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1. MOPS Mathematical OPtimization System MOPS Mathematical OPtimization System User manual MOPS Version 9 x 16 07 2008 MOPS Optimierungssysteme GmbH amp Co KG Alfener Weg 20 D 33100 Paderborn Telefon 49 0 30 838 55009 49 0 5251 66149 E mail uwe suhl mops optimizer com http www mops optimizer com 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS is a registered trade mark Deutsches Patentamt Nr 2017758 All rights reserved No parts of this work may be reproduced in any form or by any means graphic electronic or mechanical including photocopying recording taping or information storage and retrieval systems without the written permission of the publisher Products that are referred to in this document may be either trademarks and or registered trademarks of the respective owners The publisher and the author make no claim to these trademarks While every precaution has been taken in the preparation of this document the publisher and the author assume no responsibility for errors or omissions or for damages resulting from the use of information contained in this document or from the use of programs and source code that may accompany it In no event shall the publisher and the author be liable for any loss of profit or any other commercial damage caused or alleged to have been caused directly or indirectly by this document Printed Juli 2008 in Berlin MOPS User Manual Table of Co
2. The most recent versions of MOPS DLL provide besides the Basic Functions a set of Extended Functions that make it easier to set retrieve and modify single items of a model like costs dual values right hand sides etc Steps for optimization with MOPS DLL The following flowchart shows the necessary steps when building and optimizing a model We use Visual Basic Syntax and assume that the model is transferred via PutModel to the MOPS DLL 1 Data extraction and model generation Primary data is extracted from a database or other sources and modified according to the given problem A model generator in your favorite programming language stores the model data in the following arrays ia ja a Ib ub c typ See PutModel for a description of the arrays 2 Initializing a new model to defaults A new feature since MOPS v9 x is the function Initialize which replaces the former functions AllocateMemory and InitModel and which allocates memory automatically rc Initialize If rc lt gt 0 then exit 3 Setting of non default parameters Use IPM engine for inititial LP and do not use IP heuristic before the B amp C rc SetPameter xlptyp 4 xheutp 0 If rc lt gt 0 then exit 4 Transferring model to the DLL rc PutModel intyp inf m n nz ia 1 ja 1 a 1 Ib 1 ub 1 c 1 typ 1 If rc lt gt O Then exit 5 Optimize model LP and IP rc Optimize 1 Istatus Iphase dfunct check return code and
3. Values lt 0 IPM engine always solves the primal LP gt 0 if m n gt xipdua 100 the dual LP will be solved by the IPM engine Default 150 Type Long See also xIptyp kkkk Back to index KIptyp xlptyp sets the algorithm used to solve the initial LP Values 0 Primal Simplex 2 Dual Simplex 4 Interior point method Default 2 Type O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 74 Long Back to index xluctr A new LU Factorization will be calculated if the number of elements of the current LU Factorization divided by the number of elements of the last Factorization is greater than xluctr Range 1 1 5 0 Default 2 0 Type Double See also xfrinv Back to index xnproc Specifies how many processors should be used for the execution of the IPM engine on a multiprocessor system For example on an Intel Core Duo architecture xnproc should be set to 2 resulting in a 40 reduction of the CPU time Note that the value of xnproc is only relevant ifthe IPM engine is used to solve the initial LP xIptyp 4 Note CP time will increase if you specify xnproc gt 1 and the machine has less than xnproc processors Default 1 Type Long See also xlptyp Back to index xnwluf A new LU factorization uses memory more efficiently The old LU factorization of MOPS can be used by specifying xnwluf 0 The old LU factorization offers a small advantage on ve
4. Eventually you have to change also the size ofthe memory block with AllocateMemory beforehand Input Output MaxRows 14 Maximal number of constraints MaxCols 14 Maximal number of columns MaxNz 14 Maximal number of nonzero elements Re 14 0 OK lt gt 0 Error Example Rc GetMaxDim m n nz Back to index GetNonzero 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 33 GetNonzero Rowindex Collndex Element returns a single nonzero element from the matrix Input Rowindex 14 Row index Collndex 14 Column index Output Element R8 Matrix element Rc 14 0 OK 1 Bad index 10 Model locked Example Re GetNonzero 1 2 Element reads nonzero in row 1 column 2 and stores the coefficient in Element Back to index GetNumberOfColumns GetNumberOfColumns NCols returns the number of columns of the present model Input Output NCols 14 Number of columns Re 14 0 OK 10 Model locked Example Re GetNumberOfColumns 1NCols Back to index GetNumberOfNZ GetNumberOfNZ NNz returns the number of nonzeros of the present model Input Output NNZ 14 Number of nonzeros Re 14 0 OK 10 Model locked Example Re GetNumberOfNZ 1NNz 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 34 Back to index GetNumberOfRows GetNumberOfRows NRows returns the number of rows of the present model Input Output
5. Values min Model is minimized max Model is maximized Default min Type String 8 Back to index xnwcon If the mps input model is in free format and has long names for the identifiers then xnwcon must be set to 1 Note that the convert time is significantly longer if the new convert is used for traditional mps files in fixed format In such a case xstorn is set automatically to 1 and the names are stored in additional arrays Values 0 the standard convert according to the IBM specification is used i e max 8 characters fixed format embedded leading and trailing blanks are significant 1 free format max 255 characters for identifiers no imbedded blanks leading and trailing blanks are not significant Default 0 Type Integer 4 Back to index xoutlv Output level for logging Controls creation of log and sta files Values 0 No logging no statistics 1 Write statistic file after optimization no log file 2 Write statistic file and log file 3 Write statistic file and log file with extended information After each xfrlog iterations a information will be written to the log file Default 2 O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 93 Type Long See also xfnsta xfrlog Back to index xoutsl Determines if IP LP solution will be written to solution file s Values 0 No output to solution file 1 only the column information of an LP IP solu
