Threaded Applications ccesccesceseeetecseececseecseeeeeeneenes 29 Use Based Licensing eeir ii t E E ved tiie deed K E TR 29 Dynamic Link Library Solver User s Guide Contents e i ii e Introduction Calling the Solver DLL from C C 31 C G Compilers AERE A E E ind oteesacudiesseh neseeedivhas thee neGewome is ne reesesst 31 Basic Steps oct oor eevee ae ae eon es Ed cee ee en ee 31 Building a 32 Bit C C 4 Program sisisi ienris gien ai EEEE E ia 32 Building a 16 Bit C C Program ssesssssessesserssssrersssrsresreseestsstesessteressesteseserstsseeresseseesre 33 C C Source Code Linear Quadratic Problems cccccssccessceesscceseceesseceseceeseecseeeeseecses 34 C C Source Code Nonlinear Nonsmooth Problems cccccccssccessceesscceeceesseceseeeesseeeses 42 Solver Memory Usa gesnoer ieta i i i REEE R EA NER R 50 Lifetime of Solver Arguments cccccceccesseesseesceseceesceeceseceseceaeceseceecaeeeseeeaeeaeeeneenes 51 Solving Multiple Problems Sequentially ccceeccescecceseceeeceseceseceeeaeenneenee
32. LP problems as if they were general nonlinear problems it is likely to take considerably more time to solve such problems and it may find solutions which are less accurate or less exact than solutions found by the Solver engine most appropriate to the task Problems such as poor scaling or degeneracy also cause greater difficulty for the NLP Solver than for the QP or LP Solver If you have a linear or quadratic problem or a mix of nonlinear and linear or quadratic problems we highly Dynamic Link Library Solver User s Guide recommend that you experiment with each of the Solver engines and compare both solution time and accuracy of the results Nonsmooth Evolutionary Solver The nonsmooth Evolutionary Solver based on genetic or evolutionary algorithms is the most general purpose Solver engine in that it makes no assumptions about the mathematical form of the problem functions objective and constraints They may be linear quadratic smooth nonlinear nonsmooth or even discontinuous and nonconvex functions Moreover for smooth nonlinear problems where the GRG Solver is guaranteed to find only a locally optimal solution the Evolutionary Solver can often find a better globally optimal solution Like the nonlinear Solver it calls a function funceval that you write to evaluate the objective and constraints for given values of the decision variables However this generality comes at a considerable price of both
33. PARAM NOIMP 1 1 second setlpcallbackfunc lp showiterS printf Calling loadnltype n loadnitype lp NULL NULL optimize lp solution lp amp stat amp objval x NULL NULL NULL printf nStatus ld Objective g n stat objval printf Final values x1 g x2 g n x 0 x 1 varstat lp 0 1 mid disp lower upper printf nxl mid g disp g lower g upper g n mid 0 disp 0 lower 0 upper 0 printf x2 mid g disp g lower g upper g n mid 1 disp 1 lower 1 upper 1 unloadprob amp lp return 0 Example C program calling the Evolutionary Solver DLL Solves the problem Maximize if X gt 10 then Y Z else Y Z 0 lt X Y Z lt 20 Solution is X gt 10 Y Z 20 objective 40 INTARG _CC funceval HPROBLEM lp INTARG numcols INTARG numrows LPREALARG objval LPREALARG lhs LPREALARG var INTARG varone INTARG vartwo objval 0 var 0 gt 10 0 var 1 var 2 var 1 var 2 objective return 0 Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 49 int example double obj 3 double 1b 3 0 0 0 0 0 0 double ub 3 20 0 20 0 20 0 int stat double objval double x 3 5 0 5 0 5 0 HPROBLEM lp NULL printf nExample NSP problem 6 IF function n setintparam lp PARAM ARGCK 1 lp loadnlp PROBNAME 3 0 1 obj
34. Solver problems 20 e Designing Your Application Dynamic Link Library Solver User s Guide Solving Nonsmooth Problems You define and solve a problem with nonsmooth or discontinuous functions in much the same way as you would for a problem defined by smooth nonlinear functions In a nonsmooth problem however the first partial derivatives of the objective and constraints may not be continuous functions of the variables and they may even be undefined for some values of the variables Because of this property the gradient based methods used by the nonlinear GRG Solver are not appropriate and instead the Evolutionary Solver engine must be used to solve the problem As for smooth nonlinear problems you write a callback function funceval that computes values for the problem functions for any given values of the variables and you supply the address of this function as an argument to Joadnip But you cannot use the optional jacobian callback function described below to speed up the solution of a nonsmooth problem Your program should first call Joadnip which returns a handle to a problem Then you must call oadnitype supplying this problem handle to tell the Solver that some or all of your problem functions are nonsmooth or discontinuous This can be as simple as loadnltype lp NULL NULL nonsmooth problem You may optionally call oadctype to specify integer variables defining an integer nons
35. Visual Basic matrix is passed as the matval argument matcnt amp matind arguments This example also shows how to obtain LP sensitivity analysis info functions only dual values are available These calls are valid the piout for MIP problems no This example uses a callback function to display the LP iterations Dynamic Link Library Solver User s Guide lb 1 0 ReDim ub 0 To 1 ub 0 INFBOUND ub 1 INFBOUND ReDim x 0 To 1 As Double ReDim piout 0 To 2 As Double ReDim slack 0 To 2 As Double ReDim dj 0 To 1 As Double ReDim varlow 0 As Double ReDim varupp 0 As Double ReDim conlow 0 As Double ReDim conupp 0 As Double As Double Form2 Show End Sub Private Sub Command2_Click 1 1 1 1 1 1 1 1 Example 2 Solves the MIP model Maximize 2 xl 3 x2 Subj to 9 x1 6 x2 lt 54 6 x1 7 X2 lt 42 5 x1 10 x2 lt 50 xl x2 non negative integer MIP solution xl 2 x2 4 Objective 16 This example illustrates the full set of arguments potentially sparse matrix to loadlp For each variable column i matbeg i and matcnt i are the beginning index and count of non zero coefficients in the matind and matval arrays For each such coefficient matind k is the constraint row index and matval i is the coefficient value See the documentation for more details used to pass a In this example we also use two debugging features of the Solver DLL 1 We call setintparam
36. Visual Basic system will load the project file the related form files vbexamp1 frm and examp1 frm and the related module file vbexamp1 bas as well as the header files frontmip bas and frontkey bas Note Since the form files in this project were saved in a format compatible with Visual Basic 4 0 you may see the message This file was saved in a previous version of Visual Basic just click OK or OK For All in response to this message 70 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide 3 By selecting these files in the project list and clicking on View Form or View Code you can examine and if desired modify the elements of this application After opening vbexamp1 vbp and clicking on View Form and View Code your screen should resemble the picture below olx Project Microsoft Visual Basic design File Edit View Project Format Debug Run Query Diagram Tools Add Ins Window Help IES sk Siegal BRM c i a SBIR AD uc wm Project Form Form Project Projecti xj amo BPRS oe ee ee ae Project1 vbexamp1 bp E Forms po Solver en Link n TA Library Version 3 5 H L Form2 EXAMP1 FRM Frontline Systems Inc Tel 775 831 0300 2 E Modules i P O Box 4288 Fax 775 831 0314 Incline Village rE z Email info frontsys com NV 89450 USA E 2 Frontkey frontkey bas 2 Frontmip FRONTMIP B 3 VBexamp1 VBEXAMP1 E Prop
37. a NULL first argument to obtain this information then allocate arrays of the appropriate size and call Joadlp plus loadquad and or loadctype to define the problem and finally call Jpread again this time with a non NULL first argument to fill in the coefficient bound and integer variable information To satisfy the Solver DLL s checks for argument validity you must initialize the sense array say with all elements equal to E the ctype array if used for integer problems say with all elements equal to C and the matbeg matcnt and matind arrays if used for sparse problems Matbeg and matcnt may be initialized as described below and matind may be initialized with all elements equal to zero Omatbeg qmatcnt and qmatind should be treated similarly If you are using sparse arrays to define matval or qmatval and you do not know the dimensions or sparsity pattern in advance you will need to call Jpread twice as outlined above passing the matcnt and or gmatcnt array arguments on the first call These arrays must be of dimension at least equal to the number of columns variables in the problem being read to create them you can either use the maximum number of columns returned by the getproblimits routine or you can call lpread one more time in advance to obtain the actual number of columns defined in the text file The number of nonzeroes in the constraint matrix the nzspace argument passed to lo
38. a call to loadquad for a quadratic problem and or a call to Joadctype for a mixed integer problem A call to loadnlp may be followed by a call to Joadnitype for a nonsmooth problem a call to Joadnitype or testnitype to specify linearly occurring variables and or a call to Joadctype for a mixed integer problem If your call to testnitype reveals that a problem is entirely linear you may call un oadprob and then call loadIp with the same arguments to solve your problem with the faster and more reliable Simplex method After calling the appropriate solution routines and or diagnostic routines you must call unloadprob to free memory allocated by your calls to other routines HPROBLEM loadlp probname numcols numrows objsen obj rhs sense matbeg matcnt matind matval 1b ub rngval colspace rowspace nzspace LPSTR probname INTARG numcols numrows objsen LPREALARG obj rhs LPBYTEARG sense LPINTARG matbeg matcnt Dynamic Link Library Solver User s Guide Solver API Reference e 111 probname numcols numrows objsen obj rhs sense matbeg matent matind matval lb ub rngval 112 e Solver API Reference HPINTARG matind HPREALARG matval LPREALARG lb ub rngval INTARG colspace rowspace nzspace A character string currently 16 characters plus a 0 terminator byte containing a unique key which is assigned to you when you license the Solver DLL from Fron
39. above which permit you to define callback procedures and pass procedure names as parameters Determining Linearity Automatically As explained above the primary difference between solving a nonlinear problem and solving a linear problem is that you must provide a callback routine funceval to evaluate the nonlinear problem functions at trial points values for the variables determined by the Solver DLL However you do not have to initialize the arrays of coefficients passed to Joadnip with values It is possible to use JoadnIp and a funceval routine for any Solver problem even if it is an entirely linear problem but this will be significantly slower than calling loadlp for a linear problem which employs the Simplex method If you are solving a specific problem or class of problems you will probably know in advance whether your problem is linear or nonlinear If you know whether each variable occurs linearly or nonlinearly in the objective and each constraint function you can supply this information to the Solver through oadnitype Such information can be used by advanced nonlinear solution algorithms to save time and or improve accuracy of the solution If you are solving a general series of problems however you might have some nonlinear and some linear problems all represented by a funceval routine The testnitype routine lets you ask the Solver to determine through a numerical test whether the proble
40. and the constraints the Jacobian The partial derivatives are estimated by a rise over run calculation in which the value of each variable in turn is perturbed and the change in the problem function values is observed For a problem with N variables the Solver DLL will call funceval N times on each occasion when it needs new estimates of the partial derivatives 2 N times if the central differencing option is used This often accounts for 50 or more of the calls to funceval during the solution process The Evolutionary Solver engine does not assume that the problem functions are smooth or differentiable and it does not attempt to estimate partial derivatives However it may make even more calls to funceval in total than the nonlinear GRG Solver would make for a problem of a given size To speed up the solution process for smooth nonlinear problems only and to give the Solver DLL more accurate estimates of the partial derivatives you can supply a second callback function jacobian which returns values for all elements of the objective gradient and constraint Jacobian matrix in one call The callback function is optional you can supply NULL instead of a function address but if it is present the nonlinear GRG Solver engine will call it instead of making repeated calls to funceval to evaluate partial derivatives INTARG funceval lp numcols numrows objval lhs var varone vartwo HPROBLEM l
41. automatically send an email message to Frontline Systems info frontsys com containing the use information returned by getuse plus your application specific key string and the Windows name of the computer on which the application is running The email message if used is sent via the Win32 Messaging API MAPI which is normally available on the Windows system where the Solver DLL is running The p argument is ignored and may be NULL A character string currently 16 characters plus a 0 terminator byte containing a unique key which is assigned to you when you license the Solver DLL from Frontline Systems the same as the argument you supply to oad p or loadnIip If used the name or complete path of the output text file that will contain the use information Reportuse will create this file which will replace any existing file of the same name If filename does not include an explicit path the file will be created in the current directory If this argument is NULL or an empty string reportuse will send an email message instead This argument is optional If reportuse is sending an email message i e the filename argument is NULL this is the profile name typically the user name of the email account used to send the message If this argument is NULL or an empty string reportuse uses the MAPI shared session to send the email message This argument is optional If reportuse is sending an email messa
42. corresponding variable found in the constraints of the problem The resulting array has the same meaning as and may be passed as the matcnt argument of the loadlp routine You may pass a NULL value for this argument if you don t need this information for example if you are using a dense matrix for the matval array of coefficients passed to loadIp If used this argument must be an integer array of dimension at least equal to the number of columns variables in the problem On return each element of the array will contain the number of nonzero coefficients of the corresponding variable found Dynamic Link Library Solver User s Guide in the quadratic objective if any of the problem The resulting array has the same meaning as and may be passed as the gmatcnt argument of the Joadquad routine You may pass a NULL value for this argument if you don t need this information for example if you are using a dense matrix for the gmatval array of coefficients passed to loadquad If you know the sense and dimensions number of variables constraints and integers of the problem you are going to read in and solve you can simply call oad p plus loadquad and or loadctype to define the problem with arrays of the correct dimension then call pread once to fill in the coefficient bound and integer variable information If you do not know the sense and or dimensions of the problem in advance you can call pread with
43. create a file vbexamp1 containing an algebraic statement of its problem in the Visual Basic program directory for example C DevStudio VB Example 5 uses the pread function to read this file and define and solve the same problem without setting up all of the array arguments normally required To end execution of the program click the Exit button on the Example Problem form and the Quit button on the main form 5 To trace execution of this program select Debug Step Into and press the F8 key to execute one Visual Basic statement at a time You will see that the routine Sub Command _Click that is executed when you click the Example 1 button sets up the various array arguments needed to call the Solver DLL then loads the form examp1 frm The routine Sub Command1_Click on this form that is Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 71 executed when you click Solve calls the various Solver DLL routines such as loadlp optimize and solution w Example OF x Example 1 Solves the LP model LPStatus 1 Obiective 16 4 Maximize 2x1 3x2 Subjto 9x1 6x2 lt 54 xi 28 k2 3 6 Bxl 7x2 lt 42 slack1 7 2 piouti 0 5x1 10 2 lt 50 1 x2 non negative slack2 0 piout2 0 2 slack3 0 Ipiout3 0 16 LP solution x1 2 8 x2 3 6 Objective 16 4 Obj Coefficient Lower Upper 1 5 2 57142 tk 2 33333 E Constraint RHS Lower 6 To produce a binary execu
44. dimension endidx begidx 1 where the objective function coefficient upper range values will be returned INTARG rhssa lp begidx endidx lower upper HPROBLEM 1p INTARG begidx endidx LPREALARG lower upper This routine need be called only if sensitivity ranges for the constraint right hand sides are desired The argument p of rhssa must be the value returned by a previous call to JoadIp The arguments begidx and endidx are used to limit the set of rows constraints for which the range information is computed Since range information is not meaningful for NSP NLP QP and MIP problems rissa should not be called for them rhssa returns 0 unless there is an error in its arguments in which case it returns an integer value indicating the ordinal position of the first argument found to be in error The first row number index as in loadlp arguments for which sensitivity range information should be returned The last row number index as in loadlp arguments for which sensitivity range information should be returned An array of dimension endidx begidx 1 where the constraint right hand side lower range values will be returned An array of dimension endidx begidx 1 where the constraint right hand side upper range values will be returned Dynamic Link Library Solver User s Guide Solver API Reference e 121 varstat begidx endidx mid disp lower upper constat begidx 122 e Solver API Reference INTARG
45. double rhs 3 char sense 3 EEE long matbeg 2 long matcnt 2 long matind 6 double matval 6 double 1b 2 double ub 2 char ctype 2 CC long stat nzspace i double objval double x 2 long objsen numcols numrows numints HPROBLEM lp NULL setintparam lp PARAM ARGCK 1 First we assume that the dimensions of the problem are known We call loadlp passing array arguments of the proper dimension Since the sense and ctype arrays are checked for validity we initialize them printf nExample Read in MIP problem of known size n lp loadlp PROBNAME 2 3 1 obj rhs sense NULL NULL NULL matval lb ub NULL 2 3 6 if lp return loadctype lp ctype call lpread to read in the actual array values lpread lp vcexamp1 NULL NULL NULL NULL NULL NULL call mipoptimize and display the solution mipoptimize lp solution lp amp stat amp objval x NULL NULL NULL 40 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide printf LPstatus ld Objective g n stat objval printf x1 g x2 g n x 0 x 1 unloadprob amp lp Next we assume that the dimensions of the problem are not known in advance We can call lpread with a NULL first argument to read the file and obtain the actual problem dimensions Then we would allocate arrays of appropriate size to keep this example simp
46. examine the IIS You may call Ipwrite for linear and quadratic problems only to write out a text file containing an algebraic description of the problem you have defined by calling to loadlp loadquad and or loadctype and passing the necessary parameters and arrays If you are not getting the solution you expect calling pwrite may reveal that you haven t defined the problem you expected For compatibility with previous versions of the Solver DLL Iprewrite is a synonym for pwrite You may call pread to read in a text file previously written by pwrite or perhaps hand edited or generated by another program containing an algebraic description of a linear quadratic or mixed integer programming problem This can save you the effort of writing and debugging your own code to set up the contents of the arrays needed by the oadlp loadquad and or loadctype routines INTARG findiis lp pnumrows pnumcols HPROBLEM lp LPINTARG pnumrows pnumcols Findiis computes an Irreducibly Infeasible Subset IIS of the constraints to help you identify problems in your constraint formulation which make the problem infeasible You may call this routine when the pstat argument value returned by solution is 2 PSTAT_INFEASIBLE The argument p must be the value returned by a previous call to JoadIp or loadnip If the parameter PARAM _IISBND is 0 the default both constraints and variable bounds will be consider
47. for 32 bit systems such as Windows 95 98 and Windows NT 2000 and new features of the Solver DLL are likely to be targeted to these platforms as well 72 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide Visual Basic Source Code Linear Quadratic Problems The Visual Basic source code from the files vbexamp1 bas vbexamp1 frm and examp1 frm is listed below It includes five example problems for the Solver DLL which are set up and solved when you click on the appropriate buttons The first example is a simple two variable LP problem The second example for which source code in Delphi Pascal and FORTRAN is also included is a MIP problem identical to the previous LP problem except that the decision variables are required to have integer values The third example attempts to solve an LP problem that is infeasible then it uses the IIS finder to diagnose the infeasibility The fourth example is a quadratic programming problem using the classic Markowitz method to find an efficient portfolio of five securities The fifth example uses the pread function to read in a problem in algebraic notation from a text file that was created by the pwrite function in the second example You are encouraged to study this source code or the C C source code and the comments in each problem even if you plan to use a language other than Visual Basic for most of your work The C C and Visual Basic example code
48. modify the elements of this application Delphi doesn t automatically display the header file frontmip pas which is referenced in the project s Use statements but you can add it to the project source display with File Open After you open psexamp dpr select View Project Source and open frontmip pas your screen should resemble the picture on the next page 96 e Calling the Solver DLL from Delphi Pascal Dynamic Link Library Solver User s Guide Delphi 2 0 Psexamp File Edit Search View Project Run Component Database Tools Help ela Bl bl Standard Ackional winds Data Access Data Controls Win 3 1 Dialogs System GReport OCX Samples Sle Ao lc is Font Tom Aje Properties Events HE ActiveControl AutoScroll Borderlcons biSystemMenu bsSizeable ee eo Psunit pas BEE Psunit Frontmip Frontkev pas Problem 2 Solve the NLP model Minimize X 2 2 Subject to Daa cae daa E E xX yY ow 0 ene Xi x2 non negative Recycle Bin Microsoft Solution is X 0 5 Objective 0 5 Word F lt unit Psunit Ed 2 ren Paint interface xpress a g a SysUtils WinTypes WinProcs Messages Classes Graphics Controls My Briefcase WinZip Forms Dialogs StdCtrls Frontmip I Frontkey ley tune Windows NT Explorer 154 44 3 To test run the program within the Delphi programming system select Run Run and then click on the button l
49. nonlinear occurrence of a variable The relevant variable and constraint are identified by the corresponding elements of the matbeg matcnt and matind arrays You may pass a NULL value for objtvpe and or matvaltype if you are not interested in this information The numerical test used by testnitype is effective on a broad range of problems but since it samples function values returned by the funceval routine it is not foolproof An all linear problem which is reasonably well scaled will always return 0 linear model in pstat but a very poorly scaled linear problem could return 1 nonlinear model and a nonlinear problem which behaves linearly over a significant region around the origin could return 0 linear model Given the nature of the numerical test testnitype cannot determine whether any of the variables occur in a nonsmooth discontinuous way in your problem The information used to compute function values in your funceval routine may provide a more certain way to determine the linearity or nonlinearity of your model If you have this information it is better to make the decision to call JoadnIp or loadlp based on your own test and optionally call oadnitype to supply the information to the Solver DLL If testnitype returns 0 in pstat the matval array will contain the constant Jacobian values which make up the LP coefficient matrix for the Simplex method You may switch to the Simplex method and solve the probl
50. of Visual Basic Application Edition as embedded in various application programs such as Microsoft Office To use the nonlinear GRG Solver or the Evolutionary Solver with Visual Basic however you must use Visual Basic 5 0 or above or Visual Basic Application Edition in Microsoft Office 2000 or above Earlier versions of Visual Basic do not support the AddressOf operator which is needed to pass the addresses of callback functions to the Solver DLL It is straightforward to use the Solver DLL with Visual Basic You need only include the header file frontmip bas or safrontmip bas in your Visual Basic project supply your license key for example by including the header file frontkey bas and make calls to the Solver DLL entry points at the appropriate points in your program To create a Visual Basic application that calls the Solver DLL you must perform the following steps 1 Include one of the header files frontmip bas or safrontmip bas in your Visual Basic project You should also include the license file frontkey bas to obtain the license key string 2 Call at least the routines JoadIp or loadnIp optimize solution and unloadprob in that order You can use the example Visual Basic code in vbexamp1 frm and examp1 frm when using frontmip bas or vbexamp2 frm and examp2 frm when using safrontmip bas as a guide for getting the arguments right Passing Array Arguments Before you write a Visual Basic application using
51. only one person uses the Software on one computer at a time and you may make one copy of the Software solely for backup purposes You may not rent or lease the Software but you may transfer it on a permanent basis if the person receiving it agrees to the terms of this license This license agreement is governed by the laws of the State of Nevada LIMITED WARRANTY THE SOFTWARE IS PROVIDED AS IS WITHOUT WARRANTY OF ANY KIND THE ENTIRE RISK AS TO THE RESULTS AND PERFORMANCE OF THE SOFTWARE IS ASSUMED BY YOU Frontline warrants only that the diskette s on which the Software is distributed and the accompanying written documentation collectively the Media is free from defects in materials and workmanship under normal use and service for a period of ninety 90 days after purchase and any implied warranties on the Media are also limited to ninety 90 days SOME STATES DO NOT ALLOW LIMITATIONS ON THE DURATION OF AN IMPLIED WARRANTY SO THE ABOVE LIMITATION MAY NOT APPLY TO YOU Frontline s entire liability and your exclusive remedy as to the Media shall be at Frontline s option either i return of the purchase price or ii replacement of the Media that does not meet Frontline s limited warranty You may return any defective Media under warranty to Frontline or to your authorized dealer either of which will serve as a service and repair facility EXCEPT AS PROVIDED ABOVE FRONTLINE DISCLAIMS ALL WARRANTIES EITHER EXPRESS OR IMPLIED IN
52. other systems to Windows displaying WRITE statement output in a window and entering keyboard input in response to READ statements To simplify the input output and focus on the Solver DLL routines and arguments the example application in this chapter uses simple WRITE statements for output and will be built as a QuickWin application in FORTRAN PowerStation and with equivalent options in FORTRAN 5 1 To create a FORTRAN application that calls the Solver DLL you must perform the three following steps 1 Include the header file frontmip for in your FORTRAN source program You must also include or copy and paste the one line declaration in frontkey for to define your license key string 2 Include the import library file frontmip lib in your project or your linker response file 3 Call at least the routines loadIp or loadnlp optimize solution and unloadprob in that order You can use the example code in flexamp for as a guide for getting the arguments right It calls the Solver DLL routines to solve both a simple mixed integer linear MIP problem and a simple nonlinear NLP problem Bear in mind that the Solver DLL uses the C convention for array indices starting from 0 rather than 1 to make your FORTRAN arrays compatible with this Dynamic Link Library Solver User s Guide Calling the Solver DLL from FORTRAN e 103 convention it is easiest to use lower and upper bounds in your DIMENSION statements as sh
53. routine is called to get the current value of one of the double parameters in a specified problem It returns 0 if successful or 1 if whichparam isn t one of the valid codes for double parameters One of the symbolic names or codes for double parameters PARAM_TILIM PARAM _EPOPT PARAM EPPIV PARAM EPSOL PARAM EPRHS PARAM _EPGAP PARAM CUTLO PARAM CUTHI PARAM EPNEWT PARAM_EPCONV or PARAM MUTATE THI A pointer to the location where the current value of the parameter will be stored INTARG infodblparam lp whichparam defvalue_p minvalue_p maxvalue_p HPROBLEM lp INTARG whichparam LPREALARG defvalue_p minvalue_p maxvalue_p This routine is called to get the minimum maximum and default values of one of the double parameters It returns 0 if successful or 1 if whichparam isn t one of the valid codes for double parameters The p argument is ignored and may be NULL One of the symbolic names or codes for double parameters PARAM_TILIM PARAM _EPOPT PARAM EPPIV PARAM EPSOL PARAM EPRHS PARAM _EPGAP PARAM CUTLO PARAM CUTHI PARAM EPNEWT PARAM _EPCONV or PARAM MUTATE A pointer to the location where the default value of the parameter will be stored A pointer to the location where the minimum value of the parameter will be stored A pointer to the location where the maximum value of the parameter will be stored A list of the default minimum and maximum values of each of the double parameters is shown on the next pa
54. side lhs 1 var 0 var 1 constraint left hand side funceval3 0 End Function Function funceval4 lp As Long ByVal numcols As Integer ByVal numrows As Integer ByRef objval As Double ByRef lhs As Double ByRef var As Double _ ByVal varone As Integer ByVal vartwo As Integer As Long Err 0 On Error Resume Next The use of the addressof operator can crash VB We never return an error value to the DLL Therefore use on error resume next If Nonlinear Then objval var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side Else objval 2 var 0 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 3 var 0 var 1 constraint left hand side End If funceval4 0 End Function Function funceval5 lp As Long ByVal numcols As Integer ByVal numrows As Integer ByRef objval As Double ByRef lhs As Double ByRef var As Double _ ByVal varone As Integer ByVal vartwo As Integer As Long Err 0 On Error Resume Next Dim terml As Double term2 As Double term3 As Double Dim PI As Double PI 3 141593 The use of the addressof operator can crash VB We never return an error value to the DLL Therefore use on error resume next terml var 0 PI 5 1 var 0 PI 4 5 term2 var 1 terml 6 var 1 termi 6 term3 10 1 1 PI 8 Cos var 0
55. speed and reliability Unlike the Simplex and GRG Solvers which are deterministic optimization methods the Evolutionary Solver is a nondeterministic method Because it is based partly on random choices of trial solutions it will often find a different best solution each time you run it even if you haven t changed your problem at all And unlike the Simplex and GRG Solvers the Evolutionary Solver has no way of knowing for certain that a given solution is optimal even locally optimal Similarly the Evolutionary Solver has no way of knowing for certain whether it should stop or continue searching for a better solution it is forced to rely on tests for slow improvement in the solution to determine when to stop Solving Mixed Integer Problems The Branch amp Bound method for solving mixed integer programming problems is included in all configurations of the Solver DLL It can call any of the classical Solver engines to solve its subproblems so you can solve integer linear problems with the LP Solver integer quadratic problems with the QP Solver and integer nonlinear problems with the NLP Solver The Evolutionary Solver engine handles integer variables on its own so the Branch amp Bound method is not used in conjunction with it Also because the NLP Solver or any similar method is not guaranteed to find the globally optimal solution to any subproblem the Branch amp Bound method is not guaranteed to fi
56. the header files frontmip bas or safrontmip bas frontmip pas and frontmip for respectively Linking may be accomplished with the supplied import library via entries in the IMPORTS section of a module definition file or at runtime with calls to the Windows routines LoadLibrary and GetProcAddress The Visual Basic and Delphi Pascal systems do not require the import library or a module definition file they use run time dynamic linking and implicitly call LoadLibrary and GetProcAddress for you A typical program to solve a linear programming problem consists of the following calls main Get data and set up an LP problem loadlp matval Load the problem optimize Solve it solution Get the solution unloadprob Free memory In linear and quadratic problems you pass an array or matrix of coefficients called matval above the Solver DLL can determine values for the objective and constraints by computing the sums of products of the variables with the supplied coefficients In nonlinear and nonsmooth problems however the problem functions cannot be described this way Instead you must write a callback function called funceval below which computes values for the problem functions objective and constraints for any given values of the variables The Solver DLL will call this function repeatedly during the solution process You supply the address of this callback
57. to a variable of type long where getuse will store the number of calls to optimize mipoptimize previously reported to Frontline Systems via an earlier call to reportuse or automatically as determined by the PARAM _USERP setting A pointer to a variable of type long where getuse will store the date of the last report to Frontline Systems as an integer of the form YY YYMMDD The Solver DLL stores the information returned by getuse in the system Registry under the key HKEY LOCAL MACHINE SOFTWARE FrontlineSystems SolverDLL 3 5 Under this key are six values UseLoadProb UseOptimize UseVerify UseRepLoad UseRepOpt and UseRepDate corresponding to oadprob_p optimize_p verify_p repload_p repopt_p and repdate_p respectively Frontline s use based licensing terms can take into account the number of calls to loadlp or loadnIp the number of calls to optimize or mipoptimize or both counts In many Solver DLL applications these counts may be the same However in some applications one count or the other may correspond more closely to the number of sessions with individual users served by the application INTARG reportuse lp probname filename profilename password Dynamic Link Library Solver User s Guide probname filename profilename password getproblimits type HPROBLEM lp LPSTR probname filename profilename password This function will either write a text file to disk or