6. e wi l to save the model or to save the model as e H to close the model e ES to open a MPS AMPL Mod AMPL Dat MPL Mod MPL Dat Triplet or Lindo file O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS STUDIO 60 e e ei to save the file or to save the file as er e to undo or redo D to semi maximize the model window mE 200 to split the model tab vertically or horizontally e 2 to check the model syntax amp to optimize the model N to toggle between AMPL and GNU MathProg for AMPL model processing Es e to set the MOPS parameters gt to execute an AMPL program e 9 for the MOPS Studio settings e to get help Ce to report a bug d to check online for updates Input Window An AMPL MPL MPS Triplet or LINDO Modelfile can be written or updated in the Input Window 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS STUDIO 61 MOPS Studio 101 x na i Tale SE ee 9 A set NUTR set FOOD set NUTR A B1 B2 C 7 set FOOD BEEF CHK FISH HAM MCH MTL SPG TUR param cost FOOD gt 0 param f min FOOD gt 0 param f min f max param f max j in FOOD gt f min j D 100 100 param n min NUTR gt 0 100 param n max i in NUTR gt n min i e 100 100 param amt NUTR FOOD gt 0 D 100 100 Figure 4 Input Window split The Model and Data files of an AMPL m
7. external lower bound Section 5 holds the nonzero elements of the matrix Each nonzero element is stored in a separate line as Triplet i j aij of row index i column index j and nonzero value aij The indices must be in concordance with the numbering of rows and columns used in section 3 and 4 i and j are integers with 1 lt i lt xmand 1 lt j lt xn Further format specifications Comments are only allowed at the beginning of a Triplet file Data items names and values are treated as tokens which are divided by the separator characters blank comma and semicolon These characters may not appear in tokens Integers may not contain a decimal point even if the resulting value is integer 123 0 is not allowed Floating point values must contain a decimal point Names from a Triplet file will only be stored in MOPS if xstorn 7 which is the default for xstorn If xrcmax 0 xstorn will be set to 0 and no names will be stored Error codes If an error occurs when reading a Triplet file the return code from the DLL function ReadTripletFile will be 2 and you can check MOPS parameter xertyp with DLL function GetParameter for further information If you are working with the static MOPS LIB check xrtcod and xertyp directly See Read TripletFile for information about possible error types Example Example of an IP model Min Xa R1 0 5 X1 X2 X3 X4 1 R2 0 5 X1 X2 X4 0 2007 MOPS Optimierungssysteme GmbH amp
8. public static extern int PutNonzeros int iNElements IntPtr iaRowIndices IntPtr iaColIndices IntPtr daNZs D11Import mopsFile public static extern int PutRow int iRowIndex int iMode string sRowName ref double dLhs ref double dRhs D11Import mopsFile public static extern int ReadMpsFile string sFileName D11Import mopsFile public static extern int ReadProfile string sFileName D11Import mopsFile public static extern int ReadTripletFile string sFileName D11Import mopsFile public static extern int SetMaxIPDim int iNCli int iNImp IN ANNO 2 D11Import mopsFile public static extern int SetMaxLPDim int iNRows int iNCols int iNNz int iNLunz int iRcn int iNAdRows int iNAdCols int iNAdNz D11Import mopsFile public static extern int SetParameter string sParameter D11Import mopsFile public static extern int WriteMpsFile string sFileName D11Import mopsFile public static extern int WriteTripletFile string sFileName D11Import mopsFile public static extern int Q hangeColLB int iColIndex double dLB D11Import mopsFile public static extern int ChangeColType int iColIndex int iColType D11Import mopsFile public static extern int ChangeColUB int iColIndex double dUB D11Import mopsFile public static extern int ChangeCost int iColIndex double dCost D11Import mopsFile public static extern int Changelhs int iRowIndex double dLhs LImport mopsFile public static exter
9. 1 All implications are derived and stored they will be used in all logical tests 2 Additionally to option 1 violated Implication Cuts are added during IP preprocessing Default 2 Type Long Back to index xipbnd The user can specify a tree bound to limit the search a node with a LP value worse than xipbnd will be dropped Range xinf xinf Default xinf When minimizing xinf When maximizing Type Double O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 105 See also xrimpr xlpgap xglgap Back to index xiplpt Sets the algorithm to be used to solve the LP at each node during the branch and bound process Values 0 Primal Simplex gt 0 Dual Simplex Default 1 Type Long See also xIptyp Back to index xlifo Set type of mixed LIFO Mixed LIFO is activated if xnodse lt 0 Values 0 end LIFO if node limit is reached 1 end LIFO if LP infeasible or integer 2 end LIFO if functional value is larger than the value xzubnd xzlbnd xbckpa Default 0 Type Long See also xnodse xnlbab xnlstr Back to index xlocs Sets thetype of local search to be used the neighborhood of a node is searched for integer solutions Note that local search can be costly Values 0 no local search 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 106 1 relaxation induced neighborhood search RINS 2 local branching 3
10. 1000 xga 1300 xgb 1600 xgc 1800 xgd 5000 y1 10000 y2 2000 y3 2000 y4 5000 y5 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Case Burma 144 constraints a Logical constraints P3 may only executed if both P1 and P2 are executed 2 y3 lt y1 y2 or better as disaggregated formulation y3 lt y1 y3 lt y2 P4 may only be executed if P3 is executed y4 lt y3 P5 may monly be executed if the embankment dam is build y5 lt y2 At least one of the projects must be accomplished yl y2 y3 y4 y5 gt 1 b Irrigation constraint Region A 1 5 y1 0 1 y3 0 4 y4 gt 0 25 xra 0 1 xga Region B 1 0 y3 0 2 y4 gt 0 25 xrb 0 1 xgb Region C 0 6 y4 gt 0 25 xrc 0 1 xgc Region D 1 2 y5 gt 0 25 xrd 0 1 xgd c constraint of the area under cultivation xra xga lt 5 xrb xgb lt 5 xrc xgc lt 5 xrd xgd lt 5 d Maximal wheat cultivation xga xgb xgc xgd lt 0 3 xga xra xgb xrb xgc xrc xgd xrd Types of variables y 1 y2 y3 y4 y5 are binary variables xga xgb xgc xgd xra xrb xrc xrd are nonnegative continues variables Tableau representation of the model APRA AAA E EE Ea E Aaa a a A E O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual Case Burma 145 9 3 sa JAH pes pn See ES E 55 A m ua EI E AREA E ESA NK EEE O A O EE a EE KPA era E DA E A E ES E AA O A 4 E ES AA E E E A jaw EE E AAA
11. Array of LP solution values Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of rows Example Fills array daLPSol with LP solution values for rows 3 4 and 5 Re GetRowLPSolution 3 5 daLPSol Back to index GetRowLhs GetRowLhs Rowindex Lhs gets left hand side lower bound of a row Input Rowindex 14 Row index Output Lhs R8 Lower bound left hand side Re 14 0 OK 1 Bad row index 10 Model locked Example Re GetRowLhs 1 dLhs Back to index GetRowRhs GetRowRhs Rowlndex Rhs gets right hand side upper bound of a row Input Rowindex 14 Row index Output 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 38 Rhs R8 Upper bound right hand side Re 14 0 OK 1 Bad row index 10 Model locked Example Rc GetRowRhs 1 dRhs Back to index GetRowType GetRowType Rowlndex RowType gets type of a row Input Rowindex 14 Row index Output RowType 14 Type of constraint 1 Unbounded 2 Wea 3 z 4 5 Ranged Rc 14 0 OK 1 Bad row index 10 Model locked Example Rc GetRowType 1 lRowType Back to index GetSolutionStatus GetSolutionStatus gets the status of an IP or LP solution Input Output GetSolutionStatus 4 1 Status undefined Optimal LP solution found LP infeasible LP unbounded LP iteration limit xmiter reached LP time limit
12. ByVal 1StartIndex As Integer ByVal lEndIndex As Integer ByVal pdVal As IntPtr As Integer GetColLB Lib mops dl1 ByVal 1ColIndex As Integer ByRef dLB As Double As Integer 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 46 Declare Function GetColLPSolution Lib mops dl1 ByVal 1StartIndex As Integer ByVal lEndIndex As Integer ByVal paval As IntPtr As Integer Declare Function GetColType Lib mops dl1 ByVal 1ColIndex As Integer ByRef 1ColTyp As Integer SNE en Declare Function GetColUB Lib mops dl1 ByVal 1ColIndex As Integer ByRef dUB As Double As Integer Declare Function GetCost Lib mops dl1 ByVal 1ColIndex As Integer ByRef dCost As Double As ITNLEGSrK Declare Function GetNumberOfColumns Lib mops dl1 ByRef 1NCols As Integer As Integer Declare Function GetNumberOfNZ Lib mops dll ByRef 1NNz As Integer As Integer Declare Function GetNumberOfRows Lib mops dl11 ByRef 1NRows As Integer As Integer Declare Function GetRedCost Lib mops dl1 ByVal l1StartIndex As Integer ByVal 1ColIndex As Integer ByVal pdRedCost As IntPtr As Integer Declare Function GetRowBase Lib mops dll ByVal 1StartIndex As Integer ByVal lEndIndex As Integer ByVal plSta As IntPtr As Integer Declare Function GetRowDualValues Lib mops dl1 ByVal 1StartIndex As Integer ByVal lEndIndex As Integer ByVal pdVal As IntPtr As Integer Declare Function GetRowIPSolution Lib mops dl1 ByVal
13. ByVal lRowIndex8 ByVal lColIndex amp dElement As Long Declare Function GetParameter Lib mops dll ByVal sParameter ByVal sValue As String As Long Declare Function GetRow Lib mops dll ByVal lRowIndex amp ByVal sRowName lRowTypes dLhs dRhs 1Status amp dActivity dRedCost As Long Declare Function Initialize Lib mops dl1 As Long Declare Function InitModel Lib mops dl1 As Long Declare Function MOPS Lib mops dl1 ByVal sFileName As Long Declare Function Optimize Lib mops dll ByVal lDirection 1Status amp lPhaseg dObjFunc As Long Declare Function OptimizeIP Lib mops dll1 ByVal 1FrNod amp 1Nodes amp 1NIntSolg lErrtype amp dObjFunc dLpBound As Long Declare Function OptimizeLP Lib mops dll ByVal 1FrLog amp lIter amp 1NInfeas amp 1LPStatus amp dObjFunc dSumInfeas As Long Declare Function PutCol Lib mops dll ByVal lColIndex amp ByVal lModes ByVal sColName ByVal 1ColTypesg dCost dLB dUB As Long Declare Function PutModel Lib mops dl1 ByVal lIntypes ByVal INF ByVal 1NRows amp ByVal 1NCols amp ByVal 1NNz amp laRowIndices amp laColIndices amp daNZs daLBs daUB daCosts laColTypes amp As Long Declare Function PutNonzeros Lib mops dl1 ByVal 1NElements amp laRowIndices amp laColIndices amp daNZs As Long Declare Function PutRow Lib mops dll ByVal lRowIndex amp ByVal lModes ByVal sRowName dLhs dRhs As Long Declare Functio
14. Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function GetLPSolution Lib mops dl1 ByRef 1IPSta As Integer ByRef dLPFunct As Double ByVal pdXs As IntPtr ByVal pdDj As IntPtr ByVal 1Sta As IntPtr As Integer GetMaxDim Lib mops dl1 ByRef lMaxRows As Integer ByRef lMaxCols As Integer ByRef lMaxNz As Integer As Integer GetModel Lib mops dl11 ByVal lIntyp As Integer ByRef dInf As Double ByRef INRows As Integer ByRef 1NCols As Integer ByRef 1NNz As Integer ByVal plRowIndices As IntPtr ByVal plColIndices As IntPtr ByVal pdAij As IntPtr ByVal pdLBs As IntPtr ByVal pdUBs As IntPtr ByVal pdCosts As IntPtr ByVal plColTyps As IntPtr As Integer GetNonzero Lib mops dl1 ByVal iRowIndex As Integer ByVal 1ColIndex As Integer ByRef dElement As Double As Integer GetParameter Lib mops dll ByVal sParameter As String ByVal sert As StringBuilder As Integer GetRow Lib mops dl1 ByVal lRowIndex As Integer ByVal sRowName As StringBuilder ByRef lRowTyp As Integer ByRef dLoRhs As Double ByRef dUpRhs As Double ByRef 1Status As Integer ByRef dActivity As Double ByRef dRedCost As Double As Integer Initialize Lib mops dl1 As Integer InitModel Lib mops dl1 As Integer Mops Lib mops dl1 ByVal fnpro As String As Integer Optimize Lib mops dl1 ByVal
15. If the model is an IP model the IP run starts automatically after the model has been solved initially as an LP If an error occurs the return code gives further information The output variable Phase states from which optimization phase LP or IP the function returns Input Direction 14 Output Status 14 Optimization direction gt 0 Minimization lt 0 Maximization Solution status 0 Optimal LP or IP solution found 1 LP or IP is infeasible 2 LP model is unbounded 3 Only a suboptimal LP IP solution has been found when a resource limit e g time limit was reached 4 No LP IP solution has been found when a resource limit e g time limit was reached 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 15 Phase 14 Current phase of optimization 0 LP 1 IP ObjFunc R8 Objective function value of the LP IP solution if Status 0 or 3 Re 14 0 OK 1 Resource limit time memory iterations nodes number of IP solutions 2 Input error e g error in model 3 Output error e g no hard disk space 4 Numerical problem Example Running an IP optimization minimization The model has already been loaded rc Optimize 0 stat phase funct if rc lt gt 0 exit If phase 0 Then Stopping in LP phase This can happen 1 If an error occurred when solving the initial LP 2 If the model is an LP 3 an IP model is solved as an LP xlpmip 0 If stat
16. Index 152 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter Introduction MOPS User Manual Introduction 2 1 1 1 Introduction Introduction MOPS Mathematical OPtimization System is a high performance solver for large LP and IP models The abbreviation LP stands for Linear Programming which describes a class of optimization models where all relations are linear and only continuous variables are allowed IP stands for Integer Programming which means pure integer or mixed models with integer and continuous variables The mathematical formulation for these model classes is Maximize Minimize c x rl lt Ax lt ru I lt x lt u x integer forje JI lt J where J 1 n X C l u R rl ru R and Ais a real m n matrix The vectors u rl ru may have elements representing plus or minus infinity This formulation includes free variables and ranged constraints This representation is called the external model representation EMR in contrast to the internal model representation IMR which is the way a model is mapped into the MOPS internal data structures MOPS V 8 x supports the following integer variable types Name Definition Continuous variable can take on any real value in a specified range Binary variable can take on only the values zero or one Integer variable can take on only integer values in a specified range Semi continuous variable This variable is either zero or can t