58. varstat lp begidx endidx mid disp lower upper HPROBLEM lp INTARG begidx endidx LPREALARG mid disp lower upper This routine need be called only if statistical information about the variable values in the final population of candidate solutions found by the Evolutionary Solver engine is desired The argument p of varstat must be the value returned by a previous call to JoadnIp The arguments begidx and endidx are used to limit the set of columns variables for which the statistical information is computed Since this information is meaningful only for NSP nonsmooth optimization problems varstat should not be called for other types of problems Varstat returns 0 unless there is an error in its arguments in which case it returns an integer value indicating the ordinal position of the first argument found to be in error The first column number index as in Joadnip arguments for which statistical information should be returned The last column number index as in loadnlp arguments for which statistical information should be returned An array of dimension endidx begidx 1 where the mean of each variable s values in the final population of candidate solutions will be returned An array of dimension endidx begidx 1 where the standard deviation of each variable s values in the final population of candidate solutions will be returned An array of dimension endidx begidx 1 where the minimum of e
59. 0 REAL 8 rhs 0 2 54 0 42 0 50 0 CHARACTER 3 sense LLL INTEGER 4 matbeg 0 1 0 3 INTEGER 4 matent 0 1 3 3 INTEGER 4 matind 0 5 0 1 2 0 1 2 Dynamic Link Library Solver User s Guide Calling the Solver DLL from FORTRAN e 107 REAL 8 matval 0 5 9 0 REAL 8 1b 0 1 0 0 0 0 REAL 8 ub 0 1 1 0e30 1 0e30 CHARACTER 2 ctype II INTEGER 4 stat ret REAL 8 objval x 0 1 INTEGER 4 lp INTEGER 4 NullL 0 1 1 1 REAL 8 NullD 0 1 1 0 1 0 0 BO 620 Fs Oy TOO SN OD C Display MessageBoxes on invalid arguments for both problems ret setintparam 0 PARAM ARGCK 1 WRITE 100 100 FORMAT Example LP MIP problem Cc Set up the LP portion of the problem lp loadlp PROBNAME 2 3 1 obj rhs sense matbeg matcnt matind matval lb ub NullD 2 3 6 C Now define the integer variables ret loadctype lp ctype C Write out the problem as a text file in algebraic format ret lpwrite lp flexamp SIF DEFINED WIN32 C Set up the callback function to display iteration and objective ret setlpcallbackfunc lp lpcallback SENDIF C Solve the mixed integer problem ret optimize lp C Obtain and write out the solution ret solution lp stat objval x NullD NullD NullD WRITE 110 stat objval 110 FORMAT LPstatus I3 Objective F7 2 WRITE 120 x 0 x 1 120 FORMAT x1 F7 2 x2 F7 2 SIF DEFINED WIN32
60. 25 Use Control Routines n E A O A E OR ae ee 127 PESE r stands E E EERE E EE RE EEA EEO OREA E 128 IKE 10I UI LAE E T EE stgtoserdevaan povetoaescometens 128 Getproblimits TANA E EE E vests AAS E TA A ees Rte eS 129 Callback Routines for Nonlinear Problems ccccccceseesseeseeseeeeeeeseeesceeeceeeeeeneeneenseenseenaes 130 funceval i204 ce eenen li oheiiten Giese rata oA Gee hee ese ade 130 JACODIAN AA fos tect hole ett E eat 8 Aa rls td da heat cat A bate a etd tote 131 Other Callback Routines cceccceeceseceseceseeecesecaecsaecaeecaeeeseeeeeeeeeeecsrenseenaeeeaeenseeaeeeaeenaees 132 setIpcallbacktunes h 3 cco eee rach ee ean be ee 132 getlpcallbackfune iz si scsdece cevesseacedesacsecess ceva E RE EE EARE ERKE 133 setimipcallbaGkfune eonan ha haga wie Satan ites seed oh wees odes 133 getmipcallbaCkMUney isnie vie He s a e hier anet 133 getcallbackiniGynscuctxhrcaced atin eat ie Res ea eA ee a 133 Solver Parameters onen rer delish cs vee sie sees dea R E E e EEE E eR EN 134 Integer Parameters General 0 00 0 cccceecceesceseceseceseceneeeecaeecseesseeeeeseeeeseeeeeeeeeeeensees 134 Integer Parameters Solver Engines 0 cccccsccessceseeeseceeeceeeseeneeeneeeereneeeneeeeensees 135 Integer Parameters Mixed Integer Problems ccsccsseceseeseeeseeeeeeeeeeeeeeerenrens 138 Double Parameters ss 2ccecccvieees c csceccccsgiese ctdeeetecieecas celececec cease cate deeban tenses RR i 139 SOtINtPAL AIM 3 2 5 0 sc
61. 3 1 obj 0 rhs 0 sense 0 1 1 1 matval 0 1b 0 ub 0 1 2 3 6 If lp 0 Then Exit Sub solve the problem optimize lp obtain the solution display objective and variables solution lp stat objval x 0 1 1 1 Form2 Text3 LPStatus amp Trim Str stat Form2 Text4 Objective amp Trim Str objval if infeasible find and display an Irreducibly Infeasible Subset IIS of the constraints If stat PSTAT INFEASIBLE Then findiis lp iisrows iiscols MsgBox Findiis iisrows amp Trim Str iisrows amp iiscols amp Trim Str iiscols Form2 Textl iisrows amp Trim Str iisrows Dynamic Link Library Solver User s Guide Form2 Text2 iiscols amp ReDim rowbdstat iisrows 1 ReDim colbdstat iiscols 1 ReDim rowind iisrows 1 As ReDim colind iiscols 1 As getiis lp stat rowind 0 colind 0 colbdstat 0 Form2 TextS5 rowindl amp Form2 Text6 rowbdstatl Form2 Text7 colindl amp Form2 Text8 colbdstatl Form2 Text24 colind2 Form2 Text25 colbdstat2 iiswrite lp iisexamp txt End If call unloadprob unloadprob lp rowbdstat 0 iiscols Trim Str iiscols As Long As Long Long Long iisrows rowind 0 amp rowbdstat 0 colind 0 amp colbdstat 0 amp colind 1 amp colbdstat 1 to release memory The LP portion it could be elaborated sense 0 Case Ex
62. AFEARRAY containing exactly one element whose value is 1 e For Byte arrays only e g the sense argument of oadnip for an unconstrained nonlinear problem a pointer to a Byte value of 0 or a pointer to a pointer to a SAFEARRAY containing exactly one Byte element whose value is 0 In the first two cases the integer value must be 4 bytes long In the third case the single element of the SAFEARRAY may be a 4 byte integer or an 8 byte double as required by array s normal data type An example declaration and initialization in Visual Basic would be Dim Nul1lL 0 As Long NullL 0 1 or for an argument which is a Byte array Dim Nul1lB 0 As Byte Nul1lB 0 0 In languages such as C C which can easily manipulate NULL pointers you can use the symbolic name NULL which is defined as 0 In Visual Basic using C style arrays header file frontmip bas you would use 1 which will be passed by reference In Visual Basic when using SAFEARRAYs and including header file safrontmip bas you would declare an array of one element such as NullL or NullB above and pass the array name as the argument In Delphi Pascal use a variable of the appropriate type Longint or Double initialized to 1 Problem Definition Routines loadip The following Solver DLL routines are used to define an optimization problem The definition of every problem starts with a call to either JoadIp or loadnIp A call to Joadlp may be followed by
63. ByRef obj As Double _ ByRef matbeg As Long ByRef matcnt As Long _ ByRef matind As Long ByRef matval As Double ByRef var As Double ByRef objtype As Byte ByRef matvaltype As Byte As Long Err 0 On Error Resume Next Value of the objective function objval var 0 var 0 var 1 var 1 Partial derivatives of the objective obj 0 2 var 0 obj 1 2 var 1 Partial derivatives of X Y variable matval 0 var 1 matval 2 var 0 Partial derivatives of X Y variable matval 1 var 1 matval 3 var 0 jacobian3 0 End Function Sub Showlimits Dim cols As Long rows As Long ints As Long ret getproblimits PROB LP cols rows ints MsgBox LP limits amp Trim Str cols amp variables _ amp Trim Str rows amp constraints amp Trim Str ints amp integers ret getproblimits PROB QP cols rows ints MsgBox QP limits amp Trim Str cols amp variables _ 86 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide amp Trim Str ret getproblimits MsgBox NLP limits amp Trim Str ret getproblimits MsgBox NSP limits amp Trim Str End Sub Sub Adjust detail Sub omitted End Sub Adjust detail Sub omitted End Sub Adjust detail Sub omitted End Sub Adjustfor4a detail omit Sub ted End Sub Adjust detail Sub omitted End
64. CLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE WITH RESPECT TO THE SOFTWARE AND THE MEDIA THIS WARRANTY GIVES YOU SPECIFIC RIGHTS AND YOU MAY HAVE OTHER RIGHTS WHICH VARY FROM STATE TO STATE IN NO EVENT SHALL FRONTLINE BE LIABLE FOR ANY DAMAGES WHATSOEVER INCLUDING WITHOUT LIMITATION DAMAGES FOR LOSS OF BUSINESS PROFITS BUSINESS INTERRUPTION LOSS OF BUSINESS INFORMATION AND THE LIKE ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE OR THE MEDIA EVEN IF FRONTLINE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES BECAUSE SOME STATES DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES THE ABOVE LIMITATION MAY NOT APPLY TO YOU In states which allow the limitation but not the exclusion of such liability Frontline s liability to you for damages of any kind is limited to the price of one copy of the Software and Media U S GOVERNMENT RESTRICTED RIGHTS The Software and Media are provided with RESTRICTED RIGHTS Use duplication or disclosure by the Government is subject to restrictions as set forth in subdivision b 3 ii of The Rights in Technical Data and Computer Software clause at 252 227 7013 Contractor manufacturer is Frontline Systems Inc P O Box 4288 Incline Village NV 89450 THANK YOU FOR YOUR INTEREST IN FRONTLINE SYSTEMS INC Contents Introduction 5 The Solver Dynamic Link Libraries ccceeccescesecesecese
65. DLL application flexamp exe which runs under Windows 3 x may be built using the Microsoft FORTRAN 5 1 Programmer s Workbench as follows Note that the FORTRAN Programmer s Workbench is a DOS application 1 Start the Programmer s Workbench Select File Open navigate to the appropriate directory and select the file flexamp for 2 Select Options Environment and add the path to the import library for example e frontmip win16 to the Library Files Search Path 3 Select Options Build Options Set the Main Language to FORTRAN and the Initial Build Options to Windows EXE 4 Select Options LINK Options In the Additional Libraries field enter frontmip lib 5 Select Options FORTRAN Compiler Options and check that the choice for FORTRAN Libraries is Windows and that the Windows Entry Exit Code box is checked 6 Select Rebuild All to compile flexamp for and produce the program flexamp exe You may run the program from the Windows Program Manager or File Manager using File Run or from the Programmer s Workbench The latter option starts up Windows automatically The result should be a window display like the one shown on the next page Dynamic Link Library Solver User s Guide Calling the Solver DLL from FORTRAN e 105 im FLEXAMP Unit Bel x BD Fie Edit State Window Help la x Example LP MIP problem LPstatus 161 Objective 16 66 x1 2 00 x2 4 08 Finished As you can see the 16 bit versi
66. E raram usere o o 2 raram usep o o i Param ITLIM 2147483647 o 214783647 PARAM NDLIM 2147483647 o 2147483647 PARAM_MIPLIM 2147483647 o 2147483647 param samesz o o omms paanome __ o 2147483647 param scaIND o EES param emvarn o o param perv o o param esM o o PARAM DIREC o o eaae e a param prepro o o param orix o oo oa param rgorpe o o J i param imppnp o f o Jo oir param ReoBND 1 J o i setdblparam INTARG setdblparam lp whichparam newvalue HPROBLEM lp INTARG whichparam REALARG newvalue 142 e Solver API Reference Dynamic Link Library Solver User s Guide whichparam newvalue getdblparam whichparam value_p infodblparam whichparam defvalue_p minvalue_p maxvalue_p This routine is called to set the current value of one of the double parameters in a specified problem It returns 0 if successful 1 if whichparam isn t one of the valid codes for integer parameters or 2 if newvalue is outside the range of valid values for the chosen parameter One of the symbolic names or codes for double parameters PARAM_TILIM PARAM _EPOPT PARAM EPPIV PARAM EPSOL PARAM EPRHS PARAM _EPGAP PARAM CUTLO PARAM CUTHI PARAM EPNEWT PARAM_EPCONV or PARAM MUTATE The desired new value for the chosen parameter INTARG getdblparam lp whichparam value_p HPROBLEM lp INTARG whichparam LPREALARG value_p This
67. ELAX Setting this parameter to 1 causes the Solver DLL to ignore any integer variables defined by a call to Joadctype and instead to solve the relaxation of the mixed integer programming problem It is effective for both linear and nonlinear problems When this parameter is set to 0 the default the integer variables are taken into account and the Branch amp Bound algorithm is used to find an integer optimal solution PARAM PREPRO Setting this parameter to 1 activates the Probing strategy for MIP problems in the Solver DLL Plus The Probing strategy allows the Solver to derive values for certain binary integer variables based on the settings of others prior to actually solving the problem When the Branch amp Bound method creates a subproblem with an additional tighter bound on a binary integer variable this causes the variable to be fixed at 0 or 1 In many problems this has implications for the values of other binary integer variables which can be discovered through Probing For example your model may have a constraint such as x x x x x lt 1 where x through x are all binary integer variables Whenever one of these variables is fixed at 1 all of the others are forced to be 0 Probing allows the Solver to determine this before solving the problem In some cases the Feasibility tests performed as part of Probing will determine that the subproblem is infeasible so it is unnecessary to solve it at all This is a sp
68. HPROBLEM lp LPSTR filename Dynamic Link Library Solver User s Guide Ipwrite lpread filename You may call this routine for linear or quadratic programming problems only when the pstat argument value returned by solution is 2 PSTAT_INFEASIBLE The iiswrite routine calls findiis if necessary to compute an Irreducibly Infeasible Set of constraints and bounds as described above It then writes an ASCII text file to disk named filename which lists the objective the constraints included in the IIS and the variable bounds included in the IIS in the same algebraic format used by Ipwrite This file is designed to be quickly readable in a text editor and you can use it to identify the problem s in your constraints which are causing the overall model to be infeasible INTARG lpwrite lp filename HPROBLEM lp LPSTR filename This routine may be called at any time after Joadlp loadquad and or loadctype have been called and before unloadprob is called It cannot be called for a nonlinear problem defined via loadnip Lpwrite will write an output text file filename containing an algebraic statement of the problem you have defined By calling Ipwrite and examining the resulting file you can verify that the problem defined by your arguments is the one you intended You can also use pwrite to save a problem to disk and pread to read it in and solve it later For compatibility with previous versions of the
69. INT message WPARAM wParam LPARAM 1Param HDC hDC display context variable PAINTSTRUCT ps paint structure TEXTMETRIC textmetric int nDrawX nDrawY nSpacing char szText 80 szObj 12 szVar1 12 szVar2 12 We call the Solver DLL on each WM_PAINT message RunSolver lpRunSolver char szWinTitle szProblem szResults long stat 0 calls 0 double obj 0 0 double x 2 0 0 0 0 if hWnd hWnd1 lpRunSolver PROBLEM1 szWinTitle szWinTitlel else hWnd hWnd2 lpRunSolver PROBLEM2 szWinTitle szWinTitle2 if lpRunSolver RunLPSolver szProblem WinExamp MIP problem szResults MIP Problem Results else lpRunSolver RunNLPSolver szProblem WinExamp NLP problem szResults NLP Problem Results switch message case WM PAINT hDC BeginPaint hWnd amp ps GetTextMetrics hDC amp textmetric nSpacing textmetric tmExternalLeading textmetric tmHeight Initialize drawing position to 1 4 from the top left nDrawX GetDeviceCaps hDC LOGPIXELSX 4 1 4 nDrawY GetDeviceCaps hDC LOGPIXELSY 4 1 4 calls lpRunSolver hWnd amp stat amp obj x SetWindowText hWnd szWinTitle wsprintf szText Call ld s calls szProblem TextOut hDC nDrawX nDrawY szText strlen szText nDrawY 2 nSpacing FPSTR obj szObj FPSTR x 0 szVarl FPSTR x 1
70. L Solves the problem Minimize x 2 Y 2 Subject to i PE a AE l KF Ye SSO Solution is X Y 0 5 Objective 0 5 rhs 0 1 rhs 1 0 sense 0 Asc E sense 1 Asc G 1b 0 INFBOUND 1lb 1 INFBOUND ub 0 INFBOUND ub 1 INFBOUND x 0 0 x 1 ak setintparam 0 PARAM_ARGCK 1 lp loadnlp PROBNAME 2 2 1 obj rhs sense _ NullL NullL NullL matval x lb ub NullD 4 AddressOf funcevall AddressOf jacobian1 If lp 0 Then Exit Sub Ask the Solver DLL to call the partial derivatives we derivative calculations our jacobian routine and check supply against its own rise over run setintparam lp PARAM DERIV 3 optimize lp solution lp stat objval x piout slack dj Form2 Text3 Status amp stat Form2 Text4 Objective amp objval Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 Form2 Text5 slackl amp slack 0 Form2 Text7 Slack2 amp slack 1 Form2 Text6 pioutl amp piout 0 Form2 Text8 piout2 amp piout 1 Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 89 call unloadprob unloadprob lp Case 3 to release memory Example program calling the nonlinear Solver DLL Attempt to solve the problem A A Minimize x 2 Ms Subject to f x Y xe XY 1 0 This problem is infeasible We will call findiis of the infeasibility 2
71. L are always allocated statically or on the heap or by calling all of the Solver DLL routines from a single function in your program Solving Multiple Problems Sequentially In all versions of the Solver DLL you can call the DLL routines repeatedly to solve a series of optimization problems in memory But you must start each problem with a call to JoadIp or loadnIp and end each problem with a call to unloadprob in order to ensure that all memory allocated by the Solver DLL is freed before the next problem begins You must also ensure that any memory allocated by your own application code is freed at the appropriate time In the single threaded versions of the Solver DLL which are serially reusable but not reentrant you can solve a series of problems sequentially but you cannot solve multiple problems at the same time If you call loadlp or loadnip a second time without calling unloadprob to end the first problem the returned problem handle will be NULL and if PARAM ARGCK is 1 an error message will appear Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 51 Solving Multiple Problems Concurrently In the multi threaded versions of the Solver DLL you can solve multiple problems at the same time Even in a single threaded application you can start multiple problems with calls to Joadip or loadnip keeping track of the separate problem handles that they return and freely call the oth
72. L will fill in this array when it calls your funceval and or jacobian routines If the matbeg matcnt and matind arrays are present these arrays and the matval array must account for all of the partial derivatives which could become nonzero at any time during the solution process You may pass NULL values for matbeg matcnt and matind if your matval array is a full size dense matrix i e consisting of numcols numrows elements and the elements of each column are consecutive If matbeg matcnt and matind are not NULL values the array matval contains the nonzero coefficients grouped by column i e all coefficients for the same variable are consecutive matbeg i contains the index in matval of the first coefficient for column i matcnt i contains the number of coefficients in column i Note that the indices in matbeg must be in ascending order Each entry matind i is the row number of the corresponding coefficient in matval i The entries in matind are not required to be in ascending row order The coefficient M i j in the full constraint matrix if it is nonzero would be stored in matval matbeg j k where k is between 0 and matcnt j 1 inclusive and the corresponding entry matind matbeg j k i the row index An array of dimension numcols containing initial values for the variables These values may influence the progress of the nonlinear Solver engine and determine which of several locally optimal points are fo
73. LIM parameter The arguments rowind and rowbdstat should be arrays of integers with dimension at least equal to the pnumrows argument value returned by findiis On return rowind contains the indices same as those used in the sense and rhs arguments of loadIp and loadnIp of the constraints rows included in the HS The corresponding elements of rowbdstat will contain 0 if the constraint normally with sense G is at its lower bound 1 if the constraint normally with sense E is fixed at one value and 2 if the constraint normally with sense L is at its upper bound The arguments colind and colbdstat should be arrays of integers with dimension at least equal to the pnumcols argument value returned by findiis On return colind contains the indices same as those used in the b and ub arguments of loadlp and loadnip of the variable bounds columns included in the IIS The corresponding elements of colbdstat will contain 0 if the variable is at its lower bound 1 if the variable is fixed at one value and 2 if the variable is at its upper bound If the value returned via pstat is 2 meaning that a complete IIS was not found the information returned by gefiis may still be useful It will identify a subset of the constraints and variable bounds containing the source of infeasibility even though this subset may contain more rows and columns than would be included in an IIS INTARG iiswrite lp filename
74. LINVAR PARAM _DERIV PARAM _ESTIM PARAM DIREC PARAM RELAX PARAM PREPRO PARAM _OPTFIX PARAM REORDR PARAM _IMPBND PARAM REQBND A pointer to the location where the current value of the parameter will be stored INTARG infointparam lp whichparam defvalue_p minvalue_p maxvalue_p HPROBLEM lp INTARG whichparam LPINTARG defvalue_p minvalue_p maxvalue_p This routine is called to get the minimum maximum and default values of one of the integer parameters It returns 0 if successful or 1 if whichparam isn t one of the valid codes for integer parameters The p argument is ignored and may be NULL One of the symbolic names or codes for integer parameters PARAM ARGCK PARAM ARRAY PARAM USERP PARAM _IISBND PARAM _ITLIM Dynamic Link Library Solver User s Guide Solver API Reference e 141 PARAM NDLIM PARAM MIPLIM PARAM SAMPSZ PARAM NOIMP PARAM SCAIND PARAM CRAIND PARAM LINVAR PARAM DERIV PARAM ESTIM PARAM DIREC PARAM RELAX PARAM PREPRO PARAM OPTFIX PARAM REORDR PARAM IMPBND PARAM REQBND defvalue_p A pointer to the location where the default value of the parameter will be stored minvalue_p A pointer to the location where the minimum value of the parameter will be stored maxvalue_p A pointer to the location where the maximum value of the parameter will be stored Below is a list of the default minimum and maximum values of each of the integer parameters PARAM ARGCK o o i raram array o o
75. LL NULL hiInstance NULL if hWnd return FALSE ShowWindow hWnd nCmdShow UpdateWindow hWnd return TRUE LRESULT CALLBACK MainWndProc HWND hWnd UINT message WPARAM wParam LPARAM 1Param HDC hDC display context variable PAINTSTRUCT ps paint structure TEXTMETRIC textmetric int nDrawX nDrawY nSpacing co har szText 80 szObj 12 szVar1 12 szVar2 12 We call the Solver DLL on the 1st WM PAINT message static long LPstat 0 NLPstat 0 static double LPobj 0 0 NLPobj 0 0 static double LPx 2 0 0 0 0 NLPx 2 0 0 0 0 static char LPtitle MIP Problem Results static char NLPtitle NLP Problem Results switch message case WM PAINT hDC BeginPaint hWnd amp ps GetTextMetrics hDC amp textmetric nSpacing textmetric tmExternalLeading textmetric tmHeight Initialize drawing position to 1 4 from the top left nDrawX GetDeviceCaps hDC LOGPIXELSX 4 1 4 nDrawY GetDeviceCaps hDC LOGPIXELSY 4 1 4 strcpy szText WinExamp MIP and NLP problems with callbacks TextOut hDC nDrawX nDrawY szText strlen szText nDrawY 2 nSpacing if LPstat RunLPSolver amp LPstat amp LPobj LPx RunNLPSolver amp NLPstat amp NLPobj NLPx SetWindowText hWnd szAppTitle FPSTR LPobj szObj FPSTR LPx 0 szVarl FPSTR LPx 1 szVar2 TextOut hDC nDrawX
76. LPBYTEARG objtype LPBYTEARG matvaltype printf jacobian evaluated at xl g x2 g n var 0 var 1 Value of the objective function objval 0 var 0 var 0 var 1 var 1 Partial derivatives of the objective obj 0 2 0 var 0 obj 1 2 0 var 1 Partial derivatives of X Y constant matval 0O 1 0 matval 2 1 0 44 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide Partial derivatives of X Y variable matval 1 var 1 matval 3 var 0 return 0 void example2 void double obj 2 double rhs 2 1 0 0 0 char sense 2 EG double matval 4 double 1lb INFBOUND INFBOUND double ub INFBOUND INFBOUND long i stat double objval double x 2 0 25 0 25 double piout 2 slack 2 dj 2 HPROBLEM lp NULL printf nExample NLP problem 2 n setintparam lp PARAM ARGCK 1 lp loadnlp PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval x lb ub NULL 4 funcevall lp return jacobianl if Ask the Solver DLL to call the partial derivatives we derivative calculations our jacobian routine supply against its own rise over run and check setintparam lp PARAM DERIV 3 optimize lp solution lp amp stat amp objval x piout slack dj printf nStatus d Objective g n stat objval printf Final values x1 g x2 g n
77. M_NOIMP indicate nonsmooth 1 1 second AddressOf showiter1 solution lp stat objval x NullD NullD NullD varstat lp 0 1 mid disp lower upper Form2 Text3 Status amp stat Form2 Text4 Objective amp objval Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 Form2 Text5 midl amp mid 0 Form2 Text7 mid2 amp mid 1 Form2 Text6 displ amp disp 0 Form2 Text8 disp2 amp disp 1 Form2 Text10 lowerl amp lower 0 92 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide Form2 Text11 lower2 amp lower 1 Form2 Text24 upperl amp upper 0 Form2 Text25 upper2 amp upper 1 setlpcallbackfunc lp 0 call unloadprob to release memory unloadprob lp Case 6 Example C program calling the Evolutionary Solver DLL Solves the problem Maximize if X gt 10 then Y Z else Y Z Kres Ko MZ lt 22 0 Solution is X gt 10 Y Z 20 objective 40 Dim 1b2 0 To 2 As Double Dim ub2 0 To 2 As Double Dim x2 0 To 2 As Double Dim obj2 0 To 2 As Double 1b2 0 0 1b2 1 0 1b2 2 0 ub2 0 20 ub2 1 20 ub2 2 20 x2 0 5 x2 1 5 x2 2 5 setintparam 0 PARAM ARGCK 1 lp loadnlp PROBNAME 3 0 1 obj2 NullD NullB _ NullL NullL NullL NullD x2 1b2 ub2 NullD 0O AddressOf funceval 6 0 If lp 0 Then Exit Sub loadnitype lp NullB NullB indicate nonsmoot
78. NTARG _CC funcevall HPROBLEM lp INTARG numcols INTARG numrows LPREALARG objval LPREALARG lhs LPREALARG var INTARG varone INTARG vartwo objval 0 var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side return 0 Define and solve the example NLP problem long RunNLPSolver HWND hWnd long pstat double pobj double x double obj 2 double rhs 2 1 0 0 0 char sense 2 EG double matval 4 double lb INFBOUND INFBOUND double ub INFBOUND INFBOUND HPROBLEM lp NULL _FUNCEVAL lpFuncEval _CCPROC lpPivot setintparam lp PARAM ARGCK 1 lpFuncEval _FUNCEVAL MakeProcInstance FARPROC funcevall hInst lp loadnip PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval x lb ub NULL 4 lpFuncEval NULL if lp return 0 if hWnd hWnd1 lpl1 lp else lp2 lp lpPivot _CCPROC MakeProcInstance FARPROC pivot hInst setlpcallbackfunc lp lpPivot optimize lp solution lp pstat pobj x NULL NULL NULL unloadprob amp lp return Calls 68 e Native Windows Applications Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic Basic Steps You can use many features of the Solver DLL with both 32 bit and 16 bit versions of Visual Basic 4 0 and above and with most versions
79. Solver DLL prewrite is a synonym for pwrite Lpwrite returns 0 unless there is an error in its arguments in which case it returns 1 for an invalid p argument or 2 for any I O error related to opening and writing the contents of filename The name or complete path of the output text file Lpwrite will create this file which will replace any existing file of the same name If filename does not include an explicit path the file will be created in the current directory As an example the following text appears in filename when Ipwrite is called for Example 2 in the sample source programs supplied with the Solver DLL Maximize LP MIP obj 2 0 x1 3 0 x2 Subject To cls 9 0 x1 6 0 x2 lt 54 0 C2 6 0 x1 7 0 x2 lt 42 0 C3 5 0 x1 10 0 x2 lt 50 0 Bounds 0 0 lt x1 lt infinity 0 0 lt x2 lt infinity Integers x1 x2 End INTARG lpread lp filename objsen_p numcols p numrows p numints_p matcnt qmatcnt HPROBLEM lp LPSTR filename Dynamic Link Library Solver User s Guide Solver API Reference e 125 lp filename objsen_p numcols_p numrows_p numints_p matcnt qmatent 126 e Solver API Reference LPINTARG objsen_p numcols_p numrows_p numints p LPINTARG matcnt qmatcnt This routine can be used to read in the definition of a linear quadratic or mixed integer problem in algebraic format from a text file The file may be previously written by the pwrite routin
80. Solver User s Guide Lifetime of Solver Arguments Storage for the arguments passed to the Solver DLL routines may be allocated statically outside a function definition or by using the static keyword on the stack at runtime the normal case for a variable declared within a function or on the heap when allocated with malloc or operator new But you must ensure that storage remains allocated for the arguments from the time you call loadlp or loadnIp to the time you call unloadprob or exit your program Statically allocated and heap based arguments normally will not present a problem in this regard The situation you must avoid is illustrated below void main HPROBLEM lp lp setup solve lp HPROBLEM setup long matbeg 100 matcnt 100 return loadlp matbeg matcnt void solve HPROBLEM lp optimize lp The arrays matbeg and matcnt and perhaps others are allocated on the stack when the routine setup is entered When setup exits it returns the problem handle provided by loadlp but at this point the arrays matbeg matcnt etc are deallocated and the stack space is reused in subsequent calls This means that the call to optimize in the routine solve will fail probably with a General Protection fault in the Solver DLL when the Solver tries to reference the memory formerly allocated to matbeg and matcnt You can avoid this situation by ensuring that arguments passed to the Solver DL
81. Solver User s Guide stability during the solution of large LP models where the cumulative effect of the small errors inherent in finite precision computer arithmetic would otherwise compromise the solution process These same methods often result in solution speeds far beyond earlier generations of LP solvers Thanks to these methods the Large Scale Solver DLL can readily handle all of the problems in the well known NETLIB test suite virtually all with the default tolerance settings The Large Scale Solver DLL is also a well behaved Microsoft Windows Dynamic Link Library Like the Small Scale Solver DLL it respects Windows conventions for loading and sharing program code Under Windows NT 2000 or Windows 95 98 the Solver runs in 32 bit protected mode and supports preemptive multitasking When used under Windows 3 1 the Large Scale Solver DLL shares the processor with other applications through Windows non preemptive multitasking and draws upon Windows global memory resources in an efficient manner The Large Scale Solver DLL uses many of the best published solution methods and has been proven in use on large LP models in industry and government around the world These algorithmic methods include e Simplex method with two sided bounds on both variables and constraints e Memory efficient Branch amp Bound method for mixed integer problems e Matrix factorization using the LU decomposition with the Bartels Golub update e Refactori
82. Village NV 89450 USA Tel 775 831 0300 Fax 775 831 0314 Email info frontsys com kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Problem 1 Solve the MIP model Maximize 2 x1 3 x2 Subj to 9 x1 6 x2 lt 54 6 xl 7 X2 lt 42 5 x1 10 x2 lt 50 x1 x2 non negative integer MIP solution xl 2 x2 4 Objective 16 0 Dynamic Link Library Solver User s Guide Native Windows Applications e 63 Problem 2 Solve the NLP model Minimize X 2 Y 2 Subject to X Y 1 X Y gt 0 xl x2 non negative Solution is X Y 0 5 Objective 0 5 This is a multi threaded Windows application It creates two threads and two windows One thread repeatedly solves Problem 1 and displays the results in the first window while the other thread repeatedly solves Problem 2 and displays the results in the second window If your copy of the Solver DLL does not include the LP or NLP Solver engine you may change the defines PROBLEM1 and PROBLEM2 so that they both refer to the routine either RunLPSolver or RunNLPSolver that calls the Solver engine that you have then the same results will appear in both windows include lt windows h gt include lt stdlib h gt include lt string h gt include frontmip h include frontkey h define PROBLEM1 RunLPSolver define PROBLEM2 RunNLPSolver Prototype the procedures to follow int WINAPI WinMain HINSTANCE HINSTANCE LPSTR
83. abeled Solve LP MIP This will execute the statements found in procedure TForm1 LPButtonClick calling oadIp loadctype Ipwrite setlpcallbackfunc optimize solution and unloadprob During the execution of optimize the Solver DLL will call the callback function which displays a MessageBox like the one shown below callback Ed Iteration 1 Objective 15 0000 Cancel After optimize returns the Pascal code calls solution and places the solution values in the first pair of text edit fields Clicking on the button Solve NLP will execute the statements found in procedure TForm1 NLPButtonClick calling loadnlp setlpcallbackfunc optimize solution and unloadprob This will display the iterations of the nonlinear Solver assuming that your version of the Solver DLL includes the nonlinear Solver engine In this case the Pascal code will call solution and place the solution values in the second pair of text edit fields At this point the Delphi Pascal form should look like the one shown on the next page Dynamic Link Library Solver User s Guide Calling the Solver DLL from Delphi Pascal e 97 ai Form Iof x LP MIP Problem Status 101 Objective 16 0000 x1 2 0000 x2 4 0000 NLP Problem Status 1 Objective 0 5000 fa 0 5000 x2 0 5000 Solve LP MIP Solve NLP 4 To end execution of the program click on the Close button in the upper right hand corner of the wi
84. able are consecutive matbeg i contains the index in matval of the first coefficient for column i matcnt i contains the number of coefficients in column i Note that the indices in matbeg must be in ascending order Each entry matind i is the row number of the corresponding coefficient in matval i The entries in matind are not required to be in ascending row order The coefficient M i j in the full constraint matrix if it is nonzero would be stored in matval matbeg j k where k is between 0 and matcnt j 1 inclusive and the corresponding entry matind matbeg j k i the row index An array of dimension numcols containing the lower bound on each variable A lower bound less than or equal to INFBOUND will be treated as minus infinity An array of dimension numcols containing the upper bound on each variable A upper bound greater than or equal to INFBOUND will be treated as plus infinity An array of dimension rows containing the range value of each constraint right hand side Ranged rows are specified in the sense array If the row is not ranged the corresponding rngval element should be 0 0 A range value for row 1 means that the constraint left hand side must be between rhs i and rhs i rngval i rngvalfi may be positive or negative If there are no ranged rows at all rngval may be NULL it is ignored when the Small Scale Solver DLL is used Dynamic Link Library Solver User s Guide colspace rowspace nz
85. accept a matrix of coefficients matval for the linear constraints and another matrix of coefficients qmatval for the quadratic objective function In a portfolio optimization problem the objective function is normally the portfolio variance and the gmatval coefficients are the covariances between pairs of securities in the portfolio If you wish to minimize variance in a portfolio optimization problem the QP Solver is the preferred Solver engine since it will be faster and more accurate than the NLP Solver If however you wish to maximize portfolio return and treat portfolio variance as a constraint your problem will not be a QP since its constraints are not all linear and you will need to use the NLP Solver Nonlinear Solver The nonlinear GRG Solver can solve smooth nonlinear quadratic and linear programming problems It may also be the easiest to use Solver engine if it is natural for you to describe the optimization problem by writing a function called funceval later in this Guide that evaluates the objective and constraints for given values of the decision variables However this generality comes at a price of both speed and reliability On smooth nonlinear problems the NLP Solver like all similar gradient based methods is guaranteed only to find a locally optimal solution which may or may not be the true globally optimal solution within the feasible region Moreover since the NLP Solver treats QP and
86. ach variable s values in the final population of candidate solutions will be returned An array of dimension endidx begidx 1 where the maximum of each variable s values in the final population of candidate solutions will be returned INTARG constat lp begidx endidx mid disp lower upper HPROBLEM lp INTARG begidx endidx LPREALARG mid disp lower upper This routine need be called only if statistical information about the constraint values in the final population of candidate solutions found by the Evolutionary Solver engine is desired The argument p of constat must be the value returned by a previous call to JoadnIp The arguments begidx and endidx are used to limit the set of rows constraints for which the statistical information is computed Since this information is meaningful only for NSP nonsmooth optimization problems constat should not be called for other types of problems Constat returns 0 unless there is an error in its arguments in which case it returns an integer value indicating the ordinal position of the first argument found to be in error The first row number index as in loadnlp arguments for which statistical information should be returned Dynamic Link Library Solver User s Guide endidx mid disp lower upper The last row number index as in oadnip arguments for which statistical information should be returned An array of dimension endidx begidx 1 wher
87. adlp is equal to the sum of the counts returned in the elements of matcnt similarly for gmatcnt and gnzspace You can initialize the matbeg array based on the counts in matcnt similarly for gmatbeg and qmatcnt For example in C C for nzspace i 0 i lt numcols i nzspace matecnt i for i 0 i lt nzspace i matind i 0 for i 0 i lt numcols i matbeg i i 0 0 matbeg i 1 matcnt i 1 Use Control Routines The multi threaded version of the Solver DLL can be distributed under a license based either on the number of users seats or on the number of uses calls to the optimize or mipoptimize routines Use based licensing is advantageous in situations such as public Web server applications where the number of users is not known or is so large that user based licensing would be potentially too expensive To facilitate use based licensing the Solver DLL includes routines that can be called to determine the number of uses to date write this information to a text file or automatically email this information to Frontline Systems all under the control of the application program The Solver DLL is shipped in multiple configurations that include only the Solver engines that you need for your application and that place specific upper limits on Dynamic Link Library Solver User s Guide Solver API Reference e 127 getuse loadprob_p optimize p verify _p repload_p repopt_p
88. against this value This argument should be an array of numcols elements containing initial values for the decision variables These initial values are relevant only if the Q matrix is semi Dynamic Link Library Solver User s Guide Solver API Reference e 113 loadctype ctype loadnip probname 114 e Solver API Reference definite or indefinite in which case they will influence the path that the Solver DLL takes and the final solution to which it will converge Loadquad returns 0 unless there is an error in its arguments in which case it returns an integer value indicating the ordinal position of the first argument found to be in error Note objsa and rhssa which return LP range information may not be used when Joadquad has been called Loadquad uses a numerical test to determine whether the Q matrix is at least positive semi definite for minimization problems or negative semi definite for maximization problems Ifthe Q matrix is indefinite Joadquad will return 5 the ordinal position of the gmatval argument and if PARAM ARGCK is 1 it will display an error message dialog indicating this condition See the section Solution Properties of Quadratic Problems in the chapter Designing Your Application INTARG loadctype lp ctype HPROBLEM lp LPBYTEARG ctype This routine is called only for mixed integer problems The first argument must be the value returned by a previous call to JoadIp or loa
89. al and matind will be filled in by our next call to lpread we need only initialize matbeg based on matecnt for i 0 i lt numcols i matbeg i i 0 0 matbeg i 1 matent i 1 Next call loadlp and loadctype to define the problem and pass in arrays of appropriate dimension lp loadlp PROBNAME numcols numrows objsen obj rhs sense matbeg matcnt matind matval 1b ub NULL numcols numrows nzspace if lp return loadctype lp ctype Now we call lpread to read in the actual array values lpread lp vcexamp1 NULL NULL NULL NULL NULL NULL Finally we call mipoptimize and display the solution mipoptimize lp solution lp amp stat amp objval x NULL NULL NULL printf LPstatus ld Objective g n stat objval printf xl g x2 g n x 0 x 1 unloadprob amp lp Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 41 int main void char buf 32 printf TEST CASES FOR FRONTMIP DLL n examplel example2 gets buf example3 example4 gets buf example5 return 0 C C Source Code Nonlinear Nonsmooth Problems The source code file vcexamp2 c is listed below It includes four example problems using the nonlinear GRG Solver which are set up and solved in turn The first example is a simple two variable nonlinear optimization problem which defines a
90. ally use reports are created only when your application calls the reportuse function which can either write a text file or send an email message containing a report of cumulative uses Dynamic Link Library Solver User s Guide Designing Your Application e 29 Calling the Solver DLL from C C C C Compilers Basic Steps To use the Solver DLL from C or C you must have an appropriate compiler and linker capable of building Windows applications such as Microsoft Visual C Borland C Symantec C or WATCOM C This Guide will give explicit instructions for use with Microsoft Visual C 5 x and 6 x 32 bit and Visual C 1 5x 16 bit but use with other compilers should be similar Most C compilers for Windows allow you to easily port DOS or UNIX C and C applications which use printf or cout for glass teletype output to Windows To simplify the input output and focus on the Solver DLL routines and arguments the example applications in this chapter use printf calls for output and will be built as Win32 console applications in Microsoft Visual C or as QuickWin applications in 16 bit Visual C To build a native Windows application in C or C you ll have to learn something about the Windows API and or a C class library such as the Microsoft Foundation Classes A single threaded and a multi threaded example application using the Windows API and the Solver DLL s callback functions are presente
91. ample problems for the Solver DLL which are set up and solved in turn The first example is a simple two variable LP problem The second example for which source code in Visual Basic Delphi Pascal and FORTRAN is also included is a MIP problem identical to the previous LP problem except that the decision variables are required to have integer values The third example attempts to solve an LP problem that is infeasible then it uses the IIS finder to diagnose the infeasibility The fourth example is a quadratic programming problem using the classic Markowitz method to find an efficient portfolio of five securities The fifth example uses the pread function to read in a problem in algebraic notation from a text file that was created by the pwrite function in the second example You are encouraged to study this source code or the Visual Basic source code and the comments in each problem even if you plan to use a language other than C C for most of your work The C C and Visual Basic example code is more extensive than the examples for the other languages and illustrates most of the features of the Solver DLL including the Quadratic Solver the Evolutionary Solver automatic diagnosis of infeasible problems and use of the pread and Ipwrite functions 34 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxk Frontli
92. ample Q set up the LP portion of the problem of the objective is all 0 s here to include transaction costs or other factors lp loadlp PROBNAME 5 2 1 obj 0 rhs 0 7 matbeg 0 matcnt 0 matind 0 matval 0 1b 0 ub 0 1 5 2 10 If lp 0 Then Exit Sub now set up the Q matrix to define the quadratic objective loadquad lp qmatbeg 0 25 x 0 solve the problem obtain and optimize lp solution lp stat objval x 0 Form2 Text3 LPStatus Form2 Text4 Obj Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 Form2 Text5 x3 amp x 2 Form2 Text6 x4 amp x 3 Form2 Text7 x5 amp x 4 call unloadprob unloadprob lp Case Example 5 we merely pass the right sizes on we do initialize them checked for validity qmatcnt 0 gmatind 0 qmatval 0 display the solution al 2 421 amp Trim Str stat amp Trim Format objval O 0 H to release memory Since sense and ctype get sense 0 Asc L sense 1 Asc L sense 2 Asc L ctype 0 Asc C ctype 1 Asc C lp loadlp PROBNAME 2 3 1 obj 0 rhs 0 sense 0 1 1 1 matval 0 1b 0 ub 0 1 2 3 6 Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 81 If lp 0 Then Exit Sub loadctype lp ctype 0 Now we read in the textfile vbexamp1 and all arrays are fi
93. ample Visual Basic project vbexamp1 vbp uses frontmip bas and C style arrays it can be opened and run in Visual Basic 4 0 16 bit or 32 bit or in Visual Basic 5 0 and above 32 bit only The example project vbexamp2 vbp uses safrontmip bas and SAFEARRAYs it can be opened and run only in Visual Basic 5 0 and above You can pass array arguments as C style arrays in Visual Basic 5 0 or above if you wish However any callback function funceval that you write for use with the nonlinear or nonsmooth Solver engines will only be able to access the first element of the array arguments passed to it which means that you can solve at most a nonlinear problem with one variable and one constraint Building a 32 Bit Visual Basic Program You can run the compiled versions of the Visual Basic examples vbexamp1 exe and vbexamp2 exe using Start Run These programs like all Visual Basic applications rely on the Visual Basic runtime system DLLs if you have installed either the Visual Basic programming system or some other Visual Basic program these DLLs should already be present in your Windows system directory You can edit build and test the source code of vbexamp1 exe vbexamp2 exe is similar as follows 1 Start the Visual Basic programming system In the New Project dialog click on the Existing tab navigate to the Visual Basic example subdirectory for example c frontmip examples vbexamp select vbexamp1 vbp and click Open 2 The
94. analyze However finding the minimal size IIS can be computationally very expensive hence the IIS finder is designed to find an IIS that contains as few constraints rows as possible in a reasonable amount of time Since variable bounds are easier to analyze than full constraints the IIS finder favors fewer rows over fewer bounds Solution Properties of Quadratic Problems A quadratic programming QP problem is one in which the objective is a quadratic function and the constraints are all linear functions of the variables A general quadratic function may be written as the sum of a quadratic term x Q x and a linear term cx FQ x Ox cx The matrix Q is the Hessian matrix of second partial derivatives of the objective function Because the function is quadratic or second degree all elements of this matrix are constant You supply the elements of the Q matrix when you call the loadquad function and the elements of the c vector when you call the loadIp function via the obj argument Depending on the properties of the Q matrix a quadratic function may have one many or no optimal minimum or maximum values If the Q matrix is positive definite for a minimization problem negative definite for a maximization problem the function will have a bowl shape and a single optimal solution a strong minimum If the Q matrix is positive semi definite the function will have a trough and infinitely many optimal s
95. ation and return to your program For LP problems you can specify a callback routine which will obtain control on each pivot or Simplex iteration For MIP problems you can also specify a routine which will obtain control on each branch or Branch amp Bound LP subproblem Both callback routines should be declared as follows INTARG _CC MyCallback lpinfo wherefrom HPROBLEM lpinfo INTARG wherefrom _CC calling convention is a typedef for callback routines under Windows It is export far pascal in 16 bit Windows 3 x and stdcall in 32 bit Windows 95 98 and NT _CCPROC is a typedef for the address of a routine with this signature Both of these symbols are defined in frontmip h You pass the address of your callback routine to the Solver DLL via a call to setlpcallbackfunc or setmipcallbackfunc In 16 bit Windows 3 x the address you pass should be obtained from the Windows routine MakeProclnstance An example would be CCPROC IpCallback _CCPROC MakeProcInstance FARPROC MyCallback hInst where hInst is the instance handle of the currently running application The pinfo argument is a problem handle identifying the current LP or MIP problem but its only use should be as the first argument in calls to getcallbackinfo see below The wherefrom argument indicates whether this is an LP pivot wherefrom CALLBACK PRIMAL 1 ora MIP branch wherefrom CALLBACK MIP 101 this makes it easy to use a singl
96. ays a window like the one shown on the next page Press the ENTER key to continue running the program and produce more output Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 33 gt VCEXAMP1 Iof Xx File Edit View State Window Help i Stdin Stdout Stderr let Example LP problem LPstatus 1 Objective 16 4 x1 2 8 x2 3 6 Slack 8 7 2 piout 6 5 Slack 1 6 piout 1 6 2 slack 2 6 piout 2 6 16 Obj coefficient 2 Lower 1 5 Upper 2 57143 Obj coefficient 3 Lower 2 33333 Upper 4 Constraint RHS 54 Lower 46 8 Upper 1e 636 Constraint RHS 42 Lower 35 Upper 4S Constraint RHS 56 Lower 43 3333 Upper 66 Example MIP problem LPstatus 161 Objective 16 xi 2 x2 4 Running Input pending in Stdin Stdout Stderr The first few lines of output have scrolled beyond the top of this window You should also note that the C source code in vcexamp1 c uses a callback function to display the LP iterations only in the Win32 version of this example In Windows 3 x you must set up callback function addresses with the MakeProcInstance API call This call requires an instance handle argument that is not readily available in a QuickWin program For an example of the use of callback functions in both Win32 and Win16 programs see the chapter Native Windows Applications C C Source Code Linear Quadratic Problems The source code file vcexamp1 c is listed below Note that it includes five ex
97. bdstat 2 double objval double x 2 HPROBLEM lp NULL printf nExample IIS diagnosis of infeasible problem n setintparam lp PARAM ARGCK 1 set up the LP problem lp loadlp PROBNAME 2 3 1 obj rhs sense NULL NULL NULL matval lb ub NULL 2 3 6 if lp return attempt solve the problem optimize lp check the status of the solution solution lp amp stat amp objval x NULL NULL NULL printf LPstatus ld Objective g n stat objval if infeasible find and display an Irreducibly Infeasible Subset IIS of the constraints if stat PSTAT_ INFEASIBLE findiis lp amp iisrows amp iiscols printf nfindiis iisrows ld iiscols ld n iisrows iiscols getiis lp amp stat rowind rowbdstat amp iisrows colind colbdstat amp iiscols for i 0 i lt iisrows i printf rowind ld ld rowbdstat ld ld n i rowind i i rowbdstat i for i 0 i lt iiscols i printf colind ld ld colbdstat ld ld n i colind i i colbdstat i iiswrite lp iisexamp txt printf n don t forget to free memory unloadprob amp lp 38 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide Example 4 Use the QP solver to perform Markowitz style portfolio optimization Variables are the percentages to be allocated to each investment or asset class 0 lt Xl X2
98. by oadnip Testnitype computes the gradient for your objective function and Jacobian values for your constraints at the origin storing them in the obj and matval arrays that you supplied in your call to Joadnip It then tests whether these gradient and Jacobian values remain constant over a range around the origin Your matval array must be of appropriate size and if they are used your matbeg matcnt and matind arrays must be correctly initialized to indicate which elements of the Jacobian matrix can be nonzero for any variable values over the domain of your functions Testnitype will ignore elements of the Jacobian that you have indicated are zero through your matbeg matcnt and matind arrays hence it will not diagnose linearity correctly if you have missed some Jacobian entries which can be nonzero for certain variable values Remember that you can always pass NULL values for matbeg matcnt and matind and pass a matval array of size numcols numrows Indicates the number of tests performed to validate the gradient and Jacobian values Each test is performed by choosing test values for each variable computing the objective and constraint values using the gradient and Jacobian just determined computing the objective and constraint values by calling your funceval routine and comparing the results If you supply a NULL value for testvals the test values for the variables are chosen randomly If you supply an array
99. c Link Library Solver User s Guide A Multi Threaded Application The source file winexamp2 c found in the Examples Vcexamp subdirectory is a very simple example of a multi threaded application It will run and exhibit multi threaded behavior only when compiled for a Win32 target system and only when used with a multi threaded version of the Solver DLL Since the Win32 API calls to create threads are surrounded by ifdefs winexamp2 c will compile and run on Win16 systems such as Windows 3 1 but it won t exhibit multi threaded behavior Winexamp2 c is similar in structure to winexamp1 c in that it begins with the WinMain InitApplication and InitInstance procedures common to almost all Windows applications However in WinMain we call InitInstance twice to create two windows both using the same window procedure MainWndProc and on Win32 systems we create a thread corresponding to each window A Solver DLL problem is created and solved in each window Code at the beginning of MainWndProc selects the appropriate problem based on the window handle passed on each call by Windows MainWndProc is similar to the corresponding function in winexamp1 c with one important difference Whereas in winexamp1 c we set up and solve both problems only on the first WM_ PAINT message and we save the results in static variables for redisplay on subsequent WM_PAINT messages in winexamp2 c we re create and re solve a problem
100. call to the Solver you can use it to set this parameter and save on solution time PARAM CUTHI This is the integer objective cutoff value for MIP minimization problems In the Branch amp Bound algorithm any subproblem whose objective is greater than this value will not be fathomed If you have an objective value for a known integer solution to this problem for example from a previous call to the Solver you can use it to set this parameter and save on solution time PARAM EPNEWT This is the tolerance within which constraints will be considered binding or satisfied with equality during the solution process PARAM EPCONV This is the tolerance used in the nonlinear GRG Solver s and the Evolutionary Solver s test for a slowly changing objective In the GRG Solver if the relative change in the objective function is less than this value for the last five iterations the Solver stops and returns PSTAT_ FRAC CHANGE in the pstat argument of the solution function In the Evolutionary Solver if 99 of the population members have fitness values that differ by less than this value the Solver stops and returns PSTAT FRAC CHANGE PARAM MUTATE This is the probability that the Evolutionary Solver engine on one of its major iterations will attempt to generate a new trial point by mutating or altering one or more variable values of a current point in the population of candidate solutions 140 e Solver API Refer
101. cedures and functions in your own code this data segment address is maintained When you call a Solver DLL routine which has its own code and data segments and the Solver DLL in turn makes a call to one of your functions which you have set up as a callback function the proper data segment address must be restored so that your function can execute and reference its local data This data segment address will be different for each instance of your application How can the Solver DLL call the same callback function every time yet have different data segment addresses restored in each instance In Windows this is done by calling the API function MakeProcInstance with the address of your callback function and the instance handle which Windows passes to your main entry point when an instance of your application is started The return value of MakeProcInstance is actually a pointer to code within Windows called a thunk which restores the data segment address and then passes control to your callback function You pass this special thunk pointer to setlpcallbackfunc or setmipcallbackfunc and the Solver DLL uses it to call your function For example you can write long _CC pivot HPROBLEM lpinfo long wherefrom _CCPROC lpPivot lpPivot _CCPROC MakeProcInstance FARPROC pivot hInst setlpcallbackfunc lpPivot Now the Solver DLL will be able to call your callback function through the IpPivot pointer Thi
102. ceeececeseecaeeeaeeeseeeeeeeeseeeeeeeesneeeeenaees 5 Thesmiall Scale Solver DEE oria fiat ceastens eaaa shal a aan a ea e O naan aaO 5 The Large ScaleSolver DEL mE eek ci Renee ee ee E ENER 6 Which Solver DLL Should Yot Use isccsesccsccccsuentesescescessayac de suscenseseaviods i ea R ia 7 Dinear Sol vetsss ii 2e seine phe Ae coal scast evs akenatese E 7 Quadratic S OlVers sie cish oasis E aes an oR ee I E ee OE 8 Nonlinear Solver priiis chests nh Sia Be ae aL acti ei 8 Nonsmooth Evolutionary Solver ccccecccesccssecssecseecseeeseeeeeeeeeeecseceesereeeeneeeeeenaees 9 Solving Mixed Integer Problems ccccccceescescceseceeceseceecseeeseeeeeeeeeeereneeneeeeenseenaes 9 L6 Bit Versus 3 2 Bit VerSlONS xiasosssetscssth T E E EEA AE 9 What s New in Version 3 5 i205 deccbat ngs cared stuoeti inlet ened eeldh ai ean gelectiees 10 Evolutionary Solver is ssccssccsecescadecetecesss ceacctskectcescecenceiddeitevies seacelouese caxeactachte beeen GE a 10 Multi Threaded Applications c cccscessseeseessesseeeeceesceeecesecnseceaeceaecaeceeeneeeaeesneeses 10 Ws Based Licensing i i 4 2ecvectvustuevvaceaneenn abet ttecenes Geb es ieee veces Midi wredeearuitstes cont 10 Problems in Algebraic Notation cecccesecssessseeseeesceeeeeecesecesecsaecnaecaecaeeeaeeeaeeeneenes 11 How to Use This Gide i i orgies tedeiies ig een ane aia he ha rears 11 Installation 15 Running the Installation Program ccesccssecsecesecseec
103. cols numrows elements numcols elements in the case of the Q matrix which may include both zero and nonzero elements you need not supply any auxiliary information In sparse form you supply a smaller array containing only the nonzero elements plus auxiliary arrays which provide the row and column indices In the load p function loadquad and loadnIp are similar you pass the constraint matrix via the arguments matbeg matcnt matind and matval To pass the matrix elements in dense form you supply NULL values for matbeg matcnt and matind and you supply a full size array of numcols numrows elements for matval Note that matval must be a single dimensioned array where the elements are stored so that the row constraint index is varied most rapidly To pass the matrix elements in sparse form you supply arrays for all four of matbeg matcnt matind and matval The matbeg array contains column variable indices the matcnt array contains counts of elements in a column the matind array contains row constraint indices and the matval array contains the nonzero elements All column and row indices are 0 based As an example consider the following sparse matrix 1 2 0 0 3 4 0 0 5 6 0 0 7 8 0 0 0 0 0 0 9 0 0 0 Here numcols 3 and numrows 4 there are nzspace 5 nonzero elements To pass this matrix in sparse form you d supply matbeg and matcnt arrays of numcols elements and matind and matval arrays of nzspace e
104. d in the application window title bar a real application would use a dialog box or other user interface element Then it returns with a code indicating whether the solution process should continue or stop at this point The PeekMessage function lets you peek at a message in the application s message queue without actually processing it If there are no pending messages PeekMessage returns 0 In this code we look for the specific Windows message WM_KEYDOWN the user pressed a key while our application had the focus and if it arrives we check the virtual key code We take the ESCape key as a signal from the user that he or she wants to interrupt the optimization process and we return the value PSTAT_ USER ABORT defined in frontmip h to the DLL A similar approach can be used to respond to a mouse click or a menu command Another strategy would be to set a global flag when the appropriate message was processed in your window procedure and check this flag in the LP pivot or MIP branch callback routine Non Preemptive Multitasking The Solver DLL lets you easily write applications that will optimize in the back ground while the user performs other tasks In Windows 95 98 and Window NT 2000 which are preemptive multitasking systems this is straightforward the operating system periodically interrupts each application and lets another one run However Windows 3 x relies on cooperative non preemptive multitaskin
105. d in the later chapter Native Windows Applications To create an application that calls the Solver DLL you must perform the three following steps 1 Include the header file frontmip h in your C or C source program You should also include the license file frontkey h to obtain the license key string 2 Include the import library file frontmip lib in your project or your linker response file Alternatively you can write code to use run time dynamic linking by calling Windows API routines such as LoadLibrary 3 Call at least the routines oadIp or loadnIp optimize solution and unloadprob in that order Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 31 You can use any of the example programs as a guide for getting the arguments right Vcexampl c contains five examples of solving linear integer and quadratic programming problems including an example using the infeasibility IIS finder an example of portfolio optimization using the QP Solver and an example that reads a problem from a text file using the pread function Vcexamp2 c contains four examples of solving nonlinear programming problems including an example using the IIS finder and an example of testing a problem for linearity and switching between the NLP and LP Solvers It also contains two examples that use the Evolutionary Solver to find the global optimum in a problem with multiple local optima and to find the o
106. de frontcbi for FORTRAN header file use with callback functions It also contains a license key file which declares a character string constant containing your own customized license key frontkey h C C license key file reference in your source code frontkey bas Visual Basic license key file add to your VB project frontkey pas Delphi Pascal license key file add to your project frontkey for FORTRAN license key file reference in your source The Win16 and Win32 subdirectories contain the Solver DLL and import library files These files have the same names in each subdirectory but Win16 contains 16 bit versions and Win32 contains 32 bit versions of the files frontmip dll Solver DLL Dynamic Link Library executable code frontmip lib Import library used by linker in C FORTRAN As you write compile and link and execute your application program you will need to reference the Solver DLL files mentioned above Since only single files are needed at each step you may find it convenient to copy the Solver DLL files to the directory where you are building or running your application If your application may be run from many different directories you may wish to place the Solver DLL file in the c windows or c windows system directory in Windows 3 x or Windows 95 98 or the c winnt system32 directory for the 32 bit version of the DLL in Windows NT 2000 Dynamic Link Library Solver User s Guide e When you compil
107. differencing 2 Use supplied jacobian function 3 Use and check supplied jacobian Dynamic Link Library Solver User s Guide Solver API Reference e 135 1 Quadratic NLP search direction 0 Quasi Newton Conjugate Gradient PARAM SAMPSZ_ 6001 Evolutionary Solver population sample size PARAM NOIMP 6002 Evol Solver max time with no improvement PARAM SCAIND The scaling option determines how the LP matrix variable and constraint bounds are re scaled during the solution process A value of 1 means no scaling 0 means normal scaling and 1 means aggressive scaling used only by the Large Scale LP MIP Solver DLL The default value of 0 will usually yield good results including more accurate solutions and fewer total iterations PARAM CRAIND The crashing option is used only by the Large Scale LP MIP Solver DLL A value of 1 indicates that the Solver should start by constructing an advanced basis in which so called artificial variables are eliminated in favor of structural variables wherever possible This often results in fewer total iterations A value of 0 means that the Solver should start from a normal basis PARAM LINVAR This parameter determines whether the nonlinear Solver engine will attempt to recognize variables occurring linearly in all of the problem functions and then save time by assuming that first partial derivatives with respect to these variables are constant and ne
108. dnIp An array of dimension numcols indicating the types of variables in MIP problems The element ctype i indicates the type of variable i as follows ctype i C Continuous variable ctype i T General integer variable ctype i B Binary 0 1 integer variable loadctype returns 0 unless there is an error in its arguments in which case it returns 1 or 2 to indicate the ordinal position of the argument found to be in error HPROBLEM loadnlp probname numcols numrows objsen obj rhs sense matbeg matcnt matind matval var lb ub rngval nzspace funceval jacobian LPSTR probname INTARG numcols numrows objsen LPREALARG obj rhs LPBYTEARG sense LPINTARG matbeg matcnt HPINTARG matind HPREALARG matval LPREALARG var lb ub rngval INTARG nzspace _FUNCEVAL funceval _JACOBIAN jacobian A character string currently 16 characters plus a 0 terminator byte containing a unique key which is assigned to you when you license the Solver DLL from Frontline Systems The DLL that is licensed to you recognizes your specific key string if it is not supplied when oadIp or loadnIp is called these routines will return NULL and calls to these and other routines will not be successful Dynamic Link Library Solver User s Guide numcols numrows objsen obj rhs sense matbeg matent matind matval var lb ub rngval The number of columns in the constraint matrix i e
109. e created by hand or generated by another program As long as the problem definition follows the format and syntax described here and illustrated above under pwrite and is within the size limits of your version of the Solver DLL you can read it in through pread and solve it The text file should consist of lines ending in a newline linefeed or a carriage return linefeed combination The keywords Maximize or Minimize Subject To Bounds Integers and End should appear on separate lines The objective expression must be preceded by obj and each constraint expression preceded by cC1 c2 etc but otherwise the expressions may be split across multiple lines Each variable occurrence must have a form such as x1 x123 etc the highest variable index found in the file is returned in the variable pointed to by numcols_p Lower and upper bounds on variables should either be numbers infinity or infinity The quadratic part of the objective if used must be surrounded by brackets and each term should consist of a number followed by either two variable names separated by or one variable name followed by 2 For example x1 2 x1 x2 x2 2 Either NULL or a pointer to a problem previously returned by loadIp If this argument is NULL pread will scan the input text file and return values for the objsen_p numcols_p numrows_p numints_p matcnt and qmatcnt arguments if they are specified but it will not store any of the coef
110. e integer MIP solution x1 2 x2 4 Objective 16 0 Problem 2 Solve the NLP model Minimize X 2 Y 2 Subject to X Y 1 X Y gt 0 x1 x2 non negative Solution is X Y unit Psunit interface uses SysUtils Forms Dialogs I Frontkey WinTypes WinProcs Stdctrls type TForml class TForm LPLabel TLabel LPEdit1 TEdit LPEdit2 TEdit LPButton TButton NLPLabel TLabel NLPEdit1 TEdit NLPEdit2 TEdit NLPButton TButton 0 5 Objective Messages Frontmip 0 5 Classes Graphics Controls procedure LPButtonClick Sender TObject procedure NLPButtonClick Sender private Private declarations public obj array 0 1 of double rhs array 0 2 of double sense array 0 2 of char matbeg array 0 1 of Longint matcnt array 0 1 of Longint matind array 0 5 of Longint matval array 0 5 of double lb array 0 1 of double ub array 0 1 of double Dynamic Link Library Solver User s Guide TObject Calling the Solver DLL from Delphi Pascal e 99 ctype array 0 1 of char stat Longint objval double x array 0 1 of double NullL Longint NullD Double lp Longint ret Longint end var Formi TForm1 implementation SR DFM SIFDEF WIN32 Define a callback function that displays the iteration number and current objective value function callback lpinfo Longint wherefrom Longint Longint stdcall var i
111. e Systems Inc P O Box 4288 Incline Village NV 89450 USA Tel 775 831 0300 Fax 775 831 0314 Email info frontsys com Example LP MIP problem in FORTRAN Build as QuickWin project contain ing files FLEXAMP FOR and FRONTMIP LIB the import library Use FORTRAN Powerstation 4 0 with WIN32 defined or FORTRAN 5 1 16 bit kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk G Cc Cc Cc Cc Cc Cc Cc C SIF DEFINED WIN32 C Define a callback function that displays the iteration number C and current objective value INTEGER 4 FUNCTION lpcallback STDCALL lp wherefrom INTEGER 4 lp VALUE wherefrom VALUE INCLUDE frontcbi for INTEGER 4 ret iter mip ret getcallbackinfo lp wherefrom CBINFO MIP ITERATIONS mip ret getcallbackinfo lp wherefrom CBINFO_ITCOUNT iter WRITE 10 mip iter 106 e Calling the Solver DLL from FORTRAN Dynamic Link Library Solver User s Guide 10 SENDIF C SB SENDIF FORMAT MIP subproblem I3 LP Iteration I3 lpcallback 0 END FUNCTION Define a callback function that computes the objective and constraint left hand sides for any supplied values of the variables INTEGER 4 FUNCTION funceval1l STDCALL lp numcols numrows objval lhs var varone vartwo INTEGER 4 lp VALUE numcols VALUE numrows VALUE REAL 8 objval REFERENCE REAL 8 lhs 0 1 var 0 1 INTEGER 4 varone VALUE vartwo VALUE objval var 0