17. Redim RowIndices maxnonzero Redim ColIndices maxnonzero Redim Aij maxnonzero Rc PutNonzeros NoElements RowIndices 1 Collndices 1 Aij 1 2 Changing a single matrix coefficient Re PutNonzeros 1 4 2 10 0 Replaces element in row 4 column 2 with coefficient 10 If not present the element will be added 3 Deleting a nonzero element Re PutNonzeros 1 4 2 0 0 Back to index PutRow PutRow Rowlndex Mode RowName Lhs Rhs adds a new row to the matrix if Mode 0 or updates an existing row if Mode lt gt 0 A new row will be inserted before Row ndex i e if a new row 17 is inserted the present row 17 becomes row 18 18 becomes 19 and so on 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 41 Input Rowindex 14 Mode 14 RowName C64 Lhs R8 Rhs R8 Output Re 14 Example Row index 0 Insert 1 Update Row name max 64 characters Lower bound left hand side Upper bound right hand side 0 OK 1 Bad row index 2 Not enough memory 3 Lower bound is greater than upper bound 4 Not able to check for identical row names 5 Another row already has got the same name 10 Model locked Note Return codes 4 and 5 serve only for information purposes they are no severe errors and the process of inserting or updating a row will be continued 1 Adding an unbounded constraint DIM xinf As Double lb As Double ub As Double
18. See also xzlbnd xzubnd Back to index xadcol Maximum number of additional columns for extending the LP IP model Default 0 Type Long Back to index xadnon Maximum number of additional nonzeros for LP and IP preprocessing Default O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 80 400000 Type Long Back to index xadrow Maximum number of additional constraints for which can be added during IP preprocessing Default 2000 Type Long Back to index xglgap Relative global gap The Branch and Cut search will be stopped if the relative difference between the objective function value of the best integer solution xzubnd and the objective function value of the best waiting node xzibnd is less than xglgap Thus the search is stopped if xzlbnd xzubnd lt xglgap 1 xzubnd Range 0 xinf Default 1 d 4 Type Double See also xrimpr xabgap xzlbnd xzubnd Back to index xmiter Iteration limit Maximum number of simplex iterations to solve the initial LP Optimization will be stopped after xmiter iterations Default 20 000 000 Type Long 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 81 Back to index xmitip Maximum number of simplex iterations per node during Branch and Bound process Default 30 000 Type Long Back to index xmmax Maximum number of constraints Default 30 000
19. SetMaxIPDim Lib mops dll1 ByVal lMMax As Integer ByVal lNMax As Integer ByVal 1NZMax As Integer As Integer SetMaxLPDim Lib mops dll1 ByVal 1MMax As Integer ByVal 1NMax As Integer ByVal 1NZMax As Integer As Integer SetParameter Lib mops dl11 ByVal s As String As Integer WriteMpsFile Lib mops dl1 ByVal sFileName As String As Integer WriteTripletFile Lib mops dl1 ByVal sFileName As String As Integer GetIPObjValue Lib mops dl1 As Double GetLPObjValue Lib mops dl1 As Double ChangeColLB Lib mops dl1 ByVal 1ColIndex As Integer ByVal dLB As Double As nteger ChangeColType Lib mops dl1 ByVal 1ColIndex As Integer ByVal 1ColTyp As nteger As Integer ChangeColUB Lib mops dl1 ByVal 1ColIndex As Integer ByVal dUB As Double As nteger ChangeCost Lib mops dl1 ByVal 1ColIndex As Integer ByVal dCost As Double As nteger ChangeNonzeros Lib mops d11 ByVal 1NElements As Integer ByVal plRowIndices As IntPtr ByVal plColIndices As IntPtr ByVal pdAij As IntPtr As Integer Changelhs Lib mops dl1 ByVal lRowIndex As Integer ByVal dLhs As Double As nteger ChangeRhs Lib mops dl1 ByVal lRowIndex As Integer ByVal dRhs As Double As nteger GenFileNames Lib mops dl1 ByVal sFileName As String As Integer GetColBase Lib mops dl1 ByVal 1StartColIndex As Integer ByVal 1EndColIndex As Integer ByVal plSta As IntPtr As Integer GetColIPSolution Lib mops dll
20. Type Long Back to index xmreal Size of the memory block in Megabyte MB that MOPS tries to allocate for model s solutions and temporary data If a positive value is specified for mreal this value is taken overriding the automatic allocation However a too small value for mreal might result in an error message There are rare cases where the automatic computation can fail because the Cholesky or the LU factorization has an extraordinary amount of fill Note that there is the possibility to allocate the Choleky factorization in a separate block of memory if the barrier method is used to solve the initial LP depending on the setting of the parameter xipmem Range 0 memory is allocated automatically 64 2000 allocated memory on a 32 Bit platform 64 8000 allocated memory on a 64 Bit platform Default 0 Type Long See also xipmem Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 82 xmxdsk Maximum disk space in MB used for the node file during the Branch and Bound Cut process Note Previous versions of MOPS saved the tree if xmxdsk has been reached and if xfrtree 1 so that the optimization could be continued later on starting with that tree xipbeg 1 This functionality is not supported anymore in recent versions Range 0 xinf Default 100 MB Type Double See also xmxnod Back to index xmxint The branch and cut search is term
21. _ stdcall GETREDCOST long long double typedef long _ stdcall GETROWBASE long long long typedef long _ stdcall GETROWDUALVALUES long long double typedef long _ stdcall GETROWIPSOLUTION long long double typedef long _stdcall GETROWLHS long double typedef long __stdcall GETROWLPSOLUTION long long double typedef long __stdcall GETROWRHS long double typedef long _ stdcall GETROWTYPE long long typedef long __stdcall GETSOLUTIONSTATUS 25 5 CH In C MOPS DLL functions calls must be encapsulated into a class You call the static methods of this class from the model generator Add a new class to your project and copy this code to the class file CMops using System CS using System Runtime InteropServices using System Text namespace CS_Caller MOPSDLL C Inclusion class for MOPS DLL v9 x 12 07 Copy this class to your C code and call the static methods of the class Prefixes of variable names indicate type d double s 24 a integer public class CMops private const string mopsFile Al IO IL IO natal 1 external mport mopsFile mport mopsFile mport mopsFile mport mopsFile ref int iIndex D11 IO KEREN mport mopsFile mport mopsFile mport mopsFile StringBuilder sColName unmanaged string Zwee SD ds DLL functions mu public static extern public static extern pub
22. integer Cost R8 Objective function coefficient LB R8 Lower bound UB R8 Upper bound Output Re 14 0 OK 1 Bad column index 2 Not enough memory 3 Lower bound is greater than upper bound 4 Not able to check for same column names 5 Another column already has got the same name 10 Model locked Note Return codes 4 and 5 serve only for information purposes they are no severe errors and the process of inserting or updating a column will be continued Example Re PutCol 17 0 MyCol 17 1 10 0 0 100 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 40 Back to index PutNonzeros PutNonzeros NElements RowIndices Collndices NZs adds NElements nonzeros to the model Before using this function you must define rows and columns If you want to modify a nonzero coefficient NElements must be 1 so only single nonzeros can be modified For deleting a nonzero element call PutNonzeros with Aij lt xdropm Aji 0 Input NElements 14 Number of elements to be transferred NElements lt xmaxnz Rowindices 14 Array of row indices Collndices 14 Array of column indices NZs R8 Array of nonzero elements Output Re 14 0 OK 1 No constraints defined 2 No variables defined 3 Bad row index 4 Bad column index 5 Not enough memory 10 Model locked Examples 1 Transferring several matrix coefficients Dim RowIndices As Long ColIndices As Long Aij As Double