112. e and Sparse Array Arguments In most large optimization problems the constraint coefficient matrix the Jacobian and in some quadratic problems the Q matrix are sparse meaning that most of the matrix elements are zero For example in many larger problems there are groups of constraints that are functions of a small subset of the variables but that do not depend on any of the other variables leading to many zero coefficients in the constraint matrix When these matrices are sparse it is more efficient to store and to process only the nonzero matrix elements A common way of doing this is to have auxiliary arrays that supply the row and column indices of the nonzero elements This means that no storage at all is needed for the zero elements which can include 90 to 95 of all elements in large sparse problems 26 e Designing Your Application Dynamic Link Library Solver User s Guide For further memory savings the nonzero elements can be ordered by column i e by variable so that the column index need be stored only once for a set of consecutive nonzero elements Alternatively they could be ordered by row i e by constraint but the Solver DLL uses the column wise method of storage In the loadIp loadquad and loadnIp functions the Solver DLL allows you to pass the constraint matrix and the Q matrix if used in either dense or sparse form In dense form you supply a full size array of num
113. e as early as possible since its setting will eliminate many other possibilities which would otherwise have to be considered during the solution of each subproblem If this parameter is set to 0 the selection of integer variables to branch upon is guided by the order of the variables in the arrays defining your problem PARAM _IMPBND Setting this parameter to 1 activates the Bounds Improvement strategy for MIP problems in the Solver DLL Plus The Bounds Improvement strategy allows the Solver to tighten the bounds on variables which are not 0 1 or binary integer variables based on the values which have been derived for the binary variables before the problem is solved Tightening the bounds usually reduces the effort required by the Simplex or other Solver engine to find the optimal solution and it some cases it leads to an immediate determination that the subproblem is infeasible and need not be solved Double Parameters The following parameters have double values Parameters whose names begin with EP are used to set tolerances in the LP QP and MIP solution algorithms PARAM_TILIM PARAM_EPOPT PARAM_EPPIV PARAM_EPSOL PARAM_EPRHS PARAM_EPGAP PARAM_CUTLO PARAM_CUTHI PARAM_EPNEWT PARAM_EPCONV PARAM_MUTATE PARAM TILIM This is the maximum number of seconds that the Solver spend on the overall LP or MIP problem When this limit is exceeded the optimize routine will return and the solution routine s pstat argument will be set
114. e partial derivatives you can supply a second callback function jacobian which returns values for all elements of the objective gradient and constraint Jacobian matrix in one call The callback function is optional you can supply NULL instead of a function address but if it is present the Solver DLL will call it instead of making repeated calls to funceval to evaluate partial derivatives Writing a jacobian function can be difficult it is easy to make errors in computing the various partial derivatives To aid in debugging the Solver DLL has the ability to call your jacobian function and compute its own estimates of the partial derivatives by calling funceval It will compare the results and display error messages for mismatching partial derivatives To use this feature set the PARAM _DERIV parameter value to 3 see the chapter Solver API Reference The Evolutionary Solver engine which is used if any of your problem functions are nonsmooth or discontinuous as indicated by oadnItype does not make use of the jacobian function even if you supply it as an argument to JoadnIp Diagnosing Infeasible Problems When a call to optimize finds no feasible solution to your optimization problem the Solver DLL returns a status value indicating this result when you call solution This means that there is no combination of values for the variables that will satisfy all of the constraints and bounds on the var
115. e routine for both types of callbacks In the body of your callback routine you can obtain information about the progress of the optimization by calling getcallbackinfo with arguments specifying exactly the information you want You return a zero value to indicate that the optimization process should continue or a nonzero value to indicate that the optimization should be halted and the Solver DLL should return to its caller There is a typedef enum PSTAT in frontmip h which can be used to return values from your callback routine or to test the pstat values returned by solution PSTAT_ CONTINUE which equals 0 means continue the solution process PSTAT USER ABORT signals that the user wants to interrupt the solution process setipcallbackfunc INTARG setlpcallbackfunc lp callback 132 e Solver API Reference Dynamic Link Library Solver User s Guide callback HPROBLEM lp _CCPROC callback Your program should call this function prior to calling optimize or mipoptimize to specify the callback function which the Solver DLL should call on each pivot or Simplex iteration The address of a user written callback routine i e a procedure pointer declared as shown above To eliminate use of the callback function pass an argument value of NULL to setlpcallbackfunc getlpcallbackfunc callback_p void getlpcallbackfunc lp callback_p HPROBLEM lp _CCPROC callback_p The address of a procedure pointer variable
116. e sess covnesdceyaseccetahascasuedinees E S E anise 141 GetlitParanmis 2 s i cu RR eens nih hae ee MR ea nie ee BR eee eka 141 infointparaini sei hk A Ros RAR Sh eee ROR A 141 setdbl param lt iicivecci fesse eeveiceces ces elec i a E E E E a a 142 peAa raho iar Eana a VAAS ENEE EE E T 143 INPOU IP aT ater 225 Ia E AEE EA A EE E E TT 143 setdefa lts enrere a E aad saa E E A we A A a 144 Dynamic Link Library Solver User s Guide Contents e iii Introduction The Solver Dynamic Link Libraries The Small Scale Welcome to Frontline Systems Small Scale Solver Dynamic Link Library DLL The Solver DLL provides the tools you need to solve linear quadratic nonlinear and nonsmooth optimization problems and mixed integer problems of varying size It can be called from a program you write in any programming language macro language or scripting language for Microsoft Windows that is capable of calling a DLL Some of the possibilities that will be covered in this User Guide are Microsoft Visual C Visual Basic Delphi Pascal and Fortran Powerstation There are many others including Visual Basic Application Edition in each of the Microsoft Office applications Frontline offers two Solver DLL product lines with compatible calling conventions the Small Scale Solver DLL which handles smaller dense matrix problems and the Large Scale Solver DLL which handles larger sparse matrix problems The Small Scale Solver DLL handle
117. e still specified with the obj argument of loadlp They are analogous to the matxxx arguments of oadlp however both the row and column indices refer to decision variables which are multiplied together and by the coefficient then summed to form the objective You may pass NULL values for gmatbeg qmatcnt and gmatind if your gmatval array is a full size dense matrix i e consisting of numcols numcols elements which is often the case for quadratic problems In this case the elements for each matrix column should be consecutive If gmatbeg qmatcnt and qmatind are not NULL values the array gmatval contains the nonzero coefficients grouped by column i e all coefficients for the same variable are consecutive gmatbeg i contains the index in gmatval of the first coefficient for column i gmatcnt i contains the number of coefficients in column i Note that the indices in gmatbeg must be in ascending order Each entry gmatind i is the row number of the corresponding coefficient in gmatval i The entries in gmatind are not required to be in ascending row order The coefficient M i j in the Q matrix if it is nonzero would be stored in gmatval qmatbeg j k where k is between 0 and qmatcnt j 1 inclusive and the corresponding entry gmatind qmatbeg j k i the row index This argument should be equal to the number of elements in the arrays gmatind and qmatval IF PARAM_ ARRAY is 1 the actual sizes of the arrays are checked
118. e the mean of each constraint s values in the final population of candidate solutions will be returned An array of dimension endidx begidx 1 where the standard deviation of each constraint s values in the final population of candidate solutions will be returned An array of dimension endidx begidx 1 where the minimum of each constraint s values in the final population of candidate solutions will be returned An array of dimension endidx begidx 1 where the maximum of each constraint s values in the final population of candidate solutions will be returned Diagnostic Routines findiis The following Solver DLL routines may be called to diagnose a problem when the linear quadratic or nonlinear Solver engine has reported that no feasible solution could be found to validate that your calls to loadlp loadquad and or loadctype have programmatically defined the problem as you intended or to read in a problem previously saved to disk or generated by another program You may call findiis or for linear and quadratic problems iiswrite at any time after solution has reported that a problem is infeasible and before you ve called unloadprob These routines compute an Irreducibly Infeasible Subset IIS of the constraints such that your problem with just those constraints is still infeasible but if any one constraint is dropped from the subset the problem becomes feasible Call getiis to programmatically
119. e the program that calls the Solver DLL routines you will reference the appropriate header file frontmip h frontmip bas safrontmip bas frontmip pas or frontmip for e If you are using load time dynamic linking when you link the program that calls the Solver DLL routines you will use the import library frontmip 1ib If you are using run time dynamic linking the import library is not used Note that Visual Basic and Delphi Pascal use run time dynamic linking e When you execute the program that calls the Solver DLL routines you will reference the dynamic link library file frontmip d11 No other files are needed at execution time Licensing the Solver DLL Please bear in mind that in order to lawfully distribute copies of the Solver DLL within your organization or to external customers or to lawfully use the Solver DLL in a server based application that serves multiple users you will need an appropriate license from Frontline Systems Licenses to use and or distribute the Solver DLL in conjunction with your application are available at substantial discounts that increase with volume As discussed in the Introduction you have the option of choosing either user based seat based or use based licensing Please contact Frontline Systems for licensing and pricing information The copy of the Solver DLL that you license either for development purposes or for distribution is customized for use by your application program s
120. ecial case of a clique or Special Ordered Set SOS constraint the Solver recognizes these constraints in their most general form PARAM OPTFIX Setting this parameter to 1 activates the Optimality Fixing strategy for MIP problems in the Solver DLL Plus The Optimality Fixing strategy is another way to fix the values of binary integer variables before the subproblem is solved based on the signs of the coefficients of these variables in the objective and the constraints Optimality Fixing can lead to further opportunities for Probing and Bounds Improvement and vice versa PARAM REORDR Setting this parameter to 1 activates the Variable Reordering strategy for MIP problems in the Solver DLL Plus The Variable Reordering strategy attempts to improve the order in which the Branch amp Bound algorithm chooses integer variables 138 e Solver API Reference Dynamic Link Library Solver User s Guide to branch upon based on the relative magnitudes of their coefficients in the objective and constraints The goal is to choose integer variables to branch upon which have a large impact on the values which may be assumed by other variables in the problem For example you might have a binary integer variable which indicates whether or not a new plant will be built and other variables which then determine whether certain manufacturing lines will be started up You would like the Solver to branch upon the plant building variabl
121. eclare huge pointers For example imagine that the following C code appears in a Solver DLL routine where numcols 10000 and x is an array of double for i 0 i lt numcols i x i 0 0 Since a double value requires 8 bytes the array x occupies 80 000 bytes In the for loop the address of the ith element of x is determined by adding 8 i to the base address of x Even if the array x is located at the very beginning of a 64K segment when i reaches 8192 the address will overflow the segment boundary The C C compiler will provide for this situation if the base address of x is a huge pointer at the expense of extra space and time for code to handle the overflow situation In frontmip h the two arguments matind and matval representing the nonzero coefficients of the LP matrix are prototyped as HPINTARG and HPREALARG respectively Similar comments apply to the arguments gmatind and qmatval for quadratic problems In 16 bit Windows these typedefs represent huge pointers Hence these arrays can specify as many nonzeroes as desired For efficiency other arguments such as obj and rhs are prototyped as far pointers since the maximum size of a far data object is 64K bytes and a double value requires 8 bytes you must use no more than 8192 variables and 8192 constraints with the 16 bit versions of the Large Scale LP MIP Solver DLL Default conversions are performed for huge pointer arguments just as they are for far point
122. econds specified by this parameter it will stop and return from the call to optimize with the best solution found so far An improved solution is a feasible solution where the relative improvement in the objective compared to the best solution found previously exceeds the PARAM_EPGAP setting Dynamic Link Library Solver User s Guide Solver API Reference e 137 Integer Parameters Mixed Integer Problems Symbolic Name Usage in Solver DLLs PARAM NDLIM 2017 limit on Branch amp Bound nodes explored PARAM MIPLIM 2015 limit on Branch amp Bound IP solutions found PARAM RELAX 2501 Solve relaxation 0 normal problem 1 ignore integer variables PARAM_PREPRO PARAM_OPTFIX PARAM_REORDR PARAM_IMPBND PARAM NDLIM This is the maximum number of nodes or LP subproblems that the Branch amp Bound algorithm will fathom on a MIP problem When this limit is exceeded the mipoptimize routine will return and the solution routine s pstat argument will be set to PSTAT_MIP_ NODE LIM FEAS or PSTAT_ MIP NODE LIM _INFEAS depending on whether a feasible integer solution has been found PARAM MIPLIM This is the maximum number of feasible integer solutions that the Branch amp Bound algorithm will find on a MIP problem When this limit is exceeded the mipoptimize routine will return and the solution routine s pstat argument will be set to PSTAT_MIP_SOL_LIM there is always a feasible integer solution at this point PARAM R
123. ed and eliminated Dynamic Link Library Solver User s Guide Solver API Reference e 123 pnumrows pnumcols getiis pstat rowind rowbdstat pnumrows colind colbdstat pnumcols swrite 124 e Solver API Reference from the IIS if possible If PARAM HSBND is 1 only the constraints will be considered for elimination from the IIS leaving all variable bounds in force On return the variable pointed to by pnumrows will contain the number of constraints rows in the IIS On return the variable pointed to by pnumcols will contain the number of variable bounds columns in the IIS To obtain details of the IS call the routine getiis The routine iiswrite calls findiis automatically if it has not already been called INTARG getiis lp pstat rowind rowbdstat pnumrows colind colbdstat pnumcols HPROBLEM lp LPINTARG pstat LPINTARG rowind rowbdstat pnumrows LPINTARG colind colbdstat pnumcols You may call this routine after calling findiis which returns the information you need to properly dimension the arrays rowind rowbdstat colind and colbdstat passed to getiis Getiis returns information about the specific constraints rows and variable bounds columns included in the IS On return the variable pointed to pstat will contain 1 if a complete IIS was found or 2 if the IIS finder stopped prior to completing the isolation of an IIS normally due to exceeding the time limit set by the PARAM_TI
124. ed by a call to unloadprob before the next call to JoadIp or loadnIp is encountered The multi threaded versions of the Solver DLL are fully reentrant They can solve multiple problems concurrently You may call JoadIp or loadnIp several times keeping track of the problem handles returned by each call and freely mix calls to any of the other Solver DLL routines passing the appropriate problem handle to each call You must still call unloadprob for each problem handle when you are finished with it to release memory The multi threaded versions may be used to solve decomposition problems which involve both a master problem and a slave problem or any recursive problem where the computation of the objective or constraints for a main problem requires the solution of another optimization subproblem The multi threaded versions may also be used in Web server or Intranet applications where the application calling the Solver DLL consists of several threads of execution executing concurrently each thread dealing with a specific user session Use of the multi threaded versions is identical to use of the single threaded versions except that calls to Joadlp or loadnip that would return an error in the single threaded versions because a previous problem had not yet been unloaded will return a new valid problem handle without an error in the multi threaded versions Your application simply needs to keep track o
125. ed not be recomputed This is an aggressive strategy which should be used only when you know that the nonlinearly occurring variables will not appear to change linearly over the intervals around their starting values PARAM DERIV This parameter controls the method used by the Solver to compute approximate first partial derivatives 0 means that forward differencing will be used perturbing variable values in one direction from the current point 1 means that central differencing will be used perturbing variable values in two opposing directions from the current point Central differencing takes more computing time but can yield better results and fewer total iterations especially if the Solver s path to the solution lies close to one or more constraint boundaries 2 means that the jacobian function which must be supplied as an argument to loadnIp will be called to compute partial derivatives 3 may be used for debugging purposes It means that the Solver will compute partial derivatives via forward differencing then call the jacobian function and compare the results If the derivatives do not match within a small tolerance the Solver will stop and return PSTAT_ FLOAT _ ERROR however if PARAM ARGCK is 1 the Solver will display Windows MessageBoxes reporting each mismatching derivative and will return PSTAT FLOAT ERROR only if you click Cancel in a MessageBox PARAM ESTIM This parameter controls the method used to esti
126. eeeenes 51 Solving Multiple Problems Concurrently cccccccceesessseeseeeseeseceeeceseenseeseeeseenseenaes 52 Special Considerations for Windows 3 x 53 Far and Huge P Ointers ys vei csesstecesnccansesiaseneg ish piadsmasateee e a E Ea E E S dees 53 Far 0 068 6 ger ge ee 53 Huge Pointers eeen cecces ni i Re ER E ERR RE O E SE ete eo 54 Callback FNO a ea a T E a oad A 54 MakeProclistane nose aene se AE A EE eo Nee SER 55 Using Callback Functions s ict clei e a dela ie el ae 55 Non Preemptive Multitasking c ccceccceseceseceecseeeseesceceecseeesecseeeeeeseeeeeeeneeeereneees 56 Native Windows Applications 57 A Single Threaded Application sonsonen n a a a e a o aat 57 A Multi Threaded Application ccccccccesccssecsseesecsseceeeeseeeseeeseeseeseecseeenseceseeeseesaeeaecaeceeeneeenes 63 Calling the Solver DLL from Visual Basic 69 Basic Steps raiser ain koh wi bee abe oti Atl a ae 69 Passing Array Arguments lt cicciccccectse eciccesessteeegies E i EEEE E NE KE E S R EE 69 Building a 32 Bit Visual Basic Program sessesesssseesssreesssesersrsseesessteresseseeseeserstsseeresseseessee 70 Building a 16 Bit Visual Basic Program sesesssssseesssreeessesersreseesessteressesesteserstsseeresseseesse 72 Visual Basic Source Code Linear Quadratic Problems cccccccssccessceessecessceeseecsseceeseeeees 73 Visual Basic Source Code Nonlinear Nonsmooth Problems cccccccssccessseessee
127. em by calling unloadprob then calling load p with the same arguments including matval you supplied in your call to loadnip unloadprob INTARG unloadprob lp HPROBLEM 1p This routine erases the current problem from the Solver DLL s memory The argument p must be a pointer to the value returned by a previous call to oadIp or loadnip After this call the value of p is invalid and should no longer be used As noted above after calling un oadprob you may change or free the memory for the arguments passed to loadlp or loadnIp Note The single threaded version of the Solver DLL handles only one problem at a time Hence you may call loadlp or loadnIp for a second problem only after you have called unloadprob for the first problem The multi threaded version of the Solver DLL supports multiple concurrent or recursive calls to these routines Unloadprob returns 0 unless its Jp argument is invalid in which case it returns 1 Solution Routines The following Solver DLL routines are used to solve an optimization problem which has been previously defined by a call to either Joadlp or loadnip 118 e Solver API Reference Dynamic Link Library Solver User s Guide optimize mipoptimize solution You should call optimize to find the solution to a linear quadratic or nonlinear problem without integer variables i e one where you have not called Joadctype You should call mipoptimize if the pr
128. ems e Evolutionary Solver based on genetic algorithms for solving nonsmooth optimization problems e Memory efficient Branch amp Bound method for mixed integer problems e Preprocessing and Probing strategies for fast solution of zero one integer programming problems e Very fast on sparse LP models with fewer nonzero matrix coefficients e Automatic scaling degeneracy control and other features for robustness e Sensitivity analysis shadow prices and reduced costs for linear quadratic and nonlinear problems e Optional objective coefficient and constraint right hand side sensitivity range information for linear problems e Automatic diagnosis of infeasible linear and nonlinear problems computing an Irreducibly Infeasible Subset IIS of constraints Solver DLL Frontline s Large Scale Solver DLL is a state of the art implementation of linear programming LP and mixed integer programming MIP solution algorithms The 16 bit version of the Large Scale Solver DLL can handle problems of up to 8 192 decision variables and 8 192 constraints in addition to bounds on the variables The 32 bit version which can be called from a 32 bit application under Windows 95 98 or NT 2000 can handle problems of up to 16 384 variables and 16 384 constraints The Large Scale Solver DLL efficiently stores and processes LP models in sparse matrix form It uses modern matrix factorization methods to control numerical Dynamic Link Library
129. ence Dynamic Link Library Solver User s Guide setintparam whichparam newvalue getintparam whichparam value_p infointparam whichparam INTARG setintparam lp whichparam newvalue HPROBLEM lp INTARG whichparam INTARG newvalue This routine is called to set the current value of one of the integer parameters in a specified problem It returns 0 if successful 1 if whichparam isn t one of the valid codes for integer parameters or 2 if newvalue is outside the range of valid values for the chosen parameter One of the symbolic names or codes for integer parameters PARAM ARGCK PARAM ARRAY PARAM USERP PARAM _IISBND PARAM _ITLIM PARAM _NDLIM PARAM MIPLIM PARAM SAMPSZ PARAM NOIMP PARAM_SCAIND PARAM _CRAIND PARAM _LINVAR PARAM _DERIV PARAM _ESTIM PARAM DIREC PARAM RELAX PARAM PREPRO PARAM _OPTFIX PARAM REORDR PARAM _IMPBND PARAM REQBND The desired new value for the chosen parameter INTARG getintparam lp whichparam value_p HPROBLEM lp INTARG whichparam LPINTARG value_p This routine is called to get the current value of one of the integer parameters in a specified problem It returns 0 if successful or 1 if whichparam isn t one of the valid codes for integer parameters One of the symbolic names or codes for integer parameters PARAM ARGCK PARAM ARRAY PARAM USERP PARAM _IISBND PARAM _ITLIM PARAM _NDLIM PARAM MIPLIM PARAM SAMPSZ PARAM NOIMP PARAM_SCAIND PARAM _CRAIND PARAM _
130. er DLL routines passing the appropriate problem handle as an argument In a multi threaded application you can call loadlp or loadnIp as required in each thread you need only keep track of the returned problem handles in variables that are local to each thread In any case you must end each problem with a call to unloadprob to free memory Multi threaded versions of the Solver DLL can also solve problems recursively where an optimization subproblem must be solved in order to compute the objective and or constraints for a larger problem In this scenario you would call oadlp or loadnlp optimize or mipoptimize and unloadprob passing the new problem handle as an argument from within your own funceval or other callback routine One sequence of calls that is illegal in every version of the Solver DLL is a call to optimize or mipoptimize for a given problem then a second call to optimize or mipoptimize for that same problem made before the first call returns e g made from within your funceval or other callback routine Such a second call will return l and if PARAM _ARGCK is 1 an error message will appear the status value returned by a subsequent call to solution will be PSTAT_ ENTRY ERROR 52 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide Special Considerations for Windows 3 x Programming for 32 bit systems such as Windows 95 98 and Windows NT 2000 is simpler than prog
131. er Guide for details matbeg 0 0 matbeg 1 3 matcnt 0 3 matecnt 1 3 matind 0 0 matind 1 1 matind 2 2 matind 3 0 matind 4 1 matind 5 2 matval 0 9 matval 1 6 matval 2 5 matval 3 6 matval 4 7 matval 5 10 bounds on variables 1b 0 0 lb 1 0 ub 0 INFBOUND ub 1 INFBOUND integer variables ctype 0 I ctype 1 I to pass a NULL or empty array NullL 1 NullD 1 setintparam NullL PARAM ARGCK 1 lp loadlp PROBNAME 2 3 1 obj 0 rhs 0 sense matbeg 0 matent 0 matind 0 matval 0 1lb 0 ub 0 NullD 2 3 6 if lp 0 then Exit ret loadctype lp ctype ret lpwrite lp psexamp SIFDEF WIN32 setlpcallbackfunc lp callback SENDIF ret optimize lp ret solution lp stat objval x 0 NullD NullD NullD str objval 4 4 objtext LPEditl text Status inttostr stat Objective objtext str x 0 4 4 x0 str x 1 4 4 x1 LPEdit2 text xl x0 x2 x1 end Define and solve the example NLP problem This works only in 32 bit Delphi 2 0 or above procedure TForml NLPButtonClick Sender TObject var objtext string x0 string x1l string begin right hand sides of constraints rhs 0 1 rhs 1 0 sense of constraints E is G is gt Dynamic Link Library Solver User s G
132. ers so you can for example declare double arrays for matind and matval and use them without any special casting as arguments to JoadIp Callback Functions The Joadnip routine and the setlpcallbackfunc and setmipcallbackfunc routines take arguments which are the addresses of callback functions Using these callbacks you can more closely control the optimization process and create user responsive native Windows applications In the example program vcexamp1 c a callback function is used only when a 32 bit version of the program is compiled This was done for simplicity to avoid the complications discussed in this chapter In the first example program shown in the next chapter Native Windows Applications we will create a very simple LP pivot callback procedure and pass its address as an argument to setlpcallbackfunc To make this program work in 16 bit Windows 3 x as well as in 32 bit Windows 95 98 and NT 2000 we must deal with the issues described in this section 54 e Special Considerations for Windows 3 x Dynamic Link Library Solver User s Guide MakeProclinstance Windows allows more than one instance of your application to be run at the same time Each instance executes the same compiled code but maintains its data in a different data segment Windows supplies the address of the proper instance data segment in the Data Segment or DS register when it starts up your program As you call different pro
133. erties Formi x M Project Formi Code jor x Form1 Form z Generany x Oectarations x Alphabetic categorized p EN Formi Prtion Explicit 1 3D False Private Sub Command1_Click o sHso00000F Example 1 Solves the LP model 3 s 2 Sizable Maximize 2 x1 3 x2 Subj to 9 x1 6 x2 lt 54 Exi t Txa lt 42 5 x1 10 x2 lt 50 tue 1 2 13 Copy Pen xi x non negative 0 Solid a LP solution x1 2 8 x2 3 6 Objective 16 4 Frontline Systen True Returns the name used in code to This example shows the simple form of passing arguments to loadlp identify an object 4 dense full size N by M matrix is passed as the matval argument and NULL pointers are passed as the matbeg matcnt amp matind arguments Form Layout This example also shows how to obtain LP sensitivity analysis info by calling the objsa and rhssa functions These calls are valid fw WZ WES soam stat O oa A Fush 5 Project Microsoft v 3 To test run the program within the Visual Basic programming system select Run Start and then click on one of the buttons labeled Example 1 through Example 5 This will display a form with comments output fields and Solve and Exit buttons If you click the button Example 1 and then click Solve for example the output fields will appear filled with values as shown on the following page 4 Example 2 uses the pwrite function to
134. ets gqmatval 0 0 000204 qmatval 1 0 000424 qmatval 2 0 00017 qmatval 3 0 000448 qmatval 4 0 000014 qmatval 5 0 000424 qmatval 6 0 012329 qmatval 7 0 001785 qmatval 8 0 001633 qmatval 9 0 000539 qmatval 10 0 00017 qmatval 11 0 001785 qmatval 12 0 000365 qmatval 13 0 000425 qmatval 14 0 000075 qmatval 15 0 000448 qmatval 16 0 001633 qmatval 17 0 000425 qmatval 18 0 005141 qmatval 19 0 000237 qmatval 20 0 000014 qmatval 21 0 000539 qmatval 22 0 000075 qmatval 23 0 000237 qmatval 24 0 000509 ReDim x 0 To 4 As Double AdjustFormforExample4 Form2 Show End Sub Private Sub Command5 Click End End Sub Private Sub Command6 Click Here we use the lpread function to read in the model arrays are checked for validity ReDim obj 0 To 1 As Double ReDim rhs 0 To 2 As Double ReDim sense 0 To 2 As Byte ReDim ctype 0 To 1 As Byte ReDim matbeg 0 To 1 As Long ReDim matcnt 0 To 1 As Long ReDim matind 0 To 5 As Long ReDim matval 0 To 5 As Double ReDim 1b 0 To 1 As Double ReDim ub 0 To 1 As Double ReDim x 0 To 1 As Double AdjustFormforExample5 Form2 Show First we assume that the dimensions of the problem are known We call loadlp passing array arguments of the proper dimension Since the sense and ctype we initialize them 78 e Calling the Solver DLL from Visual Basic Dynamic Link Library S
135. f each problem handle for example by saving it in local variable storage that is unique to each thread of your program Use Based Licensing The Solver DLL can be licensed for distribution to multiple users with your application or for use on a server where the application serves multiple users Licensing for a server based application is usually based on the number of users or seats However if this number is difficult to determine or if it may be very large as in a Web server application licensing may be based on the number of uses of the DLL To support this latter form of licensing the Solver DLL can track and report the number of calls your application makes to the oadIp loadnIp routines and or the optimize mipoptimize routines Use tracking and reporting is under the control of your application You determine the type of tracking and reporting with a call such as ret setintparam NULL PARAM USERP 1 If the PARAM _USERP parameter is set to 0 the default setting the Solver DLL does not track uses it operates in Evaluation Test mode where it displays a MessageBox on the system console once every ten minutes If PARAM USERP is 1 the Solver DLL does track uses the first time it runs in a new calendar month it automatically sends a report of cumulative uses to date via email to Frontline Systems If PARAM _USERP is 2 the Solver DLL tracks uses but it does not generate any reports automatic
136. ficient bound or integer variable information If Ip is non NULL pread will scan the file return values for the other arguments mentioned above and fill in values for all of the arguments previously passed to loadlp loadquad and or loadctype when the problem was defined except for matbeg and matcnt if used and gmatbeg and qmatcnt if used It is your responsibility to ensure that the arrays previously passed to these routines are of the correct dimensions for the problem being read The name or complete path of the input text file On return the variable pointed to by objsen_p will contain the sense of the optimization problem 1 for minimize 1 for maximize as used by loadip You may pass a NULL value for this argument if you don t need this information On return the variable pointed to by numcols_p will contain the number of columns variables in the problem defined by the input file the variable pointed to by numrows_p will contain the number of rows constraints in the problem and the variable pointed to by numints_p will contain the number of integer variables in the problem You may pass NULL values for any of these arguments if you don t need the corresponding information If used this argument must be an integer array of dimension at least equal to the number of columns variables in the problem On return each element of the array will contain the number of nonzero coefficients of the
137. for testvals the test values are drawn from this array An array of dimension numtests numcols containing test values for the variables to be used in validating the gradient and Jacobian determined by testnltype as described above If you supply a NULL value the Solver DLL will choose test values at random between the bounds you supply in the b and ub arrays A pointer to a long integer indicating whether the entire problem was diagnosed as nonlinear or linear pstat 1 Problem was diagnosed as smooth nonlinear pstat 0 Problem was diagnosed as linear pstat 1 Diagnosis aborted because your funceval routine returned 1 failure If pstat returns 1 at least one of the elements of either objtype or matvaltype will be N if pstat returns 0 all elements of both arrays will be L An array of dimension numcols which testnitype will fill in to indicate whether the variables occur linearly or nonlinearly in the objective function objtype i L Variable occurs linearly or not at all in the objective objtype i N Variable occurs nonlinearly in the objective Dynamic Link Library Solver User s Guide Solver API Reference e 117 matvaltype An array of dimension nzspace which testnitype will fill in to indicate whether the variables occur linearly or nonlinearly in the constraint functions matvaltype i L Matvalf i represents a linear occurrence of a variable matvaltype i N Matval i represents a
138. funceval routine to evaluate the problem functions The second example is identical to the first one except that a jacobian routine is also defined to give the Solver faster and more accurate partial derivatives of the problem functions The third example attempts to solve a nonlinear problem that is infeasible then it uses the IIS finder to diagnose the infeasibility The fourth example illustrates how you can solve a series of linear and nonlinear problems using the testnitype function to determine whether the problem defined by your funceval routine is linear and how you can switch to the LP Solver engine if testnltype finds that a problem is entirely linear Also included in vcexamp2 c are two example problems using the Evolutionary Solver The first of these finds the global optimum of a classic two variable problem the Branin function which has three local optima The second one finds the optimal solution of a three variable problem where the objective function involves an IF statement which is nonsmooth in fact discontinuous in the variable X You are encouraged to study this source code or the Visual Basic source code and the comments in each problem even if you plan to use a language other than C C for most of your work Like the example source code for linear and quadratic problems this example file is more extensive than the ones for the other languages kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
139. function as an argument to JoadnIp Dynamic Link Library Solver User s Guide Solver API Reference e 109 110 e Solver API Reference A typical program to solve a nonlinear or nonsmooth optimization problem consists of the following calls funceval Receive values for the variables compute values for the constraints and the objective function main Get data and set up an LP problem loadnip funceval Load the problem optimize Solve it solution Get the solution unloadprob Free memory For more information consult the chapter Designing Your Application Argument Types In the Solver DLL all integer arguments including array arguments such as matbeg matcnt and matind are defined as Long or 32 bit integers In Visual Basic variables of this type must be declared as Long rather than Integer The corresponding type in Delphi Pascal is Longint and in FORTRAN it is INTEGER 4 In C C type int is the same as type Long in 32 bit compilers but we recommend that such variables be declared as long The sense argument of loadlp and loadnIp the ctype argument of loadctype and the objtype and matvaltype arguments of loadnitype and testnitype are defined as arrays of unsigned characters Visual Basic Version 4 0 and above treats these arguments as arrays of type Byte whereas it treats ordinary signed character array argu
140. g return msg wParam BOOL InitApplication WNDCLASS wc we style 0 we lpfnWndProc MainWndProc we cbClsExtra 0 wc cbWndExtra 0 wce hInstance hiInstance we hIcon LoadIcon NULL wce hCursor LoadCursor NULL we hbrBackground wc lpszMenuName NULL wc lpszClassName szClassName return RegisterClass amp wc BOOL InitInstance HINSTANCE hInstance long nX long nY hinst hiInstance hWnd CreateWindow szClassName szWinTitle WS _OVERLAPPEDWINDOW nX nY nWidth nHeight NULL NULL hInstance NULL if hWnd return FALSE ShowWindow hWnd SW SHOW UpdateWindow hWnd return TRUE ifdef WIN32 DWORD WINAPI RunThread LPVOID lpVoid long nWidth hInstance amp hWnd2 szWinTitle2 330 10 300 300 LPVOID hWnd1 LPVOID hWnd2 O O amp dwID1 amp dwID1 HINSTANCE hInstance IDI_ APPLICATION IDC_ ARROW GetStockObject WHITE BRUSH HWND hWnd char szWinTitle long nHeight HWND hWnd HWND 1pVoid int i Cause Solver DLL to be called 9 more times for each window for i 1 i lt 10 i Sleep rand 1000 RAND MAX wait random time 0 1 sec InvalidateRect hWnd NULL TRUE cause WM PAINT for window UpdateWindow hWnd Dynamic Link Library Solver User s Guide Native Windows Applications e 65 return 0 endif LRESULT CALLBACK MainWndProc HWND hWnd U
141. g which requires that each running application periodically yield control to Windows which then allows another application to run The Solver DLL takes care of this for you In addition to calling your callback functions if specified the Solver DLL will periodically call the Windows API function PeekMessage in order to yield control to Windows These calls are more frequent than calls to the callback functions since in a large problem a single LP pivot or Simplex iteration can take several seconds 56 e Special Considerations for Windows 3 x Dynamic Link Library Solver User s Guide Native Windows Applications The programs winexamp1 c and winexamp2 c are native Windows applications that call Windows API functions to create a window and write the results of calling the Solver DLL into it To compile and link these programs follow the steps in the chapter Calling the Solver DLL from C C but substitute the file winexamp1 c or winexamp2 c for vcexamp1 c and select a project type of Win32 Application in Visual C 6 x or Windows Application EXE in Visual C 1 5x The multi threaded behavior of winexamp2 c can be seen only on Win32 systems A Single Threaded Application The source file winexamp1 c found in the Examples Vcexamp subdirectory begins with some includes and prototypes followed by the WinMain InitApplication and JnitInstance procedures common to almost all Windows applications In
142. ge Dynamic Link Library Solver User s Guide Solver API Reference e 143 setdefaults 144 e Solver API Reference Symbolic Name PARAM _TILIM 655350 00 65535 0 L0E4 L0E4 L0E4 L0E4 paramercar oo oo w PARAM CUTLO 2 0E 30 2 0E 30 2 0E 30 PARAM CUTHI 2 0E 30 2 0E 30 2 0E 30 PARAM EPNEWT 1 0E 6 1 0E 9 1 0E 4 PARAM _EPCONV 1 0E 4 oo 1 0 param mutate oos oo 1o INTARG setdefaults lp HPROBLEM lp This routine is called to set each of the integer and double parameters for a specified problem to their default values as shown in the tables above for infointparam and infodblparam The return value is always 0 Dynamic Link Library Solver User s Guide
143. ge i e the filename argument is NULL this is the password of the email account used to send the message If this argument is NULL or an empty string reportuse uses the MAPI shared session to send the email message INTARG getproblimits lp type pnumcols pnumrows pnumints HPROBLEM lp INTARG type LPINTARG pnumcols pnumrows pnumints This function allows you to determine the capabilities of the Solver DLL version you are using at runtime The Solver DLL V3 5 can be configured to include or exclude the nonlinear GRG and Evolutionary Solver engines the linear Solver engine or the quadratic Solver engine and the maximum number of decision variables columns and constraints rows supported by each engine can also be configured Getproblimits returns information about these characteristics of the Solver DLL The p argument is ignored and may be NULL This should be one of the following integer codes the corresponding symbolic names are defined by the PROBTYPE enum in the header file FRONTMIP H type 0 PROB LP Linear Simplex Solver type 4 PROB_ QP Quadratic extension to Simplex Solver type 12 PROB_ NLP Nonlinear GRG Solver type 20 PROB_NSP Nonsmooth Evolutionary Solver The mixed integer variants of these codes return the same results as their corresponding codes listed here Dynamic Link Library Solver User s Guide Solver API Reference e 129 pnumcols pnumrows pnu
144. h setintparam lp PARAM NOIMP 1 1 second setlpcallbackfunc lp 0 optimize lp solution lp stat objval x2 NullD NullD NullD Form2 Text3 Status amp stat Form2 Text4 Objective amp objval Form2 Textl X amp x2 0 Form2 Text2 Y amp x2 1 Form2 Text5 Z amp x2 1 call unloadprob to release memory unloadprob lp End Select End Sub Private Sub Command2_Click Unload Form2 End Sub Private Sub Form Activate Form2 Command1 SetFocus End Sub Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 93 Limitations of 16 Bit Visual Basic Visual Basic 4 0 is the last version of Visual Basic offered in a 16 bit version newer versions of Visual Basic support only 32 bit applications and operating systems such as Windows 95 98 and Windows NT 2000 Support for 16 bit applications in the Solver DLL will be limited in the future If you need to build applications for older 16 bit operating systems such as Windows 3 1 you will need to take into account the issues discussed in this section Callback Functions Because Visual Basic 4 0 does not support the AddressOf operator you cannot write callback functions in this version of Visual Basic and pass their addresses to the Solver DLL routines JoadnIp setlpcallbackfunc and setmipcallbackfunc You can however write your callback functions in C C and use a few more lines of C C code to pass t
145. has been found An array of dimension equal to the number of columns variables in which the dual values reduced costs of the variables will be stored The dj values are available only if an optimal solution to an LP or QP problem has been found Dynamic Link Library Solver User s Guide objsa begidx endidx lower upper rhssa begidx endidx lower upper INTARG objsa lp begidx endidx lower upper HPROBLEM lp INTARG begidx endidx LPREALARG lower upper This routine need be called only if sensitivity ranges for the objective function coefficients are desired The argument p of objsa must be the value returned by a previous call to JoadIp The arguments begidx and endidx are used to limit the set of columns variables for which the range information is computed Since range information is not meaningful for NSP NLP QP and MIP problems objsa should not be called for them objsa returns 0 unless there is an error in its arguments in which case it returns an integer value indicating the ordinal position of the first argument found to be in error The first column number index as in loadlp arguments for which sensitivity range information should be returned The last column number index as in oadlp arguments for which sensitivity range information should be returned An array of dimension endidx begidx 1 where the objective function coefficient lower range values will be returned An array of
146. he GRG Solver is guaranteed only to find a locally optimal solution but it may miss a better solution far from the starting point you provide The Evolutionary Solver has a much better chance of finding the globally optimal solution in such problems Multi Threaded Applications Version 3 5 of the Solver DLL is offered in both single threaded and multi threaded versions The single threaded versions like all earlier versions of the Solver DLL are serially reusable but not reentrant They can solve multiple problems serially but not concurrently nor can they solve problems recursively for example where computation of the objective or constraints for one optimization problem involves solution of another optimization subproblem The multi threaded versions of the Solver DLL V3 5 are fully reentrant They can solve multiple problems concurrently and or recursively They are especially suitable for Web server or Intranet based applications which may be accessed by many users at unpredictable moments which may overlap in time Use Based Licensing With the ability to solve multiple problems concurrently the Solver DLL Version 3 5 is being deployed in Web server and similar applications where the number of users is unknown in advance or may become very large In such cases the normal user based or seat based licensing for multiple copies of the Solver DLL may not be appropriate To meet this requirement Frontline Systems has develo
147. he number of variables See documentation for details In this case 2 constraints x 2 variables 4 Dim 1b 0 To 1 As Double Dim 1b 0 To number_of_variables 1 Dim ub 0 To 1 As Double Dim 1b 0 To number_of_variables 1 Dim rngval 0 To 1 As Double Dim rngval 0 To number constraints 1 Note that rngval can only be used Dynamic Link Library Solver User s Guide with the Large Scale DLL Calling the Solver DLL from Visual Basic e 87 Dim ctype 0 To 1 As Byte Dim ctype 0 To number of variables 1 Dim stat As Long objval As Double Dim x 0 To 1 As Double Dim x 0 To number_of variables 1 Dim piout 0 To 1 As Double Dim piout 0 To number_of constraints 1 Dim slack 0 To 1 As Double Dim slack 0 To number_of constraints 1 Dim dj 0 To 1 As Double Dim dj 0 To number of variables 1 Dim varlow 0 To 1 As Double varupp 0 To 1 As Double Dim varlow and varupp 0 to number of variables 1 Dim conlow 0 To 1 As Double conupp 0 To 1 As Double Dim conlow and conupp 0 to number of constraints 1 Dim objtype 0 To 1 As Byte matvaltype 0 To 3 As Byte Dim objtype 0 to number of variables 1 Dim matvaltype same as matval Dim iisrows As Long iiscols As Long Dim rowbdstat As Long colbdstat As Long Dim rowind As Long colind As Long Dim lp As Long Dim ret As Long Dim nlstat As Long set up the LP problem use Safearrays setintparam 0 PARAM ARRAY 1 Note that i
148. her regions of the search space where a better solution may later be found The use of a population of solutions helps the evolutionary algorithm avoid becoming trapped at a local optimum when an even better optimum may be found outside the vicinity of the current solution Third inspired by the role of mutation of an organism s DNA in natural evolution an evolutionary algorithm periodically makes random changes or mutations in one or more members of the current population yielding a new candidate solution which may be better or worse than existing population members There are many possible ways to perform a mutation and the Evolutionary Solver actually employs three Dynamic Link Library Solver User s Guide Designing Your Application e 21 different mutation strategies The result of a mutation may be an infeasible solution and the Evolutionary Solver attempts to repair such a solution to make it feasible this is sometimes but not always successful Fourth inspired by the role of sexual reproduction in the evolution of living things an evolutionary algorithm attempts to combine elements of existing solutions in order to create a new solution with some of the features of each parent The elements e g decision variable values of existing solutions are combined in a crossover operation inspired by the crossover of DNA strands that occurs in reproduction of biological organisms As with mutation
149. hese function addresses to the Solver DLL routines Then your main program can still be written in Visual Basic and the Solver DLL will call your C C callback functions at the appropriate times These callback functions would be written independently of the rest of your Visual Basic program but could display a message or dialog box using direct calls to the Windows API You should not use the header file safrontmip bas with Visual Basic 4 0 Because of the different representation of SAFEARRAYs in 16 bits Visual Basic 4 0 will not accept array names passed as arguments to the Solver DLL routines Instead use frontmip bas and pass the first element of each array argument e g obj 0 to the Solver DLL routines Array Size Limitations The 16 bit version of Visual Basic has limitations on the size of data objects it can handle In particular the maximum array subscript value is 32 767 Although this is larger than any array you might use with the Small Scale Solver DLL in exceptional cases it can be a limiting factor when using the Large Scale Solver DLL For example if you were trying to solve a problem with 8 192 decision variables and 8 192 constraints you might have more than 32 767 nonzero coefficients in the LP matrix depending on the sparsity of the problem but you could not construct the matind and matval arrays that you would need in 16 bit Visual Basic The most straightforward solution is of course to use the 32 bit ver
150. iables at the same time If your model correctly describes the real world problem it may be that no solution is possible unless you can find a way to relax some of the constraints But more often this result means that you made a mistake in specifying some constraint s such as indicating G for gt when you meant to use L for lt If you have many constraints it can be difficult to determine which of them contains a mistake or conflicts with some other combination of constraints To aid you the Solver DLL includes a facility to find a subset of your constraints such that your problem with just those constraints is still infeasible but if any one constraint is dropped from the subset the problem becomes feasible Such a subset of constraints is called an Irreducibly Infeasible Set IIS of constraints 24 e Designing Your Application Dynamic Link Library Solver User s Guide Note Ifa call to mipoptimize finds no feasible solution your first step in diagnosing the problem should be to try to solve the relaxation of the MIP problem ignoring the integer restrictions on the variables You can do this by calling setintparam lp PARAM RELAX 1 before you call mipoptimize again If the relaxation of the original problem is still infeasible you can use the API calls described in this section to isolate the infeasibility To find an Irreducibly Infeasible Set of constraints call the routine findiis This rout
151. ich summarizes the LP MIP problem in algebraic form This can help us verify that the arguments we pass have defined the right problem 36 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide void example2 void double obj double rhs char sense LLL long matbeg long matcnt long matind double mated double lb 0 double ub e INFBOUND char ctype II long stat double objval double x 2 HPROBLEM lp NULL ol m m v N De _ oO o w D e NO e uo can o we I l mn Wo WwW Ow printf nExample MIP problem n enable display of error MessageBoxes on argument errors since the arguments are correct none will appear Note on argument errors loadlp returns a NULL pointer and all other routines return a non zero value you can and should check for this But the MessageBoxes can help you identify errors early setintparam lp PARAM ARGCK 1 set up the LP portion of the problem lp loadlp PROBNAME 2 3 1 obj rhs sense matbeg matcnt matind matval lb ub NULL 2 3 6 if lp return now define integer variables for each variable i ctype i is C for continuous I for general integer and B for a binary integer variable loadctype lp ctype lpwrite can be called anytime after the problem is defined and before unloadprob is called It will write out the following text in file
152. ine returns the number of rows constraints and the number of columns variable bounds contained in the IIS these numbers should always be less than or equal to the total number of constraints and bounds in your problem In many cases there will be only a few constraints in the IIS and by inspecting your code which sets up these constraints you can often quickly identify the source of the infeasibility To obtain the IIS itself call the routine getiis This routine returns the indices of the constraints and the indices of the variable bounds that are included in the IIS If you have both lower and upper bounds on the same variable s getiis tells you which bound is contributing to the infeasibility If your problem is a linear or quadratic programming problem i e if you are calling loadIp there is an even more convenient way to obtain the IIS Call the routine iiswrite This routine calls findiis for you if it has not already been called and then writes out a text file in the same algebraic format used by pwrite but containing only the constraints and bounds that are included in the US When you use iiswrite you don t have to write any code to analyze or display the information returned by getiis In general when a model is infeasible there can be more than one subset of constraints possibly many subsets that qualify as an IIS Some of these will contain fewer constraints than others making them easier to
153. ing may be used to tell the Solver to stop if the best solution so far is close enough The Solver computes the absolute value of the difference between the objective value for the best integer solution so far the incumbent and the best bound on the objective value found so far by the Branch amp Bound process divided by the best bound s objective value If this relative difference is less than the integer gap toler ance the Solver stops and returns the incumbent as the solution Initially the objective value of the LP relaxation of the problem ignoring the integer constraints serves as the best bound since the all integer solution can be no better than this During the Branch amp Bound process the best bound is updated based on the subproblems that have already been explored By default the integer gap tolerance is zero which means that the Solver will continue searching until all alternatives have been explored and the optimal integer solution has been found You can often save significant solution time by setting an integer gap tolerance greater than zero which is sufficient for your application PARAM CUTLO This is the integer objective cutoff value for MIP maximization problems In the Branch amp Bound algorithm any subproblem whose objective is less than this value will not be fathomed If you have an objective value for a known integer solution to this problem for example from a previous
154. ions Sum xi 1 and portfolio return Sum Ri xi gt 0 085 The efficient portfolio is the QP solution approx xl 0 462 x2 0 x3 0 313 x4 K5 0 225 The objective approx 0 00014 minimum variance Both the constraint matrix and the Q matrix are passed using the full set of arguments for sparse matrices Dim i As Long ReDim obj 0 To 4 As Double For i 0 To 4 obj i 0 Next ReDim rhs 0 To 1 As Double rhs 0 1 rhs 1 0 085 ReDim sense 0 To 1 As Byte sense 0 Asc E sense 1 Asc G ReDim matbeg 0 To 4 As Long ReDim matcnt 0 To 4 As Long ReDim matind 0 To 9 As Long ReDim 1b 0 To 4 As Double ReDim ub 0 To 4 As Double For i 0 To 4 matbeg i 2 i matent i 2 matind 2 i 0 matind 2 i 1 1 lb i 0 ub i 1 Next ReDim naval To 9 As Double matval 0 1 matval 1 0 086 matval 2 1 matval 3 0 071 matval 4 1 matval 5 0 095 matval 6 1 matval 7 0 107 matval 8 1 matval 9 0 069 ReDim qmatbeg 0 To 4 As Long ReDim qmatcnt 0 To 4 As Long ReDim qmatind 0 To 24 As Long For i 0 To 4 qmatbeg i 5 Fi qmatent i 5 qmatind i i Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 77 qmatind i 5 i qmatind i 10 i qmatind i 15 i qmatind i 20 i Next ReDim qmatval 0 To 24 As Double The Q matrix specifies the covariance between each pair of ass
155. is more extensive than the examples for the other languages and illustrates most of the features of the Solver DLL including the Quadratic Solver the Evolutionary Solver automatic diagnosis of infeasible problems and use of the pread and Ipwrite functions VBEXAMP1 BAS Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global Global The obj rhs sense ctype matbeg matent matind matval qmatbeg qmatecnt qmatind qmatval lb As Double ub As Double stat As Long objval As Double x As Double piout As Double slack As Double dj As Double varlow As Double varupp As Double conlow As Double conupp As Double lp As Long As Double As Double As Byte As Byte As Long As Long As Long As Double As Long As Long As Long As Double call to lpcallback in EXAMP1 with 16 bit Visual Basic 4 0 Function lpcallback ByVal lpinfo As Long Dim Dim Dim ret ret iters As Long obj As Double ret As Long getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT FRM is commented out for compatibility ByVal wherefrom As Long As Long iters getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ obj Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 73 MsgBox Iteration lpcallbac
156. is complete pivot returns PSTAT_USER_ ABORT to its caller the DLL which will result in a return to your main line code from optimize The return status code which may be either PSTAT_ ABORT _FEAS or PSTAT_ABORT_INFEAS depending on whether a feasible solution was found is passed back to the main line code in the pstat argument of solution Dynamic Link Library Solver User s Guide Native Windows Applications e 57 Since the example problems are solved in a small fraction of a second the winexamp program will normally run to completion displaying a window like the one shown below f FRONTMIP WinExamp OF x WinExamp MIP and NLP problems with callbacks MIP Problem Results LPstatus 101 Objective 16 0000 x1 2 0000 x2 4 0000 NLP Problem Results LPstatus 1 Objective 0 5000 x1 0 5000 x2 0 5000 The complete C source code of winexamp1 c is shown on the following pages For newly written application programs you will find it preferable to use a C class library such as MFC Microsoft Foundation Classes together with the wizards or experts included in your C C development system such as the AppWizard in Visual C to create the basic structure of your application program kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk kkkkkkkkkkkkkkkkkkkk Frontline Systems Small Scale Solver Dynamic Link Library Version 3 5 Frontline Systems Inc P O Box 4288 Incline Village NV 89450 USA Tel
157. k End Function Sub Adjust detail Sub omitted End Sub Adjust detail Sub omitted End Sub Adjust detail Sub omitted End Sub Adjust detail omit End Sub ted VBEXAMP1 FRM amp Trim Str iters PSTAT CONTINUE FormforExample2 FormforExample3 FormforExampled FormforExamples Private Sub Command1_Click Example 1 Solves the LP model Maximize 2 xl 3 x2 Subj to 9 x1 6 x2 lt 54 6 x1 7 x2 lt 42 r 5 x1 10 x2 lt 50 xl x2 non negative LP solution xl 2 8 x2 3 6 Objective 16 4 amp Obj amp Trim Str obj This example shows the simple form of passing arguments to loadlp A dense by calling the obj full size N by M and NULL pointers are passed as the matbeg only for LP problems and dj arguments of solution sensitivity analysis info is available none would be meaningful and rhssa For QP problems sa ReDim obj 0 To 1 As Double obj 0 2 obj 1 3 ReDim rhs 0 To 2 As Double rhs 0 54 rhs 1 42 rhs 2 50 ReDim sense 0 To 2 As Byte L s for lt E s for G s for gt sense 0 Asc L sense 1 Asc L sense 2 Asc L ReDim matval 0 To 5 As Double matval 0 9 matval 1 6 matval 2 5 matval 3 6 matval 4 7 matval 5 10 ReDim 1b 0 To 1 As Double 1b 0 0 74 e Calling the Solver DLL from
158. k Add Now select Insert Files into Project again In the dialog open the Files of type dropdown list and select Library Files lib Navigate to the Win32 subdirec tory that contains the 32 bit version of the import library frontmip lib Select frontmip lib and click Add 3 Check Build Settings Before compiling flexamp for you must ensure that the preprocessor symbol WIN32 is defined Select Build Settings click on the Fortran tab open the Category dropdown list and select Preprocessor The Predefined Preprocessor Variables edit box should contain the symbol WIN32 if not type WIN32 in this box and then click OK 4 Build and Run the Application To compile and link flexamp for and produce flexamp exe select Build Rebuild All Then select Build Execute flexamp exe to run the program An output window like the one on the next page should appear 104 e Calling the Solver DLL from FORTRAN Dynamic Link Library Solver User s Guide i flexamp Eifel File Edit View State Window Help Example LP MIP problem a MIP subproblem O LP Iteration MIP subproblem O LP Iteration MIP subproblem 2 LP Iteration MIP subproblem 3 LP Iteration MIP subproblem 3 LP Iteration LPstatus 101 Objective 16 xi 2 00 x2 4 00 Example NLP problem MIP subproblem O LP Iteration MIP subproblem O LP Iteration LPstatus 1 Objective 50 x2 50 Finished Building a 16 Bit FORTRAN Program A 16 bit version of the example Solver
159. kkkkkkkkkkkkkkkkkk kkkkkkxk Frontline Systems Small Scale Solver Dynamic Link Library Version 3 5 Frontline Systems Inc P O Box 4288 Incline Village NV 89450 USA Tel 775 831 0300 Fax 775 831 0314 Email info frontsys com Example NLP and NSP problems in C C Build as Win32 console app or Winl6 QuickWin project containing files VCEXAMP2 C and FRONTMIP LIB kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxk include frontmip include frontkey include lt stdio h gt include lt math h gt Example routine h h to check the capabilities and problem size limits of the Solver DLL we are using A return value of 0 for the number of variables or constraints means that the corresponding Solver engine 42 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide is not included void getlimits void long cols rows ints getproblimits NULL PROB LP amp cols amp rows amp ints printf LP limits ld variables ld constraints ld integers n cols rows ints getproblimits NULL PROB OP amp cols amp rows amp ints printf QP limits ld variables ld constraints ld integers n cols rows ints getproblimits NULL PROB NLP amp cols amp rows amp ints printf NLP limits ld variables ld constraints ld integers n cols rows ints getproblimits NULL PROB NSP amp cols amp rows amp i
160. l X PI 5 1 X PI 4 5 term2 Y termi 6 2 term3 10 1 1 PI 8 cos X 10 objective term2 term3 5 lt V i e S10 3 local optima 1 global optimum approx 0 3978 define PI 3 141593 INTARG _CC funceval5 HPROBLEM lp INTARG numcols INTARG numrows LPREALARG objval LPREALARG lhs LPREALARG var INTARG varone INTARG vartwo double terml term2 term3 terml var 0 PI 5 1 var 0 PI 4 0 5 0 term2 var 1 terml 6 var 1 termi 6 term3 10 0 1 0 1 0 PI 8 0 cos var 0 10 0 objval 0 term2 term3 return 0 48 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide INTARG _CC showiter5 HPROBLEM lpinfo INTARG wherefrom int itercount double objval getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT amp itercount getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ amp objval printf Iteration ld Objective g n itercount objval return 0 int examples double obj 2 double 1b 2 5 0 5 0 double ub 2 10 0 10 0 int stat double objval double x 2 1 0 1 0 double mid 2 disp 2 lower 2 upper 2 HPROBLEM lp NULL printf nExample NSP problem 5 Branin function n setintparam lp PARAM ARGCK 1 lp loadnlp PROBNAME 2 0 1 obj NULL NULL NULL NULL NULL NULL x 1b ub NULL 0O funceval5 NULL if lp return 1 setintparam lp
161. le we ll re use the arrays from the first example above We call loadlp to define a problem and return a pointer to it Next we call lpread again to read in the actual array values Then we ll be ready to call mipoptimize printf nExample Read in MIP problem of unknown size n Call lpread to obtain the problem dimensions If the matcnt argument is passed needed only for sparse problems it must have at least as many elements as the number of variables in the largest problem to be handled If necessary you can call lpread twice the first time to get this size via the numcols argument lpread NULL vcexamp1 amp o0bjsen amp numcols amp numrows amp numints matent NULL We would now allocate the x obj lbI ub and if used ctype and matbeg arrays to have numcols elements and the rhs and sense arrays to have numrows elements For a dense problem matval should be allocated to have numcols numrows elements For a sparse problem the matind and matval arrays should be allocated to have nzspace elements where nzspace is the sum of the counts in matcnt as returned by lpread To keep this example simple we ll re use the arrays from the first example above for nzspace i 0 i lt numcols i nzspace matcnt i we could now allocate matind and matval based on nzspace for i 0 i lt nzspace i matval i matind i 0 matv
162. lement can be All integer parameters are manipulated with one set of routines setintparam getintparam and infointparam and all double parameters are manipulated with a similar set of routines setdblparam getdblparam and infodblparam You can set all parameters to their default values by calling setdefaults Each parameter is identified by a numeric code for which a symbolic name is defined in the C C and Pascal header files The parameters are summarized in this section and then each parameter manipulation routine is described in detail Integer Parameters General The following parameters have long integer values They control general features of the Solver DLL such as array argument passing conventions and the IIS finder Symbolic Name Usage in Solver DLLs PARAM ARGCK 990 on argument errors 1 MsgBox 0 retval only PARAM ARRAY 995 0 Use C style arrays 1 Use VB style OLE SAFEARRAYs user controlled reports ee eee bounds in finding IIS PARAM ITLIM 1020 limit on Solver engine iterations Dynamic Link Library Solver User s Guide PARAM ARGCK This parameter is unique to the Solver DLL and is used for debugging When it is set to 1 if your program calls a Solver DLL routine which detects an invalid argument that routine will display a Windows MessageBox describing the error This allows you to see the problem immediately without having to write code to test the value returned by the DLL routine
163. lements as follows matbeg 0 0 matbeg 1 2 matbeg 2 4 matind 0 0 matind 1 2 matind 2 1 matind 3 3 matind 4 0 matcnt 0 2 matcnt 1 2 matcnt 2 1 matval 0 1 2 matval 1 7 8 matval 2 5 6 matval 3 9 0 matval 4 3 4 The array element matbeg j contains offsets from the beginning of the matind and matval arrays where the nonzero coefficients of variable j will be found The corresponding element matcnt j contains a count of consecutive elements of matind and matval which pertain to the same variable i e are in the same column of the matrix Note that matbeg j 1 matbeg j matcnt j the Solver DLL checks the arrays you supply to ensure that this is true For k matbeg j to matbeg j 1 1 there is a nonzero coefficient M i j at column j and row i matind k with value matval k Dynamic Link Library Solver User s Guide Designing Your Application e 27 Arrays and Callback Functions in Visual Basic The Solver DLL uses the calling conventions standardized for the Windows API routines which use argument data types drawn from C C In particular array arguments are passed as pointers to the base of the block of memory containing the array values In Visual Basic however arrays declared in the language are created using the COM Automation conventions for SAFEARRAYs A SAFEARRAY consists of a block of memory called an array descriptor which contains information about a
164. lled in automatically ret lpread lp vbexamp1 1 1 1 1 1 1 If ret lt gt 0 Then MsgBox Please run Example 2 first to create a textfile containing the problem unloadprob lp Exit Sub End If we can immediately solve the problem mipoptimize lp obtain the solution display objective and variables solution lp stat objval x 0 1 1 1 Form2 Text3 LPStatus amp Trim Str stat Form2 Text4 Objective amp Trim Str objval Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 call unloadprob to release memory unloadprob lp Next we assume that the dimensions of the problem are not known in advance We can call lpread with a NULL first argument to read the file and obtain the actual problem dimensions Then we would allocate arrays of re use the arrays from the first example above We call i T appropriate size to keep this example simple we ll loadlp to define a problem and return a pointer to it Next we call lpread again to read in the actual array values Then we ll be ready to call mipoptimize Call lpread to obtain the problem dimensions If the matcnt argument is passed needed only for sparse problems it must have at least as many elements as the number of variables in the largest problem to be handled If necessary you can call lpread twice the first time to get this size via the numcols argument Dim obj