23. mops dl1 ByVal lRowIndex As Integer As Integer FindName Lib mops dl1 ByVal sName As String ByVal lMode As Integer ByRef lIndex As Integer As Integer Finish Lib mops dl1 As Integer FreeMemory Lib mops dll As Integer GetCol Lib mops dll1l ByVal 1ColIndex As Integer ByVal sColName As StringBuilder ByRef 1ColTyp As Integer ByRef 1NElements As Integer ByRef dCost As Double ByRef dLB As Double ByRef dUB As Double ByRef 1Status As Integer ByRef dActivity As Double ByRef dRedCost As Double As Integer GetDim Lib mops dl1 ByRef 1NRows As Integer ByRef 1NCols As Integer ByRef INNz As Integer As Integer GetIPSolution Lib mops dl1 ByRef 1IPSta As Integer ByRef dLPFunct As Double ByVal pdXs As IntPtr ByVal pdDj As IntPtr ByVal 1Sta As IntPtr As Integer 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 45 Declare Declare Declare Declare Beer Daollzee peclare Beeren Declare Declare Declare Deere Declare Dis Ileus Declare Declare Declare Beeren Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function
24. mops dll ByVal sFileName As Long ChangeColLB Lib mops dll ChangeColUB Lib mops dll ChangeCost Lib mops dl1 Changelhs Lib mops dl1 ChangeNonzeros Lib mops dll daNZs As Long ChangeRhs Lib mops dl1 GenFileNames Lib mops dl GetColBase Lib mops dll laStatus amp As Long ByVal 1ColIndex ByVal dLB As Long ChangeColType Lib mops dl1 ByVal 1ColIndex amp ByVal 1ColType amp As Long ByVal 1ColIndex ByVal dUB As Long ByVal 1ColIndex amp ByVal dCost As Long ByVal lRowIndex amp ByVal dLhs As Long ByVal 1NElements amp laRowIndices amp laColIndices amp ByVal lRowIndex amp ByVal dRhs As Long j ByVal sFileName As Long ByVal 1StartCollndex amp ByVal 1EndColIndex GetColIPSolution Lib mops dl1 ByVal 1StartColIndex8 ByVal lEndColIndex amp daIPSol As Long GetColLB Lib mops dl1 ByVal lColIndex amp dLB As Long GetColLPSolution Lib mops dl1 ByVal 1StartColIndex8 ByVal lEndColIndex amp daLPSol As Long GetColType Lib mops dll ByVal 1ColIndex amp 1ColType amp As Long GetColUB Lib mops dl1 ByVal lColIndex amp dUB As Long GetCost Lib mops dl1 ByVal 1ColIndex amp dCost As Long GetIPObjValue Lib mops dl1 As Double GetLPObjValue Lib mops dl1 As Double GetNumberOfColumns Lib mops dl1 1NCols amp As Long GetNumberOfNZ Lib mops dll 1NNz amp As Lo
25. partial integer variables threshold value yes SOS of type 1 2 3 weights no The threshold values of the semi continuous and semi integer variables and the weights of the SOS are saved in the lower bounds of the belonging variables There are three possible ways to define the weights for a SOS e Reference row only the first element of this set will save the row index of the reference row in the lower bound The remaining lower bounds are set to zero e Weights they are saved for all SOS variables in the lower bound e No specification the lower bounds of the SOS variable are zero The weights are the value of the decreasing order To improve the performance the weights have to be in a decreasing order The extended integer types need a enhanced MPS and Triplet Format Enhanced MPS Format Integer variables with extended integer types need an enhanced MPS format which provides additional marker in the column section and additional types in the bound section Column section In this section SOS variables and binary variables for linearized functions have to be marked SOS The SOS variables are marked with the keywords SOSORG and SOSEND see Integer Variables in MPS To define the three types of Special Ordered Sets the first field of the record include a S1 for the first a S2 for the second and blanks for the third type of SOS ROWS E SOS3 L sosl L SOS2 COLUMNS 2007 MOPS Optimierungssysteme G
26. resource limit memory etc 2 No integer variables in model 2 Input error e g in basis or tree file 3 Output error 4 Numerical problem 6 System error 999 Breakpoint reached optimization can be continued Example The IP optimization is always stopped after having processed 100 nodes and then continued xfrnod 100 Do rc OptimizelP xfrnod xnodes xnints xertyp xzbest xzubnd Tf rc 0 Then MsgBox IP optimization successfully finished Else If rc 1 Then MsgBox Resource problem memory time iterations End If Loop Until rc lt gt 999 Back to index OptimizeLP This function is discontinued and only for backward compatibility Use Optimize instead OptimizeLP FrLog Iter Ninfeas LPStatus ObjFunc Suminfeas starts the LP optimizer This function must also be called when optimizing an IP model to solve the initial LP OptimizelP will be called afterwards When using the Simplex engine see parameter x ptyp the LP optimization will be stopped after FrLog iterations You can use a loop to break and continue the LP optimization run until the model will be solved In case of an error you can use GetParameter to retrieve xertyp xline1 and xline2 to get a more specific error description O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 22 2 4 2 4 1 Input FrLog 14 Number of simplex iterations until next break Output Iter 14 Cumulated number of it
27. sorting error detected in xcomp 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 122 0432 0500 0600 0601 0602 0650 0651 0750 0759 0760 0761 0762 0763 0764 0800 0801 0802 0803 0804 0899 0900 0901 xptaij xm xn 0 function execution rejected internal model is already transformed floating value is out of range value is x range is from y to z value is out of range value is x range is from y to z xsscal must be 1 d0 or 1 d0 its value is input matrix is singular dense matrix is singular a fixed integer variable is nonintegral index is tree file incorrect wrong tree or tree clobbered unresolvable num problems in heuris at node unresolvable num problems in xipopt at node tree file empty problem was already solved disk space too small to restart increase xmxdsk unknown node selection strategy a fixed bound is plus or minus xinf xaprow row index out of range xaprow row index not increasing xaprow col index out of range xaprow lower bound is larger than upper bound your test license expired fatal error in model generator copyright statement not correct 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter MOPS Input Files MOPS User Manual MOPS Input Files 124 7 7 1 7 2 MOPS Input Files MOPS Input Files The MOPS Input Files pass data and parameter settings to MOPS e Profile e Data Input Profil