165. lp PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval x lb ub NULL 4 funceval3 NULL if lp return optimize lp solution lp amp stat amp objval x piout slack dj printf Status ld s Objective g n stat stat PSTAT INFEASIBLE INFEASIBLE FEASIBLE objval printf Final values x1 g x2 g n x 0 x 1 if stat PSTAT_ INFEASIBLE findiis lp amp iisrows amp iiscols printf nfindiis iisrows ld iiscols 1ld n iisrows iiscols getiis lp amp stat rowind rowbdstat amp iisrows colind colbdstat amp iiscols for i 0 i lt iisrows i printf rowind ld ld rowbdstat ld ld n i rowind i i rowbdstat i for i 0 i lt iiscols i printf colind ld ld colbdstat ld ld n i colind i i colbdstat i unloadprob amp lp Example C program calling the nonlinear Solver DLL for a series of problems which may be linear or nonlinear This situation might arise if you are calling some external program or using your own interpreter to evaluate the problem functions We will define and solve two example problems Nonlinear problem Minimize X 2 Y 2 Subject to 46 e Calling the Solver DLL from C C Dynamic Link Library Solver User s Guide X Y 1 X Y gt 0 Solution is X Y 0 5 Objective 0 5 Alternate linear problem Minimize 2 X Y Subject to X Y 1 3E e
166. m You also supply arrays for the objective and constraint coefficients matval as you do when you call Joadlp but these arrays need not be initialized to specific values the Solver DLL will fill them in when it calls your callback function s The overall structure of a program calling the Solver DLL to solve a nonlinear programming problem is funceval Receive values for the variables compute values for the constraints and the objective function main Get data and set up an LP problem loadnip funceval Load the problem optimize Solve it solution Get the solution unloadprob Free memory Your program should first call Joadnip Like loadIp this function returns a handle to a problem Then you ll call additional routines passing the problem handle as an argument Optionally you may call oadnitype to give the Solver more information about linear and nonlinear functions in your problem testnitype to have the Solver determine the oadnitype information through a numerical test or loadctype to specify integer variables defining an integer nonlinear problem Then call optimize or mipoptimize if there are integer variables to solve the problem To retrieve the solution and sensitivity information call solution Finally call unloadprob to free memory As with loadlp this cycle may be repeated to solve a series of
167. m is linear or nonlinear In addition testnltype computes the information you would otherwise have to supply through a call to Joadnitype and if Dynamic Link Library Solver User s Guide Designing Your Application e 23 the problem is entirely linear testnltype computes the LP coefficients and places them in the matval array that you supplied when you called oadnip You can then switch from the nonlinear Solver to the linear Simplex method by calling unloadprob and calling oad p with the same arguments used for loadnIp Supplying a Jacobian Matrix The nonlinear Solver algorithm uses the callback function funceval in two different ways 1 to compute values for the problem functions at specific trial points as it seeks an optimum and ii to compute estimates of the partial derivatives of the objective the gradient and the constraints the Jacobian The partial derivatives are estimated by a rise over run calculation in which the value of each variable in turn is perturbed and the change in the problem function values is observed For a problem with N variables the Solver DLL will call funceval N times on each occasion when it needs new estimates of the partial derivatives 2 N times if the central differencing option is used This often accounts for 50 or more of the calls to funceval during the solution process To speed up the solution process and to give the Solver DLL more accurate estimates of th
168. mate initial values for the basic variables at the beginning of each one dimensional line search 0 means that the Solver will use linear extrapolation from the line tangent to the reduced objective function 1 means that the Solver will extrapolate to the minimum or maximum of a quadratic fitted to the reduced objective at its current point PARAM DIREC This parameter controls the method used by the Solver to determine a direction vector for the variables being changed on a given iteration 0 means that the Solver will use a Quasi Newton method maintaining an approximate Hessian matrix for the reduced objective function 1 means that the Solver will use a Conjugate Gradient method which does not require the Hessian matrix PARAM SAMPSZ This parameter determines the number of points in the Evolutionary Solver s population of candidate solutions The default value is 0 which instructs the 136 e Solver API Reference Dynamic Link Library Solver User s Guide Evolutionary Solver to select a reasonable population size for the problem currently 10 times the number of variables in the problem but no more than 200 In general a larger population size will permit more diversity among candidate solutions but may slow down convergence towards an accepted solution PARAM NOIMP This parameter controls one of the stopping criteria used by the Evolutionary Solver engine Ifthe Solver does not find an improved solution within the time in s
169. may be linear or nonlinear This situation might arise if you are calling some external program or using your own interpreter to evaluate the problem functions We will define and solve two example problems Nonlinear problem Minimize x 2 Y 2 Subject to X Ye i1 X Y gt 0 Solution is X Y 0 5 Objective 0 5 Alternate linear problem Minimize 2 X Y Subject to X Ye tl 1 3 wo X Ys 0 Solution is X 0 25 Y 0 75 Objective 1 25 In this example we call testnltype to determine whether the problem is linear or nonlinear If it is linear we solve it first with the nonlinear Solver engine then solve it again with the linear Simplex Solver engine rhs 0 1 rhs 1 0 sense 0 Asc E sense 1 Asc G 1b 0 10 lb 1 10 ub 0 10 ub 1 10 x 0 0 x 1 0 setintparam 0 PARAM ARGCK 1 lp loadnlp PROBNAME 2 2 1 obj rhs sense _ NullL NullL NullL matval x lb ub NullD 4 AddressOf funceval4 0 If lp 0 Then Exit Sub Test the problem to determine linearity nonlinearity testnltype lp 1 NullD nlstat NullB NullB If nlstat Then MsgBox Testnltype NONLINEAR Else MsgBox Testnltype LINEAR End If Solve the problem using the NLP Solver optimize lp solution lp stat objval x piout slack dj Form2 Text3 Status amp stat Form2 Text4 Obj amp objval Form2 Textl xl amp
170. ments as type String String variables in Visual Basic are actually BSTRs OLE strings which may be reallocated at any time this would cause problems for the Solver DLL Hence Visual Basic programs should define these arguments as arrays of Byte and initialize them element by element In the C C header file frontmip h the name INTARG a typedef for Long is used for integer arguments and LPINTARG is used for integer array arguments The name REALARG is used for double arguments and LPREALARG is used for double array arguments The names HPINTARG and HPREALARG are used for the matind and matval arrays in loadIp so that these array arguments can be huge arrays greater than 64K bytes in 16 bit Windows they are simply arrays of long and double in the 32 bit versions And the name LPBYTEARG a typedef for pointer to unsigned char is used for the sense ctype objtype and matvaltype arguments for the reasons outlined above NULL Values for Arrays Many of the Solver DLL routines accept arrays as arguments In a number of cases these arrays are optional and you may pass a NULL value in lieu of an array In order to support multiple programming languages including those that use OLE SAFEARRAYs the Solver DLL accepts any of the following as a NULL value e ANULL pointer i e an integer value of 0 Dynamic Link Library Solver User s Guide e A pointer to an integer value of 1 e A pointer to a pointer to a S
171. mints These three arguments should be pointers to variables of type Long where getproblimits will store the maximum number of decision variables columns constraints rows and integer variables supported by the Solver engine specified by the type argument If the number returned is zero the corresponding engine is not supported in this configuration of the Solver DLL Callback Routines for Nonlinear Problems funceval 130 e Solver API Reference For nonlinear and nonsmooth optimization problems you must write a callback function called funceval below that computes values for the problem functions objective and constraints for any given values of the variables The Solver DLL will call this function repeatedly during the solution process You supply the address of this callback function as an argument to JoadnIp which defines the overall nonlinear optimization problem In 16 bit Windows 3 x the address you pass must be obtained from the Windows routine MakeProcInstance for example IpFuncEval FUNCEVAL MakeProcInstance FARPROC MyFuncEval hInst where AInst is the instance handle of the currently running application The nonlinear GRG Solver engine uses the callback function funceval in two different ways 1 to compute values for the problem functions at specific trial points as it seeks an optimum and ii to compute estimates of the partial derivatives of the objective the gradient
172. mooth problem Then call optimize or mipoptimize if there are integer variables to solve the problem To retrieve the solution and sensitivity information call solution Finally call unloadprob to free memory This cycle may be repeated to solve a series of Solver problems Genetic and Evolutionary Algorithms A non smooth optimization problem generally cannot be solved to optimality using any known general purpose algorithm But the Evolutionary Solver can often find a good solution to such a problem in a reasonable amount of time using methods based on genetic or evolutionary algorithms In a genetic algorithm the problem is encoded in a series of bit strings that are manipulated by the algorithm in an evolutionary algorithm the decision variables and problem functions are used directly Most commercial Solver products are based on evolutionary algorithms An evolutionary algorithm for optimization is different from classical optimization methods in several ways First it relies in part on random sampling This makes it a nondeterministic method which may yield different solutions on different runs Second where most classical optimization methods maintain a single best solution found so far an evolutionary algorithm maintains a population of candidate solutions Only one or a few with equivalent objectives of these is best but the other members of the population are sample points in ot
173. n VB we can not use NULL as in C Therefor we define an array of size 1 with element 1 This is recognized by the DLL as NULL Dim NullL 0 As Long NullD 0 As Double Nul1lB 0 As Byte NullL 0 1 NullD 0 1 NullB 0 0 Select Case Example Case 1 Example program calling the nonlinear Solver DLL Solves the problem Minimize x 24 Y 2 Subject to X Y 1 X Y gt 0 Solution is X Y 0 5 Objective 0 5 rhs 0 1 rhs 1 0 sense 0 Asc E sense 1 Asc G 1b 0 INFBOUND 1lb 1 INFBOUND ub 0 INFBOUND ub 1 INFBOUND x 0 0 x 1 T setintparam 0 PARAM_ARGCK 1 lp loadnlp PROBNAME 2 2 1 obj rhs sense NullL NullL NullL matval x lb ub NullD 4 AddressOf funcevall 0 88 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide If lp setlpcallbackfunc lp optimize lp 0 Then Exit Sub AddressOf showiterl solution lp stat objval x piout slack dj Form2 Text3 Status amp stat Form2 Text4 Objective amp objval Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 Form2 Text5 slack1l amp slack 0 Form2 Text7 slack2 amp slack 1 Form2 Text6 pioutl amp piout 0 Form2 Text8 piout2 amp piout 1 setlpcallbackfunc lp 0 call unloadprob unloadprob lp Case 2 to release memory Example program calling the nonlinear Solver DL
174. n a given PC it will display a MessageBox noting that the entries already exist in the Registry and it will not modify them For complete information on the Solver DLL s Registry key and associated entries see the description of the getuse function in the chapter Solver API Reference During development and testing of your application you can run the Solver DLL in Evaluation Test mode where it does not counts uses in this mode the DLL will Dynamic Link Library Solver User s Guide Installation e 17 not reference the Registry entries so they need not exist on the development system Once the DLL is placed into production it should be run in Use Counting mode where the Registry entries must be present For information on how to set the mode in which the Solver DLL runs consult the section Use Based Licensing in the following chapter Designing Your Application On Windows NT and Windows 2000 systems the CreateUseKey exe program must be run under a user account with privileges to create Registry entries Since the Solver DLL only updates existing Registry entries it does not need to run under an account with these privileges 18 e Installation Dynamic Link Library Solver User s Guide Designing Your Application Calling the Solver DLL This chapter provides an overview of the way your application program should call the Solver DLL routines to define and solve an optimization problem We ll use the
175. n any constraint the Evolutionary Solver engine is used to solve the problem An array of dimension numcols indicating whether the variables occur in a linear smooth nonlinear or nonsmooth discontinuous way in the objective function objtype i L Variable occurs linearly or not at all in the objective objtype i N Variable is smooth nonlinear in the objective objtype 1 D Variable is nonsmooth discontinuous in the objective An array of dimension nzspace indicating whether the variables occur in a linear smooth nonlinear or nonsmooth discontinuous way in the constraint functions matvaltype i L Matval i represents a linear occurrence of a variable matvaltype i N Matval i represents a smooth nonlinear occurrence matvaltype i D Matval i represents a nonsmooth discontinuous occurrence The relevant variable and constraint are identified by the corresponding elements of the matbeg matcnt and matind arrays Dynamic Link Library Solver User s Guide testnitype numtests testvals pstat objtype INTARG testnitype lp numtests testvals pstat objtype matvaltype HPROBLEM lp INTARG numtests LPREALARG testvals LPINTARG pstat LPBYTEARG objtype matvaltype This routine is optional It can be called to compute information about whether each variable occurs linearly or nonlinearly in each problem function through a numerical test The lp argument is the problem handle returned
176. n arrays of appropriate dimension lp loadlp PROBNAME numcols numrows objsen obj 0 rhs 0 sense 0 1 1 1 matval 0 1lb 0 ub 0 1 numcols numrows nzspace If lp 0 Then Exit Sub loadctype lp ctype 0 Now we call lpread lpread lp vbexamp1 Finally mipoptimize lp obtain the solution we call mipoptimize to read in the actual array values Si Hy Sy ae ee Sa and display the solution display objective and variables solution lp stat objval x 0 1 1 1 Form2 Text3 LPStatus amp Trim Str stat Form2 Text4 Objective amp Trim Str objval Form2 Textl xl amp x 0 Porm2 Text2 x2 amp x 1 call unloadprob unloadprob lp End Select End Sub Private Sub Command2_Click Unload Form2 End Sub Private Sub Form Activate Form2 Command1 SetFocus End Sub Dynamic Link Library Solver User s Guide to release memory Calling the Solver DLL from Visual Basic e 83 Visual Basic Source Code Nonlinear Nonsmooth Problems The Visual Basic source code from the files vbexamp2 frm examp2 frm and vbexamp2 bas is listed below It includes four example problems for the nonlinear GRG Solver which are set up and solved when you click on the appropriate buttons The first example is a simple two variable nonlinear optimization problem which defines a funceval routine to evaluate the problem functions The second example is identical to
177. nce of solutions currently in the population and the other based on the rate of progress recently made by the algorithm For more information see the section Solver Parameters in the chapter Solver API Reference Problems in Algebraic Notation 22 e Designing Your Application As outlined above problems for the Solver DLL are generally defined by a series of calls made by your application program In particular for linear and quadratic problems you must be careful to supply the correct values for objective and constraint coefficients and constraint and variable bounds to define the problem you want to solve Problems you define exist only in main memory for the duration of your calls to the Solver DLL they do not persist across runs of your application To make it easier to work with linear and quadratic problems the Solver DLL can read and write text files containing a problem description in a form very similar to standard algebraic notation An example of such a text file for a simple linear integer problem is shown below Maximize LP MIP obj 2 0 x1 3 0 x2 Subject To cl 9 0 x1 6 0 x2 lt 54 0 C2 6 0 x1 7 0 x2 lt 42 0 c3 5 0 x1 10 0 x2 lt 50 0 Bounds 0 0 lt x1 lt infinity 0 0 lt x2 lt infinity Dynamic Link Library Solver User s Guide Integers x1 x2 End If you define this problem via calls to oadlp and loadctype you can produce a text file with the contents sho
178. nd the true optimal solution to an integer nonlinear problem though it will often find a good but not provably optimal integer solution Solving integer linear problems with the LP Solver or integer quadratic problems with the QP Solver is an intrinsically faster and more reliable process If you have an integer linear problem with many binary or 0 1 integer variables we recommend that you try solving it with a Solver DLL configuration that includes the QP Solver Packaged with the QP Solver are a set of Preprocessing and Probing strategies for linear constraints that often greatly speed up the solution of problems with many 0 1 integer variables 16 Bit Versus 32 Bit Versions The choice of 16 bit versus 32 bit versions of the Solver DLL will probably be dictated by the programming language or other tool you are using to write your application program For example Visual Basic 3 0 is a 16 bit system which can call only the 16 bit Solver DLL whereas Visual Basic for Applications as shipped with Microsoft Office 95 97 and 2000 can call only the 32 bit versions of the DLL Dynamic Link Library Solver User s Guide Introduction e 9 The 32 bit versions of the Solver DLL takes full advantage of the instruction set features of the Intel 386 486 Pentium and above processors yielding a speed advantage which may be as great as a factor of two on larger problems Support for 16 bit versions of the Solver DLL will be limited in the future
179. ndow If you now look in the Delphi example directory you should find a new file named psexamp which was written by the call to Ipwrite You can examine this file in Notepad or another text editor it contains an algebraic statement of the LP MIP problem that you have solved 5 Delphi compiles and links your application into a binary executable before running it The file psexamp exe can be run by itself outside the Delphi environment as long as it can find and load the Solver DLL frontmip dll Building a 16 Bit Delphi Pascal Program The 16 bit Delphi 1 0 programming system is quite similar to the 32 bit Delphi 2 0 version Although there are minor differences in the menus toolbars palettes and other features you can open and use the same project file psexamp dpr example program psunit pas and header file frontmip pas as in the 32 bit system The step by step instructions outlined above for the 32 bit Delphi system can be used as is with the 16 bit system with only minor differences for example Delphi 1 0 displays the project source code by default so you don t have to select View Units View Forms or View Project Source The on screen appearance of Delphi 1 0 is very similar to Delphi 2 0 You simply need to ensure that your program finds and loads the correct 16 bit version of frontmip dll When you run the program as compiled by 16 bit Delphi 1 0 you will see the solution of the LP MIP problem but you will als
180. ne Systems Small Scale Solver Dynamic Link Library Version 3 5 Frontline Systems Inc P O Box 4288 Incline Village NV 89450 USA Tel 775 831 0300 Fax 775 831 0314 Email info frontsys com Example LP MIP and QP problems in C C Build as Win32 console app or Win16 QuickWin project containing files VCEXAMP1 C and FRONTMIP LIB kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk include frontmip h include frontkey h include lt stdio h gt Example 1 Solves the LP model Maximize 2 xl 3 x2 Subj to 9 x1 6 x2 lt 54 6 x1 7 X2 lt 42 5 x1 10 x2 lt 50 xl x2 non negative LP solution x1 2 8 x2 3 6 Objective 16 4 This example shows the simple form of passing arguments to loadlp A dense full size N by M matrix is passed as the matval argument and NULL pointers are passed as the matbeg matcnt amp matind arguments This example also shows how to obtain LP sensitivity analysis info by calling the objsa and rhssa functions These calls are valid only for LP problems For QP problems only dual values the piout and dj arguments of solution are available for MIP problems no sensitivity analysis info is available none would be meaningful This example uses a callback function to display the LP iterations The following function is called on each LP iteration in examplel long _CC lpcallback HPROBLEM lpinfo long wherefrom long iters double obj ge
181. ng _CC pivot HPROBLEM lpinfo long wherefrom void RunLPSolver long pstat double pobj double x void RunNLPSolver long pstat double pobj double x Global data HANDLE hInst HWND hWnd main window handle char szClassName ExampleClass char szAppTitle FRONTMIP WinExamp int WINAPI WinMain HINSTANCE hInstance LPSTR lpCmdLine int nCmdShow MSG msg if hPrevinstance if InitApplication hInstance return FALSE current instance HINSTANCE hPreviInstance if InitInstance hInstance nCmdShow return FALSE while GetMessage amp msg 0 0 0 TranslateMessage amp msg DispatchMessage amp msg return msg wParam BOOL InitApplication HINSTANCE hInstance WNDCLASS wc we style 0 we lpfnWndProc MainWndProc we cbClsExtra 0 wc cbWndExtra 0 we hInstance hiInstance we hIcon LoadIcon NULL IDI APPLICATION we hCursor LoadCursor NULL IDC ARROW we hbrBackground GetStockObject WHITE BRUSH wc lpszMenuName NULL wc lpszClassName szClassName return RegisterClass amp wc BOOL InitInstance HINSTANCE hInstance hInst hInstance hWnd CreateWindow szClassName szAppTitle WS OVERLAPPEDWINDOW CW_USEDEFAULT CW_USEDEFAULT Dynamic Link Library Solver User s Guide int nCmdShow Native Windows Applications e 59 60 e Native Windows Applications CW_USEDEFAULT CW_USEDEFAULT NU
182. nloadprob in that order You can use the example code in psunit pas as a guide for getting the arguments right This source file in combination with the form file psunit dfm defines a simple form with four edit boxes to display results and two buttons that call the Solver DLL routines to solve a mixed integer linear MIP and a nonlinear NLP problem respectively when they are pressed In the Pascal source code the arrays and other variables used as Solver DLL arguments are declared as public The argument values are set up and the appropriate DLL routines are called in the procedures TForm LPButtonClick and TForml NLPButtonClick which run when the appropriate button is pressed Passing Array and Function Arguments Delphi Pascal imposes strong type checking on arguments to the Solver DLL functions requiring for example an exact match in the number of elements between actual array arguments and array parameters To permit flexibility in the Solver DLL s array arguments the header file frontmip pas declares array Dynamic Link Library Solver User s Guide Calling the Solver DLL from Delphi Pascal e 95 parameters as for example var obj Double For the corresponding array argument you should pass the first element of the array for example obj 0 In many Solver DLL routines certain array arguments are optional you can instead pass a NULL value as described in NULL Values for Arrays in the chapter
183. nts printf NSP limits ld variables ld constraints ld integers n cols rows ints Example C program calling the nonlinear Solver DLL Solves the problem Minimize X 2 Y 2 Subject to X Y 1 X Y gt 0 Solution is X Y 0 5 Objective 0 5 Define a callback function which computes the objective and constraint left hand sides for any supplied values of the decision variables INTARG _CC funcevall HPROBLEM lp INTARG numcols INTARG numrows LPREALARG objval LPREALARG lhs LPREALARG var INTARG varone INTARG vartwo objval 0 var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side return 0 Define a callback function which displays progress information when called on major iterations by the nonlinear Solver engine INTARG _CC showiterl HPROBLEM lpinfo INTARG wherefrom long itercount double objval getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT amp itercount getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ amp objval printf Iteration d Objective g n itercount objval return 0 Now set up the NLP problem including the sense and right hand sides of constraints call the nonlinear Solver and display the solution Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 43 void examplel void
184. numcols As Integer ByVal numrows As Integer ByRef objval As Double ByRef lhs As Double ByRef var As Double _ ByVal varone As Integer ByVal vartwo As Integer As Long Err 0 On Error Resume Next The use of the addressof operator can crash VB We never return an error value to the DLL Therefore use on error resume next objval var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side funceval 0 End Function Function showiter1 ByVal lp As Long ByVal wherefrom As Long As Long Dim itercount As Long Dim objval As Double Dim ret As Long ret getcallbackinfo lpinfo wherefrom CBINFO_ITCOUNT itercount ret getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ objval MsgBox Iteration amp itercount amp Objective amp objval 84 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide showiterl 0 End Function Function funceval3 lp As Long ByVal numcols As Integer ByVal numrows As Integer ByRef objval As Double ByRef lhs As Double ByRef var As Double _ ByVal varone As Integer ByVal vartwo As Integer As Long Err 0 On Error Resume Next The use of the addressof operator can crash VB We never return an error value to the DLL Therefore use on error resume next objval var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand
185. o eS 70 Solution is X 0 25 Y 0 75 Objective 1 25 In this example we call testnltype to determine whether the problem is linear or nonlinear If it is linear we solve it first with the nonlinear Solver engine then solve it again with the linear Simplex Solver engine typedef enum Nonlin Linear Problem Problem Ex1 Nonlin We define one funceval routine which can compute the objective and constraint values for both of the example problems The values returned by this funceval depend on the setting of the global variable Ex1 INTARG _CC funceval4 HPROBLEM lp INTARG numcols INTARG numrows LPREALARG objval LPREALARG lhs LPREALARG var INTARG varone INTARG vartwo switch Ex1 case Nonlin objval 0 var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side break case Linear objval 0 2 0 var 0 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 3 0 var 0 var 1 constraint left hand side break return 0 void example4 void Dynamic Link Library Solver User s Guide double obj 2 double rhs 2 1 0 0 0 char sense 2 EG double matval 4 double 1b 10 0 10 0 double ub 10 0 10 0 long stat nlstat double objval double x 2 0 0 0 0 double pio
186. o feasible integer solution stat 104 PSTAT_ MIP SOL LIM integer solution limit exceeded stat 105 PSTAT MIP NODE LIM FEAS node limit exceeded feasible stat 106 PSTAT_MIP NODE LIM _INFEAS node limit exceeded not feas stat 107 PSTAT MIP TIME LIM FEAS time limit exceeded feasible stat 108 PSTAT MIP TIME LIM INFEAS time limit exceeded not feas A pstat value of 69 PSTAT_ENTRY ERROR is returned only by the single threaded version of the Solver DLL and only if optimize or mipoptimize is called directly or indirectly from a callback function that the Solver DLL called during execution of an earlier optimize or mipoptimize call In the multi threaded version of the Solver DLL these types of recursive calls are permitted A pointer to a double variable where the optimal objective function value will be stored A array of dimension equal to the number of columns variables in which the optimal values of the primal variables will be stored An array of dimension equal to the number of rows constraints in which the dual values shadow prices of the constraints will be stored The piout values are available only if an optimal solution to an LP or QP problem has been found An array of dimension equal to the number of rows constraints in which the optimal slack or surplus values for the constraints will be stored The slack values are available only if an optimal solution to an LP or QP problem
187. o find that the MessageBoxes displaying the iterations of the LP Solver engine don t appear and pressing the Solve NLP button doesn t seem to have any effect This is explained below Delphi Pascal Example Source Code The Delphi Pascal source code for the example problems is shown below This source code can be used in both the 32 bit and 16 bit Delphi systems but you will notice conditional compilation directives IFDEF WIN32 and SENDIF around the definition of the callback functions and the code to call the nonlinear Solver 98 e Calling the Solver DLL from Delphi Pascal Dynamic Link Library Solver User s Guide This is also done in the C C example file vcexamp1 c in an earlier chapter for similar reasons The 16 bit version would have to take special steps to ensure that the callback function s local data is addressable in each application instance and this complication was left out of this simple example This topic is more fully explored in the chapter Special Considerations for Windows 3 x The header file frontmip pas can also be used in both the 32 bit and 16 bit Delphi systems however it makes extensive use of conditional compilation directives in order to declare the proper calling conventions far pascal versus stdcall for 16 bit and 32 bit DLL routines Problem 1 Solve the MIP model Maximize 2x1 3 x2 Subj to 9X1 6 X2 lt 54 6 Xl 7 X2 lt 42 5 x1 10 x2 lt 50 x1 x2 non negativ
188. oblem includes integer variables During the call to optimize or mipoptimize the Solver DLL may make repeated calls to one or more callback routines that you have written and passed as arguments to loadnIp setlpcallbackfunc or setmipcallbackfunc These routines are discussed below under Callback Routines for Nonlinear Problems and Other Callback Routines Call solution to retrieve the final status of the optimization the final value of the decision variables and the objective function and if appropriate dual values basic sensitivity analysis information for the variables and constraints For linear programming problems only you may call objsa and or rhssa to obtain the ranges of values over which the sensitivity analysis information is valid For nonsmooth optimization problems only you may call varstat and or constat to obtain statistical information about the final population of candidate solutions INTARG optimize lp HPROBLEM lp The argument p of optimize must be the value returned by a previous call to loadlp or loadnIp When this function is called the Solver DLL will solve the specified linear quadratic nonlinear or nonsmooth optimization problem Optimize returns a value of 0 if successful i e the solution process ran to completion though it may or may not have found an optimal solution see solution for details If the solution process cannot be carried out optimize re
189. ocal minima and 6 An example where the Evolutionary Solver finds the optimal solution to a problem with a nonsmooth discontinuous objective If you are using the 16 bit version of the Solver DLL and you are either solving a large scale problem or you wish to use the callback functions to gain control during the solution process be sure to read the chapter Special Considerations for Windows 3 x even if you are running your 16 bit application under Windows 95 98 or NT 2000 in Windows 3 x compatibility mode The chapter Native Windows Applications provides the C source code of a native Windows application written to the Win16 Win32 API This source code can be compiled into either a 16 bit or 32 bit application and run under Windows 3 x Windows 95 98 or Windows NT 2000 It makes use of the Solver DLL s callback Dynamic Link Library Solver User s Guide functions and takes into account the special considerations for Windows 3 x Also included in this chapter is the C source code of a simple multi threaded application calling the reentrant version of the Solver DLL written to the Win32 API Dynamic Link Library Solver User s Guide Introduction e 13 Installation Running the Installation Program Most versions of the Solver DLL are provided in the form of single executable installation program file such as SolvLP exe that can be run to uncompress and install all of the Solver DLL files library and header files
190. olutions all with the same objective function value a weak minimum If the Q matrix is indefinite the function will have a saddle point Dynamic Link Library Solver User s Guide Designing Your Application e 25 which has many but not all of the properties of an optimal solution however the true optimal solution s one or many of them will lie somewhere on the boundaries of the constraints Quadratic programming algorithms are specialized for speed and accuracy to solve problems where the Q matrix is positive definite when minimizing or negative definite maximizing The QP algorithm used in the Solver DLL is somewhat more general It can handle problems where the Q matrix is positive semi definite or negative semi definite in which case it will converge to a point in the trough with the correct minimum maximum objective function value If applied to a problem where the Q matrix is indefinite however the Solver DLL may converge either to a saddle point or to one of the optimal solution s on the constraint boundary depending on the initial values of the variables In this case a call to the solution function will return a status code of PSTAT_ FRAC CHANGE to indicate that the solution is not necessarily optimal The oadquad function tests the Q matrix you supply to determine whether it is positive negative definite semi definite or indefinite If it is indefinite Joadquad will return a nonzero
191. olver User s Guide End Sub EXAMP1 FRM Private Sub Command1_Click set up the LP problem Select Case Left Form2 Labell Case Example 1 lp loadlp PROBNAME 2 1 1 1 matval 0 If lp 0 Then Exit Sub set up the callback setlpcallbackfunc lp solve the problem optimize lp obtain the solution 3 9 1 obj 0 rhs 0 1b 0 ub 0 1 sense 0 Ya 2 3 6 AddressOf lpcallback display objective and variables solution lp stat objval x 0 piout 0 slack 0 dj 0 Form2 Text3 LPStatus amp Trim Str stat Form2 Text4 Objective amp Trim Str objval display constraint slacks and dual values Form2 Textl xl amp x 0 Form2 Text2 x2 amp x 1 Form2 Text5 Sslack1l amp slack 0 Form2 Text6 pioutl amp piout 0 Form2 Text7 Slack2 amp slack 1 Form2 Text8 piout2 amp piout 1 Form2 Text24 slack3 amp slack 2 Form2 Text25 piout3 amp piout 2 obtain and display sensitivity analysis information objsa lp 0 1 varlow 0 Form2 Text9 obj 0 Form2 Text10 varlow 0 Form2 Text11 varupp 0 Form2 Text12 obj 1 Form2 Text13 varlow 1 Form2 Text14 varupp 1 rhssa lp 0 2 conlow 0 Form2 Text15 rhs 0 Form2 Text16 conlow 0 Form2 Text17 conupp 0 Form2 Text18 rhs 1 Form2 Text19 conlow 1 Form2 Text20 conupp 1 Form2 Text21 rhs 2 Form2 Text22
192. on each WM_PAINT message in each window We do this to demonstrate what happens when both problems are being solved concurrently Note if your copy of the Solver DLL doesn t include both the linear and nonlinear Solver engines you can change the defines PROBLEM1 and PROBLEM at the beginning of winexamp2 c so that the same problem will be created and solved in both windows The two threads we create in WinMain execute a common function RunThread which receives as an argument the window handle of the first or second window RunThread simply calls the Win32 Sleep function to wait for a randomly chosen number of seconds then calls InvalidateRect and UpdateWindow to generate a new WM PAINT message for the argument window The effect is to cause the MainWndProc function and the Solver DLL routines to be executed at randomly chosen and often overlapping times in the two windows If you compile link and run winexamp2 c on a Win32 system with a single threaded version of the Solver DLL you will see one or more error MessageBoxes informing you that another problem is currently loaded If you run it with a multi threaded version of the Solver DLL you ll see both windows updating concurrently with results from calling the Solver DLL routines kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Frontline Systems Small Scale Solver Dynamic Link Library Version 3 5 Frontline Systems Inc P O Box 4288 Incline
193. on of the example program solves the same LP MIP problem as the 32 bit version but the output from the callback function Ipcallback does not appear and the nonlinear Solver example which uses the funcevall and jacobian1 callback routines is not solved This is explained below FORTRAN Example Source Code The FORTRAN source code for the example problems is shown below This source code can be used with both the 32 bit and 16 bit FORTRAN compilers but you will notice conditional compilation directives J F DEFINED WIN32 and ENDIF around the definition of the callback functions and the code to call the nonlinear Solver This is also done in the Delphi Pascal example file psunit pas and the C C example file vcexamp1 c in earlier chapters for similar reasons The 16 bit version would have to take special steps to ensure that the callback function s local data is addressable in each application instance and this complication was left out of this simple example This topic is more fully explored in the chapter Special Considerations for Windows 3 x The header file frontmip for can also be used with both the 32 bit and 16 bit FORTRAN compilers however it makes extensive use of conditional compilation directives in order to declare the proper calling for 16 bit and 32 bit DLL routines kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk Frontline Systems Solver DLL Dynamic Link Library Version 3 5 Frontlin
194. ototyped with the CC calling convention which is defined as export far pascal versus _ stdcall in 32 bit Windows ensuring that the C C compiler will call them appropriately Far Pointers The Solver DLL expects many of its arguments to be passed by reference which means that a pointer to the actual data is passed to the DLL As noted above these must be far pointers in Windows 3 x The header file frontmip h defines typedefs for the required data types such as LPINTARG far pointer to long integer and LPREALARG far pointer to double Since the arguments of each DLL routine are prototyped in frontmip h the C C compiler will perform default conversions for you so you can for example write Dynamic Link Library Solver User s Guide Special Considerations for Windows 3 x e 53 char sense LLEEGG lp loadlp sense and sense will be converted if necessary to type LPSTR i e far pointer to character in Windows 3 1 Remember that array names represent the base address of the array and do not need a leading amp when passed as arguments Huge Pointers Far pointers can address data located in any segment anywhere in memory However far pointers are designed to manipulate data objects that are at most 64K bytes long the maximum segment size in the Intel 8086 architecture Larger data objects in a 16 bit environment require special address arithmetic which is provided by the C C compilers when you d
195. own in the example below If you call the Solver DLL routine getcallbackinfo in your own callback routine you should include the file frontcbi for in your source code immediately after you declare your own callback routine arguments as shown in the example flexamp for Building a 32 Bit FORTRAN Program This section will outline the steps required to compile link and run the example Solver DLL application flexamp exe using 32 bit Microsoft FORTRAN Power Station 4 0 under Windows 95 98 or Windows NT 2000 The steps involved in using other FORTRAN compilers should be similar First follow the steps in the Installation chapter which will copy the example programs into the examples subdirectory of the frontmip directory on your hard disk If you wish you can run the pre built version of flexamp exe by simply double clicking on its name before you try to compile and link it from the source code 1 Create a Project Start the Microsoft Developer Studio Select File New and in the resulting dialog select Project Workspace and click OK In the New Project Workspace dialog select QuickWin Application in the Type list box type flexamp in the Name edit box and type e frontmip examples flexamp or another path of your choosing in the Location edit box Then click Create 2 Add Files Select Insert Files into Project In the resulting dialog navigate if necessary to the proper directory select the file flexamp for and clic
196. p INTARG numcols numrows LPREALARG objval lhs var INTARG varone vartwo The funceval routine computes values for the problem functions It is passed a vector of variable values and a vector of function values including the objective to Dynamic Link Library Solver User s Guide jacobian be computed It uses the variables to compute the functions stores these into the vector of function values and returns an integer indicating success or failure The numcols and numrows arguments are the same values you supplied to Joadnip The var array has dimension numcols and the hs array has dimension numrows The objval argument is a pointer to a location where the scalar objective value should be stored The routine should compute and store the objective value compute constraint left hand side values and store them in hs and return 0 for success or 1 for failure 1 will cause the Solver DLL to stop and return from its optimize call The varone and vartwo arguments may be ignored unless your function evaluation process is designed to take advantage of information about which elements of the var array have changed since the last call to funceval When the Solver is supplying entirely new variable values i e exploring a new trial point varone and vartwo will both be 1 When the Solver is computing partial derivatives on its own via finite differencing in the absence of the jacobian callback function it calls funceval
197. ped alternative Dynamic Link Library Solver User s Guide use based licensing terms which permit any number of users or seats but which monitor the number of uses or calls to the optimizer Developers can choose user based or use based licensing On either basis they can prepay for a quantity of licenses to bring down the average cost on a steeply declining discount schedule and they can arrange that the total license cost will not exceed a certain fixed amount for a period such as a year or for the lifetime of the application To support use based licensing certain configurations of the Solver DLL V3 5 include the ability to count uses i e calls to the oadlp or loadnip functions and calls to the optimize or mipoptimize functions and report this information both to the user and to Frontline Systems Use information can be written to a text file or emailed to Frontline Systems either automatically or under the control of the application program via the new getuse and reportuse functions Problems in Algebraic Notation Previous versions of the Solver DLL featured the ability to write out a text file containing an algebraic description of a linear quadratic or mixed integer problem The primary use of this feature was in testing and debugging an application program to ensure that the problem being defined by calls to the Solver DLL routines was in fact the problem intended Version 3 5 of the Solver DLL features the new p
198. play sensitivity analysis information objsa lp 0 1 varlow varupp for i 0 i lt 1 i printf Obj coefficient 3 0f Lower 7g Upper 7g n obj i varlow i varupp il rhssa lp 0 2 conlow conupp for i 0 i lt 2 i printf Constraint RHS 3 0f Lower 7g Upper 7g n rhs i conlow i conupp i printf n ifdef WIN32 setlpcallbackfunc lp NULL remove the callback function endif important call unloadprob to release memory unloadprob amp lp Example 2 Solves the MIP model Maximize 2 x1 3 x2 Subj to 9 x1 6 x2 lt 54 6 xl 7 x2 lt 42 5 x1 10 x2 lt 50 xl x2 non negative integer MIP solution xl 2 x2 4 Objective 16 0 This example illustrates the full set of arguments used to pass a potentially sparse matrix to loadlp For each variable column i matbeg i and matcnt i are the beginning index and count of non zero coefficients in the matind and matval arrays For each such coefficient matind k is the constraint row index and matval i is the coefficient value See the documentation for more details In this example we also use two debugging features of the Solver DLL 1 We call setintparam to enable the display of error MessageBoxes by the DLL routines if they detect an invalid value in one of the arguments we pass since there are no errors none will appear 2 We call lpwrite to write out a file wh
199. ptimum in a problem with nonsmooth functions Building a 32 Bit C C Program This section will outline the steps required to compile link and run the example Solver DLL application VCEXAMP1 EXE using 32 bit Microsoft Visual C 5 x or 6 x under Windows 95 98 or Windows NT 2000 The steps required to compile link and run VCEXAMP2 EXE are the same and the steps involved in using other C C compilers will be similar First follow the steps in the Installation chapter which will copy the example programs into the examples subdirectory of the frontmip directory on your hard disk If you wish you can run the pre built version of VCEXAMP1 EXE by double clicking on the filename before you try to compile and link from the source code 1 Create a Project Start Microsoft Visual Studio Select File New and in the Projects tab of the displayed dialog select Win32 Console Application Type vceexamp1 in the Project name edit box and c frontmip examples vcexamp1 or a path of your choosing in the Location edit box Then click OK In Visual C 6 x click Finish and then OK in the New Project Wizard dialog boxes to create an empty project 2 Add Files Select Project Add to Project Files In the dialog navigate if necessary to the proper directory select the file veexamp1 c and click OK Now select Select Project Add to Project Files again In the dialog open the Files of type dropdown list and select Library Files
200. r your objective function and a Jacobian matrix for your constraints i e a procedure pointer declared as shown in the section Callback Routines below Loadnlp returns NULL if there is an error in its arguments if nonlinear problems are not supported by this version of the Solver DLL if the probname key string is not recognized or in the single threaded version of the DLL if another problem is still active i e if loadIp or loadnIp has been called without a corresponding call to unloadprob You should not change or free the memory for arguments passed to loadnip until after you make the corresponding call to unloadprob INTARG loadnitype lp objtype matvaltype HPROBLEM lp LPBYTEARG objtype matvaltype This routine is optional If called it gives the Solver DLL information about whether each variable occurs in a linear nonlinear or nonsmooth discontinuous way in each problem function The Solver can use this information to choose the appropriate Solver engine and or to speed up the solution process The argument p must be the value returned by a previous call to JoadnIp You may pass NULL values for objtype matvaltype or both to indicate that the objective or the constraints are in general nonsmooth or discontinuous functions of the variables In Version 3 5 of the Solver DLL if either of these arguments is NULL or if any variable occurs in a nonsmooth discontinuous way in the objective or i
201. ramming for 16 bit Windows 3 x most notably because the 32 bit systems feature a flat address space whereas Windows 3 x assumes a segmented address space In a flat address space all pointers are alike and can address any location in memory In the Windows 3 x segmented address space there are near pointers which can address only the current segment limited to 64K bytes in size far pointers which can address other segments and huge pointers which are used to address arrays or other data objects which are greater than 64K bytes and therefore must span more than one segment Programs can be compiled for various memory models which use certain types of pointers for code and for data The 16 bit Solver DLL code and data are in segments different from those of your application program This means that the Solver DLL routines and argument data passed to the DLL must be referenced through far pointers Moreover when the Solver DLL makes calls during the solution process to a callback function in your application it must i call your function through a far pointer and 11 ensure that the data referenced by your function is addressable when it is called from the Solver DLL This chapter discusses these special considerations for 16 bit Windows 3 x Far and Huge Pointers In Windows 3 x the Solver DLL routines themselves must be called through far pointers In the header file frontmip h these routines are pr
202. read function to complement the pwrite or Iprewrite functions With Ipread the application can read in a problem previously written to disk by pwrite or a problem generated in the correct format by another program or via hand editing of the text file This provides a wide range of new options for saving problems across multiple sessions and solving problems interactively or in combination with other programs How to Use This Guide This User Guide includes a chapter on installing the Solver DLL files and a chapter providing an overview of the Solver DLL API calls and how they may be used to define and solve linear LP quadratic QP nonlinear NLP nonsmooth NSP and mixed integer MIP programming problems It also includes chapters giving specific instructions for writing compiling and linking and testing application programs in four languages C C Visual Basic Delphi Pascal and FORTRAN We highly recommend that you read the installation instructions and the overview of the Solver DLL API calls first Then you may turn directly to the chapter that covers the language of your choice Each chapter gives step by step instructions for building and testing a simple example program included with the Solver DLL written in that language You can use these example programs as a starting point for your own applications The chapter Solver API Reference provides comprehensive documentation of all of the Solver DLL
203. reports may be generated and written to a text file or emailed to Frontline Systems under control of the user s application through calls to the reportuse routine PARAM IISBND Setting this parameter to 1 causes the Solver DLL s IIS finder to skip the steps and computing time required to eliminate variable bounds from an Irreducibly Infeasible Set of constraints When PARAM _IISBND is 1 any IIS which is found will include all of the variable bounds defined in the lb and ub arrays for the problem When this parameter is 0 the default as many variable bounds as possible will be eliminated from the IIS PARAM ITLIM This is the maximum number of iterations pivots that the Solver will perform on an NLP LP or QP problem or a subproblem of a MIP problem When this limit is exceeded the optimize routine will return and the solution routine s pstat argument will be set to PSTAT_IT_LIM_FEAS or PSTAT_IT_LIM_INFEAS depending on whether a feasible solution has been found Integer Parameters Solver Engines The following parameters have long integer values They control various features of the Nonlinear Linear and Quadratic Solver engines Symbolic Name Usage in Solver DLLs PARAM SCAIND 1033 scaling 1 none 0 normal l aggressive PARAM CRAIND 1007 crashing 0 none 1 crash initial basis PARAM En 5010 NLP linear variables 0 ignore 1 recognize linear variables NLP derivatives 0 Forward 1 Central
204. roduction the absence of severe difficulties with scaling or degeneracy to find the optimal solution if one exists or to find that there is no feasible solution or that the objective function is unbounded The LP Solver is designed to accept a matrix of coefficients called matval later in this Guide which allows the Solver itself to compute values for the problem functions objective and constraints If you supply the matrix of coefficients you don t have to write a function funceval to evaluate the problem functions In most cases the coefficients are readily available from the data accepted as input or computed by your application In other situations the coefficients might not be so readily available and you might find it easier to write a funceval routine If your Solver DLL includes both the nonlinear NLP and LP Solver engines you can ask the Solver DLL to compute the matrix of coefficients for you by calling your funceval routine and then solve the problem using the faster and more reliable LP Solver engine Quadratic Solver The quadratic QP Solver is an extension to the LP Solver which solves quadratic programming problems such as portfolio optimization problems with a quadratic objective function and all linear constraints It uses the fast and reliable Simplex method to solve a series of subproblems leading to the optimal solution for the quadratic programming problem The QP Solver is designed to
205. rray element sizes dimensions and bounds and a pointer to the memory holding the array values Visual Basic programs that call Windows API routines usually handle array arguments by declaring the argument as ByRef and passing the first element of the array rather than the whole array as the argument For example obj 0 passed by reference is a pointer to the first array element i e the base address of the block of memory holding the array values the SAFEARRAY descriptor is stored elsewhere in memory by Visual Basic and is not seen by the Solver DLL The Solver DLL is able to access additional array elements beyond the first element by indexing into the block of memory holding the array data This approach does not work in reverse however When Visual Basic is used to write a callback function such as funceval or jacobian where the Solver DLL makes the call and passes blocks of memory for C style arrays as arguments the Visual Basic code can reference only the first array element Subscripting in Visual Basic is permitted only if the argument is actually declared as an array e g obj and in this case Visual Basic expects to receive a SAFEARRAY as the argument This argument must be a pointer to a pointer to the SAFEARRAY descriptor To permit callback functions to be written in Visual Basic the Solver DLL provides an option to treat all arrays as SAFEARRAYs rather than C style arrays To use this option call setin
206. rtfolio Optimization n set up the LP portion of the problem The LP portion of the objective is all 0 s here it could be elaborated to include transaction costs or other factors lp loadlp PROBNAME 5 2 1 obj rhs sense matbeg matcnt matind matval lb ub NULL 5 2 7 if lp return now set up the Q matrix to define the quadratic objective test whether this DLL supports loadquad if not return if loadquad lp qmatbeg qmatcnt qmatind qmatval 25 x return solve the problem obtain and display the solution optimize lp solution lp amp stat amp objval x NULL NULL NULL printf LPstatus ld Objective 7 5f n stat objval printf xl 5 3f x2 5 3f x3 5 3f x4 5 3f x5 5 3f n n x 0 x 1 x 2 x 3 x 4 Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 39 once more don t forget to free memory unloadprob amp lp Example 5 Use the lpread function to read a problem definition from a disk file and solve it We read the file written by example2 Maximize LP MIP obj 2 0 x1 3 0 x2 Subject To cl 9 0 xl 6 0 x2 lt 54 0 C2 6 0 x1 7 0 x2 lt 42 0 C38 5 0 x1 10 0 x2 lt 50 0 Bounds 0 0 lt x1 lt infinity 0 0 lt x2 lt infinity Integers x1 x2 End As in Example 2 the MIP solution is xl 2 X2 4 Objective 16 0 void example5 void double obj 2
207. ry on your hard disk with standard Windows commands We recommend that you create a directory FRONTMIP in your hard disk root directory e g c frontmip if your hard disk drive letter is c and copy the entire contents of the distribution floppy disk to this directory You can Dynamic Link Library Solver User s Guide Installation e 15 Directory Paths 16 e Installation drag and drop the files in the Windows Explorer or you can use the DOS command xcopy a c frontmip s The resulting directory structure is Frontmip Examples Flexamp Psexamp Vbexamp Vcexamp Winl6 Win32 Help Include Winl6 Win32 The Examples subdirectory contains source code for example programs in four different languages C C Visual Basic Delphi Pascal and FORTRAN The Win16 and Win32 subdirectories within the Examples directory hold compressed archives examples zip containing 16 bit and 32 bit executable of the example programs compiled from the source code plus a compatible version of frontmip dll The Include subdirectory contains an appropriate header file declaring the Solver DLL entry points for each language frontmip h C C header file reference in your source code frontmip bas Visual Basic header file add to your VB project safrontmip bas VB header file w SAFEARRAYs add to your project frontmip pas Delphi Pascal header file add to your Delphi project frontmip for FORTRAN header file reference in your source co
208. s linear and quadratic programming problems with up to 2000 decision variables depending on the version and nonlinear and nonsmooth optimization problems of up to 400 decision variables Any of the variables may be general integer or binary integer It is offered in five different configurations that include only the Solver engines linear quadratic and or nonlinear nonsmooth that you need for your application The Large Scale Solver DLL handles linear and mixed integer linear programming problems of up to 16 384 decision variables At present the Large Scale Solver DLL does not include facilities for solving quadratic nonlinear or nonsmooth optimization problems but future versions may include these capabilities Both Solver DLLs are offered in 32 bit versions for Windows 95 98 and Windows NT 2000 and in 16 bit versions for Microsoft Windows 3 1 You can also run 16 bit applications which call the 16 bit Solver DLLs under Windows 95 98 or NT Solver DLL Frontline s Small Scale Solver DLL is a compact and efficient solver for linear programming LP mixed integer programming MIP and optionally quadratic programming QP problems of up to 2000 decision variables depending on the version and smooth nonlinear programming NLP problems or nonsmooth Dynamic Link Library Solver User s Guide Introduction e 5 The Large Scale 6 e Introduction optimization problems of up to 400 decision variables and 200 constraints in
209. s same code will work in 32 bit Windows 95 98 and Windows NT 2000 but in these environments the MakeProcInstance call is superfluous and Microsoft recommends that you omit it Life is simpler in 32 bits Using Callback Functions Your callback routines can perform any actions you want Usually however the LP pivot or the MIP branch callback routine will inform the user of the progress of the optimization perhaps displaying the current value of the objective function It may also check for a user interaction such as a key press or mouse click signalling that the optimization process should be aborted Here is an excerpt from the code in the next chapter Native Windows Applications which shows how the callback function can be used getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT amp NumPivot getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ amp Objective FPSTR Objective ObjStr wsprintf PivotMsg Pivot ld Obj s NumPivot LPSTR ObjStr SetWindowText hWnd PivotMsg if PeekMessage MSG FAR amp msg hWnd WM_KEYDOWN WM_KEYDOWN PM NOREMOVE if msg wParam VK_ESCAPE return PSTAT_USER_ABORT return PSTAT CONTINUE Dynamic Link Library Solver User s Guide Special Considerations for Windows 3 x e 55 This code uses the Solver API function getcallbackinfo to obtain the LP pivot number and the current value of the objective It formats these values into a string that is displaye
210. s the iteration and current objective value in the window title bar and checks for the ESC key long _CC pivot HPROBLEM lpinfo long wherefrom long NumPivot double Objective char PivotMsg 64 ObjStr 12 MSG msg getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT amp NumPivot getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ amp Objective FPSTR Objective ObjStr wsprintf PivotMsg Pivot ld Obj s NumPivot LPSTR ObjStr SetWindowText hWnd PivotMsg if PeekMessage MSG FAR amp msg hWnd WM_KEYDOWN WM_KEYDOWN PM NOREMOVE if msg wParam VK_ESCAPE return PSTAT_USER_ABORT return PSTAT CONTINUE Define and solve the example MIP problem void RunLPSolver long pstat double pobj double x double obj double rhs 2 0 3 0 54 0 42 0 50 0 a Dynamic Link Library Solver User s Guide Native Windows Applications e 61 char sense LLL long matbeg 0 3 long matcnt 3 3 long matind 0 al 2 O 1 2 double matval 9 0 6 0 5 0 6 0 7 0 10 0 double lb 0 0 0 0 double ub INFBOUND INFBOUND char ctype II HPROBLEM lp NULL _CCPROC lpPivot setintparam lp PARAM ARGCK 1 lp loadlp PROBNAME 2 3 1 obj rhs sense matbeg matcnt matind matval lb ub NULL 2 3 6 if lp return loadctype lp ctype lpPivot _CCPROC MakeProcInstance FARPROC pivot hIns
211. seccecseecaecsaecaeecsecaaecaeecaecaaecaeeeaecaeeneeenes 15 Copying Disk Files Manually 0 0 cccsccesecssecsceeseeeseeeseeeeceseceseenseceseseenseceseceaecseceeceeeseeeneeass 15 Directory Paths 22 2 ec e ce cesses feaSdesect antes reeeiw tested soestecs hentade acest ds hohe deedees iets okt 16 Licensing the Solver D D EASE S T aitele ni csening teeta sisi nie Baoan 17 Registry Entries for Use Based Licensing cescceseesseesseeseeesceeeeeseenseceseeaeenseceeeeeeseeeneenes 17 Designing Your Application 19 Calling the Solver DLL isc a a r a a a Wahi ei heey 19 Solving Linear and Quadratic Problems ccccceessessceseeeseeesceseceseceseceeceecaeeeaeeeeeeneeserensrens 19 Solving Nonlinear Probleemsete R REEERE ERE EARE 20 Solving Nonsmooth Problems ccccsccescsesessceesseeseeeeeeesceeeeseceseeesecaecaeecaeecaeeeaeeeaeeneesereeeees 21 Genetic and Evolutionary Algorithms essseseesesseesseserseseesessreresseseeseseesesseeressese 21 Problems in Algebraic Notation c cccesccescsseseseceseeseecseeeseeeseeeeeeeeseeneeeeeecaeeaecneeceeeseeeneeass 22 Using Other Solver DLL Routines horrei iiir ier e EER E E E E 23 Determining Linearity Automatically s ssseesseeeessesessseessseseessestrsessteressteresteressreesseserseseesesses 23 Supplying a Jacobian Matrix cccccscessesscessceseceseceseceecseeeseceecseecaeeeseeeeeseeeeeeesereneeneeeteeeaees 24 Diagnosing Infe sible Problems co een E E EE E
212. seeeesseeeees 84 Limitations of 16 Bit Visual Basic ccccccccccssecssccessceessecessceessecsseceeseecsseeeeseecsseeeeseeceeseeseeees 94 Callback Funict1 Om o 2s ccgscoe Sedscaci snc cath a seen Sack eae tee aes acess base Sok A R Tene OE 94 Array Size Limitations oss i5 26d ies oes ceive ar toed aes E el Bd A tans nah ad aes 94 Calling the Solver DLL from Delphi Pascal 95 Basic Steps eee ee tests Aaa ee ae ed KA Re a eA a 95 Passing Array and Function Argument cccccccssccesscesecesecesecaeecaeeeseeeeeeseeeereneenaeeeseenaeenaees 95 Building a 32 Bit Delphi Pascal Program cecccesccescceseceseeeseceecaeecseeeeeeeeeeeeeeereneenseenseensees 96 Building a 16 Bit Delphi Pascal Program cecccesccesceeseceseesseceecseeeseeeeeeeeeseeeeeenseenseenseeaees 98 Delphi Pascal Example Source Code cccecccecssessessecesecesecesecaecaeecaeeeseeseeeeeeeereeeeeneeneeeeenaees 98 Calling the Solver DLL from FORTRAN 103 FORTRAN Comipilets 05 205 deccctle ceded a bs Waseda titetk aa a eee so tee 103 Basic Steps es A ch REE EAT E NE atest teu miedo RGA shi eit nina ese 103 Building a 32 Bit FORTRAN Program cccccescceseessecseeeseeeeeeeseeeeeeceeseceseeaeenaecseeeeeneeenes 104 Building a 16 Bit FORTRAN Program cccceecceseceeesceesceceeeeeeeeeeeeeesecnseensecnaeensecneeeneeenes 105 FORTRAN Example Source Code 0 cccccessesssceseeeseceseceeecseesaeeeeeeeneecensecnaeenaeesaeenaeeneeeeeenes 106
213. sen As Long Dim numcols As Long Dim numrows As Long Dim numints As Long Dim nzspace As Long Dim i As Long MsgBox Read problem of unknown size Form2 Textl Form2 Text2 Form2 Text3 Form2 Text4 lpread 0 vbexamp1 objsen numcols numrows numints matcnt 0 1 We would now allocate the x obj lb ub and if used ctype and matbeg arrays to have numcols elements and the rhs and sense arrays to have numrows elements For a dense problem matval should 82 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide sparse problem the sum of the count To keep this exampl nzspace 0 For i 0 To numcols nzspace nzspace Next we could now allocate matind For i 0 To nzspace matval i 0 matind i 0 Next matval and matind lpread we matbeg 0 0 For i 1 To numcols matbeg i matbeg Next Next call loadlp be allocated to have numcols numrows elements the matind be allocated to have nzspace elements For a arrays should where nzspace is s in matcnt as returned by lpread e simple we ll re use the arrays and matval from the first example above ak matent i and matval based on nzspace 1 will be filled in by our next call to need only initialize matbeg based on matecnt 1 i 1 matcnt i 1 and loadctype to define the problem and pass i
214. sion of Visual Basic Another approach is to write the part of your application which calls the Large Scale Solver DLL in C C where you can declare matind and matval as huge arrays while writing the rest of the application including the user interface in Visual Basic Your Visual Basic code would then declare your own C C routine and call it as a DLL Your DLL in turn would call the Solver DLL 94 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide Calling the Solver DLL from Delphi Pascal You can use Version 3 5 of the Solver DLL in Pascal programs created in Borland Delphi either the 32 bit versions Delphi 2 0 and above under Windows 95 98 and Windows NT 2000 or the 16 bit version Delphi 1 0 under Windows 3 x It is straightforward to use the Solver DLL with Delphi You need only include the header file frontmip pas which defines a Pascal unit in your Delphi project and make calls to the Solver DLL entry points at the appropriate points in your code Basic Steps To create a Delphi application that calls the Solver DLL you must perform the following steps 1 Include the header file frontmip pas in your Delphi project and ensure that the unit Frontmip appears in your Use statement s You should also include the directive I frontkey to obtain a license key string from frontkey pas 2 Call at least the routines oadIp or loadnIp optimize solution and u
215. space loadquad qmatbeg qmatcnt qmatind qmatval qnzspace var These three arguments are included for compatibility with the Large Scale Solver DLL In the Small Scale Solver DLL colspace should be equal to cols rowspace should be equal to rows and nzspace should be equal to the number of entries in matval When PARAM ARRAY is 1 the actual size of the matval SAFEARRAY is checked and must match the value of nzspace Loadlp returns NULL if there is an error in its arguments if linear problems are not supported by this version of the Solver DLL if the probname key string is not recognized or in the single threaded version of the DLL if another problem is still active i e if loadIp or loadnIp has been called without a corresponding call to unloadprob You should not change or free the memory for arguments passed to loadIp until after you make the corresponding call to unloadprob INTARG loadquad lp qmatbeg qmatcnt qmatind qmatval qnzspace var HPROBLEM lp LPINTARG gqmatbeg qmatcnt HPINTARG qmatind HPREALARG qmatval INTARG gqnzspace LPREALARG var This routine is called only for quadratic programming problems The first argument must be the value returned by a previous call to Joadip These four arguments describe the nonzero elements of the Q matrix which provides the coefficients of the quadratic portion of the objective function The coefficients of the linear portion of the objective ar
216. syntax of the C programming language but the order of calls the names of routines the arguments and most other programming considerations are the same in other languages You build your application program with a header file specific to the language you are using which declares the Solver DLL routines their arguments and return values and various symbolic constants At run time your application program uses dynamic linking to load the Solver DLL and call various routines within it Details of the process of compiling linking and running your application with the Solver DLL are provided in the chapters on the various languages Solving Linear and Quadratic Problems The overall structure of an application program calling the Solver DLL to solve a linear programming problem is as follows main Get data and set up an LP problem loadlip matval Load the problem optimize Solve it solution Get the solution unloadprob Free memory Your program should first call oadip This function returns a handle to a problem Then you ll call additional routines passing the problem handle as an argument Optionally you may call Joadquad to specify a quadratic objective and or loadctype to specify integer variables Then you call optimize or mipoptimize if there are integer variables to solve the problem To retrieve the solution and sensitivity information call solu
217. t setlpcallbackfunc lp lpPivot optimize lp solution lp pstat pobj x NULL NULL NULL unloadprob amp lp return Define a callback function that computes the objective and constraint left hand sides for any supplied values of the decision variables INTARG _CC funcevall HPROBLEM lp INTARG numcols INTARG numrows LPREALARG objval LPREALARG lhs LPREALARG var INTARG varone INTARG vartwo objval 0 var 0 var 0 var 1 var 1 objective lhs 0 var 0 var 1 constraint left hand side lhs 1 var 0 var 1 constraint left hand side return 0 Define and solve the example NLP problem void RunNLPSolver long pstat double pobj double x double obj 2 double rhs 2 OG R h5 char sense 2 EG double matval 4 double 1lb INFBOUND INFBOUND double ub INFBOUND INFBOUND HPROBLEM lp NULL _FUNCEVAL lpFuncEval _CCPROC lpPivot setintparam lp PARAM ARGCK 1 lpFuncEval _FUNCEVAL MakeProcInstance FARPROC funcevall hInst lp loadnip PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval x lb ub NULL 4 lpFuncEval NULL if lp return lpPivot _CCPROC MakeProcInstance FARPROC pivot hInst setlpcallbackfunc lp lpPivot optimize lp solution lp pstat pobj x NULL NULL NULL unloadprob amp lp return 62 e Native Windows Applications Dynami