28. xgtlps xgtmod xgtnz xgtrow xtrdat xdefau xinitm xoptim xoptip xoptlp 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS LIB 53 PutCol xptcol PutModel xptmod PutNonzeros xptnzs PutRow xptrow ReadMpsFile xrdmps ReadProfile xrprof ReadTripletFile xrdtri SetMaxIPDim SetMaxLPDim SetParameter WriteMpsFile xstmps WriteTripletFile xsttri ChangeColLB xchclb ChangeColType xchctype ChangeColUB xchcub ChangeCost xchcost ChangeNonzeros xchnzs ChangeLhs xchihs ChangeRhs xchrhs GenFileNames xgenfn GetColBase xgtcbs GetCollPSolution xgtxx GetColLB xgtclb GetColLP Solution xgtxx GetColUB xgtcub GetColType xgtctype GetCost xgtcost GetIPObjValue GetLPObjValue 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS LIB 54 3 3 GetNumberOfColumns GetNumberOfNZ GetNumberOfRows GetRedCost xgtrco GetRowBase xgtrowbs GetRowDualValues xgtrco GetRowLhs xgtrowlhs GetRowIPSolution xgtxx GetRowLPSolution xgtxx GetRowRhs xgtrowrhs GetRowType xgtrowtype GetSolutionStatus Note For accessing MOPS LIB functions in HP Compaq Visual Fortran 6 environments former Digital Visual Fortran you must change two options Fortran gt External Procedures gt Argument Passing conventions must be set to C By Reference and Runtime Error Checking for Array and String Bounds must be disabled For Intel applies the same accordingly Calling MOPS LIB from C C The
29. 0303 0353 0355 0357 0400 0401 0402 0403 0404 0405 0406 0407 0408 0409 0410 0412 0413 0414 0415 0419 0420 0421 0422 0423 0424 0425 0426 0428 0429 0430 0431 duplicate row entry in range section xbound appears twice bound vector name missing illegal bound type column name unknown bound redefined with different value or type problem infeasible due to non integer bound wrong section card after bounds section first basis card is not aname card wrong type for basis card wrong type for basis card end marker e is missing in save basis file premature end of save basis file xm out of range xn is out of range xn xj is not equal to xm xn xnzero out of range xjep xn 1 1 is not equal to xnzero pointer xjcp is not increasing problem is unbounded duplicate row entry in column section row index out of range magnitude of element is smaller than xdropm magnitude of element is larger than xmaxel system error by checking logicals system error by checking bounds xrclen out of range inconsistency between xjcp xn 1 1 and xnzero column zero but xnenta not equal zero a fixed variable has an infinite bound index is lower bound larger than upper bound inactivated row in active part of column activate row in inactivated part of column xjcp 1 has to be positive xrcfre is greater than xrcmax xcoptr 1 has to be positive col index out of range name longer than xnamax characters xnenta negative
30. 10 Type Long Back to index xmxtlp Maximum CPU time in minutes for solving the initial LP The optimization will be terminated after xmxtlp O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 84 6 2 6 minutes if no solution has been found until then Range 0 xinf Default xinf Type Double See also xmxnod xfrbas xbatyp Back to index Tolerances Index xdropm xrimpr xtold1 xtold2 xtolin xtolpv xtolqi xtolr1 xtolr2 xtolre xtolx xtolx1 xtolx2 xtolzr xdropm A matrix coefficient smaller than xdropm will be set to 0 0 Range 0 0 1 0E 4 Default 1 0E 7 Type Double Back to index xrimpr After each IP solution found xzubnd will be set to xzbest xrimpr xzbest xsscal so the next integer solution must be xrimpr 100 better than the previously found solution with objective function value xzbest After the Branch and Bound process it will be proved that the best solution found is maximal xrimpr 100 away from the global optimum xsscal 1 when minimizing and xsscal 1 when maximizing 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 85 Range 0 0 1 0 Default 1 0E 4 Type Double Back to index xtold1 Dual feasibility tolerance in phase 1 of the Simplex Reduced costs must be greater than xtold1 to be taken into the basis Range 1 0E 10 1 0E 1 Default 1 0E 7 Type Double Ba
31. LOGISCH5 1 000 LOGISCH4 1 000 ANKANALB OBJECTIV 2000 000 WASSERA 5 LOW ANKANALB WASSERB 1 006 LOGISCH1 2 000 ANKANALB OGISCH3 OO LOGISCH5 1 000 ANKANALC OBJECTIV 2000 000 WASSERA 400 ANKANALC WASSERB 200 WASSERC 500 ANKANALC OGISCH3 1 000 LOGISCH5 1 000 KRAFTWER OBJECTIV 5000 000 WASSERD 121010 KRAFTWER OGISCHA 1 000 LOGISCH5 1 000 IEN00001 MARKER INTEND RHS RHS ANBAUA 5 000 ANBAUB 5000 RHS ANBAUC 5 000 ANBAUD 5 000 RHS LOGISCH5 1 008 BOUNDS UP BOUNDS EIKANALA 1 000 UP BOUNDS STAUDA 1 000 UP BOUNDS ANKANALB 1 000 UP BOUNDS ANKANALC 1 000 UP BOUNDS KRAFTWER 1 000 ENDATA 94 Triplet File Triplet file for the Burma model 13 13 47 202 Le 020 DH 1e7020 1100 RELSAN H Ie 020 1300 0 Ras H ler020 1400 0 REISE O legan 1600 Via SDI 167020 1000 0 CE REDES D LEO2Z0 1300 Q WG NDS H Ter020 1800 0 GENELDE D 167020 1900 Gia NS DD 0 1 5000 2 EIKANALA O 1 10000 2 STAUBDANMMN 0 1 2000 2 ANKANALB 0 1 2000 2 ANKANALC EEGEN 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Case Burma 147 H 184020 LOGISCH Y 0 ler020 VMOELS CES O le 020 LOGISCH4 167020 1 LOGISCH O le 020 WASSERA 0 le 020 WASSERB O le 020 WASSERC O le 020 WASSERD 5 le 020 ANBAUA 5 l1e 020 ANBAUB se OON ANDA WE 5 le 020 ANBAUD O Le 020 MEERE LS 1 L
32. Manual MOPS Parameter 76 values Based on the results it may detect redundant rows and fixes variables on their bound 8 Cheap dual test This procedure performs optimality tests based on the signs of the nonzero values ofthe columns 16 Dual feasibility check The same as the primal but on the dual problem Bounds on the dual variables are tightened if possible 32 Primal bound check and relaxation This procedure detects hidden free variables in the problem 64 Searching identical variables This procedure detects splitted variables in the problem and replaces them with an appropriate one The process also performs this check on the dual problem and removes duplicated rows 128 Doubleton row check This procedure generates free variables in doubleton rows This procedure modifies the bounds of the variables Therefore final dual slack values may not correspond to the original problem 256 Aggregator This procedure eliminates free variables 512 Linear dependency check This procedure detects linearly dependent rows in the constraint matrix 1024 Sparser This procedure makes the constraint matrix sparser This procedure performs row transformations therefore may changes the dual values 2048 Bound restoring MOPS restores the original bounds on the variables after the aggregator if this bit is turned on In such a case MOPS takes slightly more iterations in primal simplex or IPM in general but in special case
33. NRows 14 Number of rows Re 14 0 OK 10 Model locked Example Re GetNumberOfRows 1NRows Back to index GetRedCost GetRedCost StartCollndex EndCollndex RedCost gets the reduced cost of a number of columns after optimization The array RedCost will be filled and must have sufficient size at least EndCollndex StartCollndex 1 Input StartCollndex 14 Start index of columns EndCollndex 14 End index of columns Output RedCost R8 Array of reduced cost values Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of columns Example Fills array daRedCost with reduced cost values for columns 3 4 and 5 Re GetRedCost 3 5 daRedCost Back to index GetRow GetRow RowIndex RowName RowType Lhs Rhs Status Activity RedCost returns data for one row Wurde das Modell nicht optimal gel st sind die Werte f r Status Activity und RedCost nicht definiert The variable RowName must be long enough to receive the complete name of the constraint MOPS DLL is not able to extend an insufficiently dimensioned string variable Use Dim sRowName as string 64 in Visual Basic 6 0 for a proper dimensioning O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 35 Input Rowindex 14 Output RowName C64 RowType 14 Lhs R8 Rhs R8 Status 14 Activity R8 RedCost R8 Re 14 Example Rc GetRow 17 reads
34. O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual Introduction 3 1 2 Dynamic Linked Library MOPS DLL 32 and 64 bit Static Library MOPS LIB 32 and 64 bit Command Line Executable MOPS EXE and MOPS64 EXE MOPS Studio Clip MOPS Excel Plug In These interfaces offer a variety of functions for generating loading modifying saving and optimizing LP and IP models There is aMOPS White Paper which can be used in conjunction with this user manual The MOPS White Paper offers background to this user manual and covers history of the MOPS system basic algorithms and concepts system and its architecture research and development aspects references books and research papers What s new in MOPS 9 x MOPS 9 x has an improved memory management The required amount of main memory is allocated as a function of problem size and the parameter settings The parameter xmreal default is xmreal 0 determines if memory is allocated automatically or if xmreal gt 0 if xmreal MB are to be allocated by request MOPS 9 x uses a cut pool to store all derived cuts If the parameter xusepl is greater than zero default is xusepl 0 the cut pool is used otherwise all violated cuts are inserted into the coefficient matrix at each supernode of IP preprocessing Interior Point and Dual Simplex algorithm for solving LP models are significantly improved See parameter x ptyp for details The best ordering heuristic to be used
35. Re GetParameter xinf Value xinf CDbl Value lb xinf ub xinf Rc PutRow RowIndex 0 MyRow_1 1b ub 2 Adding a lt 5 constraint lb xinf ub 5 Rc PutRow lRowIndex 0 MyRow_2 lb ub Back to index SetMaxIPDim SetMaxIPDim NCli Nimp NZcl NNod changes the maximal IP model dimensions defined in AllocateMemory The maximal dimensions of the LP are not changed If a value is zero its default value will be used Call SetMaxIPDim before building the model and calling Optimize Input NC 14 Nimp 14 NZel 14 NNo 14 Max number of cliques Max number of entries for clique and implications Max number of entries for clique elements Max number of nodes in main memory node table 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 42 2 5 2 5 1 Output Re 14 0 OK lt gt 0 Error Example Set the number of nodes of the main memory node table to 2000 and keep defaults for the other parameters Rc SetMaxIPDim 0 0 0 2000 Back to index Back to index SetMaxLPDim SetMaxLPDim mx nx nzx lunzx renx adm adn adnz changes the maximal dimensions of an LP model set in AllocateMemory If zero is passed for a parameter its default value remains unchanged Input mx 14 Max number of constraints nx 14 Max number of structural variables nzx 14 Max number of nonzero elements in the matrix unzx l4 Max number of nonzero ele
36. Value1 Name3 Value2 Furthermore the following rules must be considered An MPS data deck should not contain more than one model Several N constraints RHS RANGES and BOUNDS vectors are possible Names are fixed length strings of 8 characters Two names with different numbers of blanks at the beginning and end are regarded as different Example The names bbJACKbb and bbbJACKb are different with b representing a blank character Row and column names are separately saved Rows and columns can have the same name but it is not recommended e MOPS does not accept Dx Rows in the ROWS section Le a row may not be a linear combination of other constraints Scaling factors identified by the keyword SCALE in field 2 and a scaling value in field 4 will be ignored e Also scaling information will not be supported in the COLUMNS section e Integer variables must have upper and lower bound in the intervall 32767 32767 If integer variables exceed these values the respective bound will be set accordingly without an error message or a warning Example Example of an IP model Min Xa R1 0 5 X1 X2 X3 X4 1 R2 0 5 X1 X2 X4 X lt 2 X22 0 X3 lt 20 Ka lt 30 and integer 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 127 7 3 2 3 1 5 15 25 40 50 NAME NONAME ROWS N OBJ FUNC DG Si E R2 COLUMNS X1 R2 0 50000 RI 0 50000 x2 R2 1 0000
37. are the ideal way of interchanging models between different MP systems Note that MOPS supports only the original MPS format from IBM where the data is positioned in fixed fields The general structure of arranging date within an MPS file is as follows NAME Name of model ROWS Here constraints and objective function are specified COLUMNS Here variables and nonzero elements are specified column wise RHS Here the right hand sides are listed RANGES Here individual bound for constraints can be specified BOUNDS Here individual bounds for single variables can be specified ENDDATA The following main rules apply to any MPS file A data deck starts always with the token NAME and ends with the ENDATA keyword e Adata deck contains different sections which start with the keywords NAME ROWS COLUMNS RHS RANGES and BOUNDS O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Input Files 126 7 3 2 2 These sections must always be there NAME ROWS and COLUMNS Other sections are optional e Within a section data is stored row wise and a row may not be longer than 80 characters e One data deck can contain several RHS RANGES and BOUNDS sections e Comments are have an asterisk in column 1 and will be ignored by the processor A data set one row of an MPS file consists of six data fields Field 1 2 3 4 5 6 Columns 2 3 5 12 15 22 25 36 40 47 50 61 Content Type Name Name
38. b and bu are real m vectors The vectors u bl bu can have elements that are plus or minus infinite inf to represent unbounded variables or constraints For equations the values b and bu must be identical 1 m and J 1 n are index sets for constraints and variables J is a subset of J and contains all indices of integer variables If JI is empty the model is pure LP The vector must be stored in positions 1 n of the input array Ib and b in positions n 1 n m of Ib Similarly the vector u must be stored in positions 1 n of the input array ub and bu in positions n 1 n m of ub Input Intyp 14 inf R8 m 14 n 14 nz 14 ia 1 nz 14 ja 1 nz 14 a 1 nz R8 Ib 1 n m R8 ub 1 n m R8 c 1 n R8 type 1 n 14 Output Re 14 Example Mode of storing the model in the returned arrays ia ja a O Triplets in ia ja a The triplets i j aij have no special order 1 Row wise storage where ia contains in positions 7 m the start position of the rows in arrays ja and a 2 Column wise storage where ja contains in positions 1 n the start positions of the columns in arrays ia und a Value that represents infinity e g 1 0820 Number of rows Number of columns Number of nonzeros Row indices intyp 0 2 or start positions of rows intyp 1 Columns indices intyp 0 1 or start positions of columns intyp 2 Nonzero elements of the matrix triplets row w