218. table version of your Visual Basic application select File Make vbexamp1 exe Note that this executable version still requires the Visual Basic runtime system DLLs as well as the Solver DLL frontmip dll Building a 16 Bit Visual Basic Program In 16 bit Visual Basic 4 0 you may open the same project file vbexamp1 vbp illustrated above for 32 bit Visual Basic 5 0 To do so 1 Start the Visual Basic programming system Select File Open Project and navigate to the Visual Basic example subdirectory for example c frontmip examples vbexamp select vbexamp1 vbp and click OK 2 The Visual Basic system will load the project file the related form and module files and the header files frontmip bas and frontkey bas Because this project 1 was saved in Visual Basic 4 0 format and ii uses frontmip bas and C style arrays it is backward compatible with the 16 bit Visual Basic system 3 When you run the program the forms and buttons look and behave in the same way You simply need to ensure that your program finds and loads the 16 bit version of frontmip dll instead of the 32 bit version by placing it in the current directory or a directory in your PATH However you cannot open and run the project file vbexamp2 vbp This project was saved in Visual Basic 5 0 format and it uses safrontmip bas SAFEARRAYs and the AddressOf operator which are not compatible with the 16 bit Visual Basic system Most new Visual Basic applications are targeted
219. tcallbackinfo lpinfo wherefrom CBINFO ITCOUNT void amp iters getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ void amp 0bj printf Iteration ld Obj g n iters obj return PSTAT CONTINUE void examplel void double obj 2 0 3 0 double rhs 54 0 42 0 50 0 char sense LLL L s for lt E s for G s for gt double matval 9 0 6 0 5 0 6 0 7 0 10 0 double 1b 0 0 0 0 double ub INFBOUND INFBOUND long stat i double objval double x 2 piout 3 slack 3 dj 2 double varlow 2 varupp 2 conlow 3 conupp 3 HPROBLEM lp NULL printf nExample LP problem n set up the LP problem Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 35 lp loadlp PROBNAME 2 3 1 obj rhs sense NULL NULL NULL matval lb ub NULL 2 3 6 if lp return ifdef WIN32 setlpcallbackfunc lp lpcallback set up the callback endif solve the problem optimize lp obtain the solution display objective and variables solution lp amp stat amp objval x piout slack dj printf LPstatus ld Objective g n stat objval display constraint slacks and dual values printf xl g x2 g n n x 0 x 1 for i 0 i lt 2 i printf slack ld 7g piout ld 7g n i slack i i piout i printf n obtain and dis
220. ters Longint obj Double objtext Msg String begin getcallbackinfo lpinfo wherefrom CBINFO ITCOUNT iters getcallbackinfo lpinfo wherefrom CBINFO PRIMAL OBJ obj str obj 4 4 objtext Msg Iteration inttostr iters Objective objtext Application MessageBox PChar Msg callback IDOK Result PSTAT CONTINUE end Define a callback function that computes the objective and constraint left hand sides for any supplied values of the decision variables function funcevall lp Longint numcols Longint numrows Longint var objval Double var lhs DimD var pvar DimD varone Longint vartwo Longint Longint stdcall begin objval pvar 0 pvar 0 pvar 1 pvar 1 objective lhs 0 pvar 0 pvar 1 constraint left hand side lhs 1 pvar 0 pvar 1 constraint left hand side Result 0 end SENDIF Define and solve the example LP MIP problem procedure TForm1 LPButtonClick Sender TObject var objtext string x0 string x1l string begin objective coefficients obj 0 2 obj 1 3 right hand sides of constraints rhs 0 54 rhs 1 42 100 e Calling the Solver DLL from Delphi Pascal Dynamic Link Library Solver User s Guide rhs 2 50 sense of constraints L is lt sense 0 L sense 1 L sense 2 L define constraint coefficients using the sparse matrix form See Solver Us
221. the window procedure MainWndProc we set up a device context paint structure and text metrics and call the API procedure TextOut to write text into the application window whenever a WM_PAINT message arrives On the first such message we call RunLPSolver and RunNLPSolver to solve two example problems Note if your copy of the Solver DLL does not include both the linear and nonlinear Solver engines one of these routines will display a MessageBox noting this fact and the corresponding example problem will display 0 0 for the variables and objective RunNLPSolver uses the callback routine funceval1 to compute values for the objective and the left hand sides of constraints during the solution process as required for all nonlinear problems Both RunLPSolver and RunNLPSolver use the callback routine pivot to display information on each major iteration about the progress of the optimization The pivot procedure uses wsprintf and a supporting procedure FPSTR to build a text message reporting the iteration number and the current objective function value These values are obtained through calls to the function getcallbackinfo The text message is set into the application window s title bar The title bar is reset after the example problems are solved in MainWndProc The pivot procedure then executes the code described in the previous chapter to watch for a press of the ESC key If ESC is pressed before the optimization
222. the Solver DLL you should read the section Arrays and Callback Functions in Visual Basic in the chapter Design ing Your Application You must decide whether to pass array arguments as C style arrays or as SAFEARRAYs C style arrays were the only option in the Solver DLL Dynamic Link Library Solver User s Guide Calling the Solver DLL from Visual Basic e 69 Versions 2 0 and 1 0 but they cannot be used with the nonlinear GRG Solver or the Evolutionary Solver in the Solver DLL Version 3 5 For new applications built with the Solver DLL V3 5 and Visual Basic 5 0 or above we recommend that you use SAFEARRAYs To pass arguments as SAFEARRAYs follow all of these steps 1 Include the header file safrontmip bas in your project 2 Set the parameter PARAM ARRAY to 1 before you call any of the other Solver DLL routines except as needed to set other parameters To do this use a statement such as setintparam PARAM ARRAY 1 3 When you pass an array argument use the name of the array such as obj or matval without any subscript To pass array arguments as C style arrays follow all of these steps 1 Include the header file frontmip bas in your project 2 Ensure that the parameter PARAM ARRAY is 0 before you call any of the other Solver DLL routines it is 0 by default unless you change it 3 When you pass an array argument use the first element of the array such as obj 0 or matval 0 with a subscript The ex
223. the first one except that a jacobian routine is also defined to give the Solver faster and more accurate partial derivatives of the problem functions The third example attempts to solve a nonlinear problem that is infeasible then it uses the IIS finder to diagnose the infeasibility The fourth example illustrates how you can solve a series of linear and nonlinear problems using the testnitype function to determine whether the problem defined by your funceval routine is linear and how you can switch to the LP Solver engine if testn type finds that a problem is entirely linear Also included in vbexamp2 frm examp2 frm and vbexamp2 bas are two example problems using the Evolutionary Solver The first of these finds the global optimum of a classic two variable problem the Branin function which has three local optima The second one finds the optimal solution of a three variable problem where the objective function involves an IF statement which is nonsmooth in fact discontinuous in the variable X You are encouraged to study this source code or the C C source code and the comments in each problem even if you plan to use a language other than Visual Basic for most of your work Like the example source code for linear and quadratic problems these example files are more extensive than the ones for the other languages VBEXAMP2 BAS Global Nonlinear As Boolean Global Example As Long Function funcevall lp As Long ByVal
224. the number of variables The number of rows in the constraint matrix not including the objective function or bounds on the variables Indicates minimization or maximization 1 minimize 1 maximize An array of dimension numcols containing the objective function gradient This array must be present and of the appropriate size but its contents need be initialized only if you are calling oadnItype to specify that some or all of objective gradient elements are constant Otherwise the Solver DLL will fill in this array when it calls your funceval and or jacobian routines An array of dimension numrows containing the constant or right hand side term for each row in the constraint matrix See also the rngval argument below An array of dimension numrows containing the sense of each constraint row sense i L lt constraint sense i E constraint sense i G gt constraint sense i R ranged constraint Note that the value R cannot be used with the Small Scale Solver DLL These four arguments describe the nonzero elements of the Jacobian matrix If the problem has no constraints you may pass NULL values for all of these arguments Otherwise the matval array at a minimum must be present and must be of the appropriate size but its contents need be initialized only if you are calling loadnitype to specify that some or all of Jacobian matrix elements are constant Otherwise the Solver DL
225. there are many possible ways to perform a crossover operation some much better than others and the Evolutionary Solver uses multiple variations of two different crossover strategies Fifth inspired by the role of natural selection in evolution an evolutionary algorithm performs a selection process in which the most fit members of the population survive and the least fit members are eliminated In a constrained optimization problem the notion of fitness depends partly on whether a solution is feasible i e whether it satisfies all of the constraints and partly on its objective function value The selection process is the step that guides the evolutionary algorithm towards ever better solutions A drawback of an evolutionary algorithm is that a solution is better only in comparison to other presently known solutions such an algorithm actually has no concept of an optimal solution or any way to test whether a solution is optimal For this reason evolutionary algorithms are best employed on problems where it is difficult or impossible to test for optimality This also means that an evolutionary algorithm has no definite rule for when to stop aside from the length of time or the number of iterations or candidate solutions that you wish to allow it to explore Aside from such limits the Evolutionary Solver uses two heuristics to determine whether it should stop one based on the converge
226. tion Finally call unloadprob to free memory This cycle may be repeated to solve a series of Solver problems Dynamic Link Library Solver User s Guide Designing Your Application e 19 When you call oadIp you pass information such as the number of decision variables and constraints arrays of constant bounds on the variables and the constraints an array of coefficients of the objective function and a matrix of coefficients called matval above of the constraint functions Solving Nonlinear Problems In a linear or quadratic problem you can describe the objective and constraints with an array or matrix of constant coefficients the Solver DLL can determine values for the objective and constraints by computing the sums of products of the variables with the supplied coefficients In a nonlinear problem however the problem functions cannot be described this way the coefficients represent first partial derivatives of the objective and constraints with respect to the variables and these derivatives change as the values of the variables change Hence you must write a callback function called funceval below that computes values for the problem functions objective and constraints for any given values of the variables The Solver DLL will call this function repeatedly during the solution process You supply the address of this callback function as an argument to loadnIp which defines the overall nonlinear optimization proble
227. tline Systems The DLL that is licensed to you recognizes your specific key string if it is not supplied when JoadIp or loadnIp is called these routines will return NULL and calls to these and other routines will not be successful The number of columns in the constraint matrix i e the number of variables The number of rows in the constraint matrix not including the objective function or bounds on the variables Indicates minimization or maximization 1 minimize 1 maximize An array of dimension numcols containing the objective function coefficients An array of dimension numrows containing the constant or right hand side term for each row in the constraint matrix See also the rngval argument below An array of dimension numrows containing the sense of each constraint row sense 1 L lt constraint sense 1 E constraint sense 1 G gt constraint sense i R ranged constraint Note that the value R cannot be used with the Small Scale Solver DLL These four arguments describe the nonzero elements of the constraint matrix You may pass NULL values for matbeg matcnt and matind if your matval array is a full size dense matrix i e consisting of numcols numrows elements where the elements for each column are consecutive If matbeg matcnt and matind are not NULL values the array matval contains the nonzero coefficients grouped by column i e all coefficients for the same vari
228. to PSTAT_TIME LIM FEAS or PSTAT_ TIME LIM_INFEAS for an LP problem depending on whether a feasible solution has been found On a MIP problem the pstat argument will be set to PSTAT_MIP_TIME LIM _FEAS or PSTAT_MIP_ TIME LIM _FEAS depending on whether a feasible integer solution has been found PARAM EPOPT This is the optimality tolerance or reduced cost tolerance for LP problems Variables whose reduced cost is less than the negative of this tolerance are candidates for entering the basis PARAM EPPIV This is the pivot tolerance for LP problems LP matrix elements must have an absolute value greater than or equal to this tolerance to be candidates for pivoting Dynamic Link Library Solver User s Guide Solver API Reference e 139 PARAM EPSOL This is the solution tolerance in the Large Scale LP MIP Solver DLL Any calculated basic variable whose absolute value is less than this tolerance is treated as Zero PARAM_EPRHS This is the feasibility tolerance within which constraints are considered satisfied and values for decision variables are treated as integer in MIP problems PARAM_EPGAP This is the relative integer objective gap tolerance for MIP problems On such problems it often happens that the Branch amp Bound algorithm will find a good solution fairly quickly but will require a great deal of time to find or verify that it has found the optimal integer solution The integer gap tolerance sett
229. to enable the display of error MessageBoxes by the DLL routines if they detect an invalid value in one of the arguments we pass since there are no errors none will appear 2 We call lpwrite to write out a file which summarizes the LP MIP problem in algebraic form This can help us verify that the arguments we pass have defined the right problem ReDim obj 0 To 1 obj 0 2 obj 1 3 As Double ReDim rhs 0 To 2 rhs 0 54 rhs 1 42 rhs 2 50 ReDim sense 0 To 2 As Double As Byte L s for lt E s for G s for gt sense 0 sense 1 sense 2 OT os an ctype 0 ctype 1 ReDim ma matbeg 0 matbeg 1 ReDim ma matcnt 0 matent 1 ReDim ma matind 0 ReDim ctype 0 To 1 Asc L Asc L Asc L teger B Asc I Asc I tbeg 0 To 1 0 pS 3 tent 0 To 1 k o 3 tind 0 To 5 0 Dynamic Link Library Solver User s Guide As Byte binary C As Long As Long As Long continuous Calling the Solver DLL from Visual Basic e 75 matind matind matind matind matind ReDim matval matval matval matval 1 2 3 4 5 tval 0 To 5 As Double NTNU NDOA ANRPONE 10 0 To 1 As Double it eee ees E ee lb 1 0 ReDim ub 0 To 1 As Double ub 0 INFBOUND ub 1 INFBOUND ReDim x 0 To 1 As Double Adjust FormforExample2 Form2 Show End Sub Private Sub Command3 Click Example 3 Attempt to sol
230. tparam as shown below before calling oadlp loadnip or any of the other problem setup routines ret setintparam NULL PARAM ARRAY 1 When this parameter is set to 1 all arrays passed to the Solver DLL must be SAFEARRAYs In Visual Basic this means that the array arguments must be declared as for example ByRef obj As Double rather than ByRef obj As Double and the array name e g obj instead of the first array element e g obj 0 must be passed as the actual argument In your callback routines you can then use subscripting to refer to elements of the arrays passed to you as arguments The Visual Basic header file frontmip bas contains declarations of the Solver DLL routines that define the arguments as C style arrays The header file safrontmip bas contains declarations of the routines that define the arguments as SAFEARRAYs If you are using Visual Basic for a new Solver DLL application you will probably want to use safrontmip bas as your header file and be sure to call setintparam NULL PARAM ARRAY before calling other Solver DLL routines 28 e Designing Your Application Dynamic Link Library Solver User s Guide Using the Solver DLL in Multi Threaded Applications The Solver DLL is offered in both single threaded and multi threaded versions The single threaded versions are serially reusable but not reentrant They can solve multiple problems serially a call to JoadIp or loadnIp must be follow
231. turns a nonzero value INTARG mipoptimize lp HPROBLEM lp This routine is called in lieu of optimize to solve a mixed integer programming problem The argument p of mipoptimize must be the value returned by a previous call to loadlp or loadnIp When this function is called the Solver DLL will solve the specified optimization problem Mipoptimize returns a value of 0 if successful i e the solution process ran to completion though it may or may not have found an optimal solution see solution for details If the solution process cannot be carried out mipoptimize returns a nonzero value INTARG solution lp pstat pobj x piout slack dj HPROBLEM lp LPINTARG pstat LPREALARG pobj x piout slack dj The argument p of solution must be the value returned by a previous call to loadlp or loadnIp The other arguments are pointers to locations where data may be written This data may include the status of the optimization the value of the Dynamic Link Library Solver User s Guide Solver API Reference e 119 pstat pobj piout slack dj 120 e Solver API Reference objective function the values of the primal variables the dual values the slacks and the reduced costs If some of the data is not required a NULL value may be passed for that argument If there is no optimal solution sensitivity analysis information is not available so the piout slack and dj arguments will be ignored If
232. tware copyright 1991 1999 by Frontline Systems Inc Portions copyright 1989 by Optimal Methods Inc Portions copyright 1994 by Software Engines User Manual copyright 1999 by Frontline Systems Inc Neither the Software nor this User Manual may be copied photocopied reproduced translated or reduced to any electronic medium or machine readable form without the express written consent of Frontline Systems Inc except as permitted by the Software License agreement on the next page Trademarks Microsoft Windows Visual C and Visual Basic are trademarks of Microsoft Corporation Delphi is a trademark of Borland International Pentium is a trademark of Intel Corporation How to Order Contact Frontline Systems Inc P O Box 4288 Incline Village NV 89450 Tel 775 831 0300 e Fax 775 831 0314 e Email info frontsys com Web http www frontsys com SOFTWARE LICENSE Unless other license terms are specified in a written license agreement between Frontline Systems Inc Frontline and you or your company or institution Frontline grants only a license to use one copy of the enclosed computer program the Software on a single computer by one person The Software is protected by United States copyright laws and international treaty provisions Therefore you must treat the Software just like any other copyrighted material except that You may store the Software on a hard disk or network server provided that
233. ues and the matbeg matcnt and matind arrays are the same ones possibly NULL pointers that you supplied to JoadnIp Objtype and matvaltype are the arrays of characters you supplied to oadnitype otherwise they will be NULL pointers The objval argument is a pointer to a location where the scalar objective value should be stored You should store the objective value in objval the gradient of the objective in the obj array and the partial derivative values in the appropriate elements of the matval array taking care not to exceed the dimension nzspace for matind and matval If all elements of the objtype array are L you can skip computing and storing the objective value and gradient if all Dynamic Link Library Solver User s Guide Solver API Reference e 131 elements of the matvaltype array are L you can skip computing the partial derivatives of the problem functions Your routine should return 0 for success or 1 for failure 1 will cause the Solver DLL to stop and return from its optimize call Other Callback Routines For all types of problems nonlinear linear quadratic and mixed integer you can arrange to have the Solver DLL periodically call a routine which you specify In this routine you can access information about the progress of the optimization check for external conditions such as a user interaction etc Your routine can return a value to the Solver DLL signalling that it should continue or halt the optimiz
234. uide Calling the Solver DLL from Delphi Pascal e 101 sense 0 E sense 1 G bounds on variables 1b 0 INFBOUND 1b 1 INFBOUND ub 0 INFBOUND ub 1 INFBOUND to pass NULL or empty arrays NullL 1 NullD 1 SIFDEF WIN32 setintparam Nu lp loadnlp NullL Nu 4 funcev 11L PARAM ARGCK 1 PROBNAME 2 2 1 obj 0 rhs 0 sense NullL 11L matval 0 x 0 1lb 0 ub 0 NullD all nil if lp 0 then Exit setlpcallbackfunc lp callback ret optimize ret solution lp str objval 4 4 objtext lp stat objval x 0 NullD NullD NullD NLPEditl text Status inttostr stat str x 0 4 4 x0 str x 1 4 4 x1 NLPEdit2 text xl x0 SENDIF end end 102 e Calling the Solver DLL from Delphi Pascal Objective objtext x1 Dynamic Link Library Solver User s Guide Calling the Solver DLL from FORTRAN FORTRAN Compilers Basic Steps To use the Solver DLL from FORTRAN you must have an appropriate compiler capable of building 32 bit or 16 bit Windows applications and calling DLLs This Guide will give explicit instructions for use with Microsoft FORTRAN PowerStation 4 0 32 bit and Microsoft FORTRAN 5 1 16 bit but use with other compilers should be similar Microsoft FORTRAN PowerStation 4 0 and FORTRAN 5 1 both allow you to easily port applications written for DOS UNIX or
235. und during the solution process An array of dimension numcols containing the lower bound on each variable A lower bound less than or equal to INFBOUND will be treated as minus infinity An array of dimension numcols containing the upper bound on each variable A upper bound greater than or equal to INFBOUND will be treated as plus infinity An array of dimension rows containing the range value of each constraint right hand side Ranged rows are specified in the sense array If the row is not ranged the Dynamic Link Library Solver User s Guide Solver API Reference e 115 nzspace funceval jacobian loadnitype objtype matvaltype 116 e Solver API Reference corresponding rngval element should be 0 0 A range value for row i means that the constraint left hand side must be between rhs i and rhs i rngval i rngval i may be positive or negative If there are no ranged rows at all 7ngval may be NULL it is ignored when the Small Scale Solver DLL is used This argument should be equal to the number of entries in matval When PARAM ARRAY is 1 the actual size of the matval SAFEARRAY is checked and must match the value of nzspace The address of a user written callback routine which computes the values of your objective function and constraints i e a procedure pointer declared as shown in the section Callback Routines below The address of a user written callback routine which computes a gradient fo
236. ut 2 slack 2 dj 2 HPROBLEM lp NULL printf nExample NLP LP problem 4 n setintparam lp PARAM ARGCK 1 Calling the Solver DLL from C C e 47 Set up the problem for solution by the NLP Solver lp loadnlp PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval x lb ub NULL 4 funceval4 NULL if lp return Test the problem to determine linearity nonlinearity testnltype lp 1 NULL amp nlstat NULL NULL printf ntestnltype s n nlstat NONLINEAR LINEAR Solve the problem using the NLP Solver optimize lp solution lp amp stat amp objval x piout slack dj printf Status ld Objective g n stat objval printf Final values x1 g x2 g n x 0 x 1 unloadprob amp lp if nlstat return The problem was linear Set it up to be solved by the linear Simplex Solver it should find the same solution printf nSolve same problem with loadlp n lp loadlp PROBNAME 2 2 1 obj rhs sense NULL NULL NULL matval 1b ub NULL 2 2 4 Solve the problem using the LP Solver optimize lp solution lp amp stat amp objval x piout slack dj printf Status ld Objective g n stat objval printf Final values x1 g x2 g n n x 0 x 1 unloadprob amp lp Example C program calling the Evolutionary Solver DLL Solves the problem Minimize the Branin function term
237. value and if you have set the PARAM ARGCK parameter to warn about errors in the arguments it will display an error message dialog Most problems based on real world data yield a Q matrix which is positive definite For example if you are solving a portfolio optimization problem where the Q matrix represents variances and covariances of pairs of securities calculated from a historical price series it can be shown that the matrix will be positive definite if the number of observations in the price series is greater than the number of variables If however you are solving problems based on arbitrary user provided data you should take care to test the return value of the Joadquad function and the status value returned by the solution function If the Q matrix is indefinite you may wish to use the nonlinear Solver engine instead of the quadratic Solver engine but you must bear in mind that either solution algorithm will find only a local optimum which is not necessarily the global optimum The oadquad function also accepts a var argument which provides initial values for the variables If the problem is positive negative semi definite or indefinite these initial values will influence the path taken by the solution algorithm and the final solution to which it converges If you must solve problems of this type you can use the var argument to exercise some control over the solutions returned by the Solver DLL Passing Dens
238. value of the wherefrom argument passed to your callback routine This selects the specific information to be returned in the resu t_p argument CBINFO_ PRIMAL OBJ The current objective function value double CBINFO_ PRIMAL INFMEAS The sum of the current infeasibilities double CBINFO_ PRIMAL FEAS 1 if current solution is feasible 0 if not long CBINFO_ITCOUNT Number of iterations so far in the LP problem long CBINFO NODE COUNT Number of branches so far in the MIP problem long CBINFO_ MIP ITERATIONS Total number of LP pivots iterations so far long CBINFO BEST INTEGER Objective value of the incumbent the best integer solution found so far double The address of a variable to receive the requested information this variable must be of the data type implied by the infonumber argument e g a pointer to a double for a call with infonumber CBINFO_ PRIMAL OBJ or a pointer to a long integer for infonumber CBINFO_PRIMAL ITCOUNT Solver Parameters 134 e Solver API Reference The Solver DLL has a number of options and tolerances which you can control to influence the behavior of the LP QP and MIP solution algorithms These are collectively called parameters and may be of either integer or double type Integer parameters are used to select algorithmic options and to set countable limits such as the maximum number of iterations Double parameters are used to set tolerances such as how small an LP matrix pivot e
239. vcexamp1 Maximize LP MIP obj 2 0 x1 3 0 x2 Subject To cl 9 0 x1 6 0 x2 lt 54 0 C2 6 0 x1 7 0 x2 lt 42 0 C3 5 0 x1 10 0 x2 lt 50 0 Bounds 0 0 lt x1 lt infinity 0 0 lt x2 lt infinity Integers x1 x2 End xf lpwrite lp vcexamp1 solve the problem obtain and display the solution mipoptimize lp solution lp amp stat amp objval x NULL NULL NULL printf LPstatus ld Objective g n stat objval printf xl g x2 g n x 0 x 1 don t forget to free memory unloadprob amp lp Dynamic Link Library Solver User s Guide Calling the Solver DLL from C C e 37 Example 3 Attempt to solve the LP model Maximize 2 x1 3 x2 Subj to 9 x1 6 x2 lt 54 6 xl 7 x2 lt 42 5 x1 10 x2 lt 50 xl x2 non negative Infeasible due to non negative variables and negative RHS When solution returns stat PSTAT_INFEASIBLE ask Solver DLL to find an Irreducibly Infeasible Subset IIS of the constraints Row 2 with the negative RHS and lower bounds on both variables The constraint matrix is passed in simple dense form in matval 2 void example3 void double obj 2 0 3 0 double rhs 54 0 42 0 50 0 char sense LLL double matval 9 0 6 0 5 0 6 0 7 0 10 0 double 1b 0 0 0 0 double ub INFBOUND INFBOUND long stat i iisrows iiscols long rowind 3 rowbdstat 3 colind 2 col
240. ve the LP model Maximize 2 x1 3 x2 Subj to 9 x1 6 x2 lt 54 1 6 xl 7 x2 lt 42 i 5 x1 10 x2 lt 50 xl x2 non negative Infeasible due to non negative variables and negative RHS When solution returns stat PSTAT INFEASIBLE ask Solver DLL I to find an Irreducibly Infeasible Subset IIS of the constraints i Row 2 with the negative RHS and lower bounds on both variables The constraint matrix is passed in simple dense form in matval ReDim obj 0 To 1 As Double obj 0 2 obj ATI 3 ReDim rhs 0 To 2 As Double rhs 0 54 rhs 1 42 rhs 2 50 ReDim sense 0 To 2 As Byte L s for lt E s for G s for gt sense 0 Asc L sense 1 Asc L sense 2 Asc L ReDim matval 0 To 5 As Double matval 0 9 matval 1 6 matval 2 5 matval 3 6 matval 4 7 matval 5 10 ReDim 1b 0 To 1 As Double 1b 0 0 lb 1 0 ReDim ub 0 To 1 As Double ub 0 INFBOUND ub 1 INFBOUND ReDim x 0 To 1 As Double 76 e Calling the Solver DLL from Visual Basic Dynamic Link Library Solver User s Guide AdjustFormforExample3 Form2 Show End Sub Private Sub Command4 Click Example 4 Use the QP solver to perform Markowitz style portfolio optimization Variables are the percentages to be allocated to each investment or asset class O lt Xi 2 3 44 x5 lt 1 Minimize portfolio variance xi Q xi Subj to allocat
241. which will be set to the address of the current LP pivot callback routine Before you set the callback with setlpcallbackfunc getlpcallbackfunc will store NULL in this variable setmipcallbackfunc callback INTARG setmipcallbackfunc lp callback HPROBLEM lp _CCPROC callback Your program should call this function prior to calling mipoptimize to specify the callback function which the Solver DLL should call on each branch or LP subproblem in a MIP problem The address of a user written callback routine i e a procedure pointer declared as shown above To eliminate use of the callback function pass an argument value of NULL to setmipcallbackfunc getmipcallbackfunc callback_p getcallbackinfo void getmipcallbackfunc lp callback_p HPROBLEM lp _CCPROC callback_p The address of a procedure pointer variable which will be set to the address of the current MIP callback routine Before you set the callback with setmipcallbackfunc getmipcallbackfunc will store NULL in this variable INTARG getcallbackinfo lpinfo wherefrom infonumber result _p HPROBLEM lpinfo INTARG wherefrom infonumber void result_p Dynamic Link Library Solver User s Guide Solver API Reference e 133 lpinfo wherefrom infonumber result_p This argument identifies the problem it must be the value of the pinfo argument passed to your callback routine This argument identifies the callback type it must be the
242. wn above by calling Jpwrite or Iprewrite This provides a convenient way to verify that the problem you defined programmatically is the problem you intended by examining the resulting text file If you have such a text file containing your problem you can define it by calling pread without setting up all of the array arguments normally required by oadlp and loadctype You can use pwrite and Ipread to persist the definition of a problem on disk between runs of your application program without having to write code to store this data in some file format of your own design You can also use an external program to generate a text file containing a problem definition in the format expected by Ipread then use the Solver DLL to read in the problem and solve it Using Other Solver DLL Routines You can set various parameters and tolerances using the routines setintparam and setdblparam or get current default and minimum and maximum values for the parameters with other routines To obtain control during the solution process in order to display a message check for a user abort action etc you can set the address of a callback routine through a call to setlpcallbackfunc for any type of problem or setmipcallbackfunc for problems with integer variables This feature and the nonlinear Solver which also requires a callback routine can be used only in languages such as C C and 32 bit Visual Basic 5 0 and
243. you are solving a MIP problem sensitivity analysis information is not meaningful and the piout slack and dj arguments must be NULL values Solution returns 0 unless its Jp argument is invalid in which case it returns 1 A pointer to a long integer where the result of the optimization will be stored The specific values which stat pointed to by pstat can take and their meanings are stat 1 PSTAT_OPTIMAL stat 2 PSTAT_ INFEASIBLE stat 3 PSTAT UNBOUNDED stat 5 PSTAT IT LIM FEAS stat 6 PSTAT_IT_LIM INFEAS stat 7 TIME LIM FEAS stat 8 TIME LIM _INFEAS stat 12 PSTAT_ABORT_ FEAS stat 13 PSTAT_ABORT_INFEAS stat 65 PSTAT_FRACT CHANGE stat 66 PSTAT_NO REMEDIES stat 67 PSTAT_ FLOAT ERROR stat 68 PSTAT_MEM_LIM stat 69 PSTAT_ENTRY_ERROR stat 101 PSTAT_MIP_OPTIMAL optimal solution found no feasible solution objective unbounded iteration limit exceeded feasible iteration limit exceeded not yet feas time limit exceeded feasible time limit exceeded not yet feasible user interrupted solution feasible user interrupted solution not yet feas objective function changing too slowly all remedies failed to find a better point error in evaluating problem functions could not allocate enough memory attempt to re enter DLL during solution MIP optimal solution found stat 102 PSTAT_MIP_ OPTIMAL TOL MIP solution within epgap tolerance stat 103 PSTAT_MIP INFEASIBLE n
244. zation using dynamic Markowitz methods for speed and stability e Steepest edge techniques which often substantially reduce the number of pivots e Sophisticated crash like methods for finding an effective initial basis e Basis restart for faster solution of MIP subproblems e Automatic row and column scaling plus control of various algorithm tolerances The Large Scale Solver DLL is described in a separate Solver User s Guide which is available on request from Frontline Systems In the rest of this User s Guide the term Solver DLL refers to the Small Scale version Which Solver DLL Should You Use The Solver DLL is offered in five different configurations that include only the Solver engines linear quadratic nonlinear and nonsmooth that you need for your application The possible configurations are e Linear Simplex Solver only e Nonlinear GRG plus Nonsmooth Evolutionary Solvers only e Both Linear Simplex Solver and Nonlinear GRG plus Nonsmooth Evolutionary Solvers e Linear Simplex Solver plus Quadratic and MIP enhancements e Both Linear Simplex Solver plus Quadratic and MIP enhancements and Nonlinear GRG plus Nonsmooth Evolutionary Solvers Linear Solver The linear LP Solver is the preferred Solver engine for linear programming problems It uses the Simplex method to solve the problem which is guaranteed in Dynamic Link Library Solver User s Guide Introduction e 7 8 e Int

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