39. breaking rule is most fractional part Default 5 Type Long Back to index xclict Determines if Cliques Cuts will be produced during IP preprocessing Values 0 No Cliques will be derived 1 All Cliques will be saved and used during logical tests 2 Additionally to option 1 violated Clique Cuts are added during IP preprocessing Default 2 Type Long 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 98 Back to index xcored Sets coefficient reduction level during IP preprocessing Values 0 No coefficient reduction 1 Simple coefficient reduction 2 Extended coefficient reduction based on Probing can be time consuming Default 1 Type Long Back to index xcovct Determines if and how Cover Cuts are derived during IP preprocessing Values 0 No Cover Cuts are derived 1 Violated Cover Cuts are derived only during the initial IP preprocessing 2 Cover Cuts are only derived when the objective function value improves 3 Cover Cuts are derived during each IP preprocessing Default 2 Type Long Back to index xeucrd Euclidean reduction of constraints during IP processing Values 0 no euclidean reduction 1 use euclidean reduction Default 1 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 99 Type Long Back to index xflwct This parameter determines if flow cuts should be derived Values flow cov
40. card missing in mps data file rows section card missing in mps data file no valid rows specified no objective function specified illegal row type row name blank row name x at record y already present row index of duplicate hash table too small increase xmxnen row limit exceeded increase xmmax name space too small increase xrcmax column section card missing column name missing nonzero limit to small increase xnzmax or xadnon col name x at record y already present col index of duplicate column hash table too small increase xmxnen col limit exceeded increase xnmax duplicate row entry in column section row name unknown illegal numerical value in mps file at record nonzero different from 1 0 in sos row a non sos variable has a nonzero in a sos row wrong section card after column section magnitude of nonzero too large preceeding marker not correctly closed row name in sosorg marker card not found sos row was already defined sos row is not equality row rhs name missing too many nonzeros increase xnzmax rhs value is different from 1 0 in sos row rhs value for an N row is illegal xrhs appears twice wrong section card after rhs section row name x in rhs section at record y already present xrange appears twice wrong section card after range section 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 121 0203 0222 0223 0224 0225 0226 0227 0228 0301
41. double Input strings must be zero terminated Output strings must be sufficiently dimensioned If the MOPS DLL returns for example a 255 byte long string than the string passed to the function must also be at least 255 bytes long the DLL will not extend the string if it is too short e Scalar numerical input variables long double are always passed By Value e Scalar numerical output variables long double are always passed By Reference Strings are always passed By Reference e Arrays are always passed By Reference Calling Convention is STDCALL Debugging All DLL functions pass back a return code which is zero if the function has been executed successfully otherwise it is nonzero Return codes should always be checked to avoid consecutive faults If a return code is not zero in most cases the MOPS parameters xertyp xline1 and xline2 provide an error code and a short description of the error Check these parameters with GetParameter for a more precise specification of the occurred error When developing your application you can activate MOPS logging for debugging purposes The parameter xoutlv determines whether a logfile with name xfnmsg will be written Most MOPS functions will write short messages into this logfile when they are called which it is a very helpful tool in the debugging process Writing a logfile of course slows down your application so don t forget to disable logging when running optimizations in productive
42. integer variables including 0 1 variables Type Long Back to index xmxj1 Current number of binary variables Type Long Back to index xn 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 117 Current number of structural variables Type Long Back to index xnints Number of integer solutions found so far Type Long Back to index xnodes Current number of nodes in Branch amp Bound process Type Long Back to index xnzero Current number of nonzero elements in the internal model Type Long Back to index xrtcod Return code of the last procedure executed Ifthe optimization of a LP model has an abnormal ending xrtcod can have following values Iteration or resource limit reached input error in IMR or basis output error numerical problem DON system error Ifthe Branch and Bound ends abnormal xrtcod can have following values 1 Node Iteration or CPU time limit reached 2 input error in IMR or Branch and Bound 3 output error 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 118 6 3 2 numerical problem 5 not enough storage for LU matrix 6 system error Type Long See also xertyp Back to index xversn MOPS version info Type C80 Back to index xzlbnd Current lower upper bound of all waiting nodes when minimizing maximizing Type Double Back to index xzubnd Current
43. large Use GetDim to retrieve the dimensions of the current model in main memory Input Intype 14 Output inf R8 m 14 n 14 nz 14 ia 1 nz 14 ja 1 nz 14 a 1 nz R8 Ib 1 n m R8 ub 1 n m R8 c 1 n R8 type 1 n 14 Re 14 Back to index GetParameter Mode of storing the model in the returned arrays ia ja a O Triplets in ia ja a The triplets i j aij have no special order 1 Row wise storage where ia contains in positions 1 m the start position of the rows in arrays ja and a 2 Column wise storage where ja contains in positions 7 n the start positions of the columns in arrays ia und a Value to represent infinity Le any bound that has inf as its absolute value is treated as unbounded Number of rows number of columns Number of nonzero elements Row indices intyp 0 2 or start positions of rows intyp 1 Columns indices intyp 0 1 or start positions of columns intyp 2 Nonzero elements of the matrix triplets row wise or column wise Lower bound for structural variables and constraints Upper bound for structural variables and constraints Objective function coefficients Type of structural variable 0 continuous lt gt 0 integer 0 OK 2 No model present or error in model 10 Model locked GetParameter Parameter Value returns a MOPS parameter The parameter is always returned as as string UseSetParameter to change a parameter See chapter MO
44. library via SetParameter when using the DLL or by setting them in a MOPS profile Most models can be solved with the default values of MOPS parameters but very often appropriate parameter tuning reduces the runtime of a model dramatically For further information refer to the MOPS White Paper The input parameter are divided into e File names e IP Parameters e LP Parameters e MPS vector names e Ressource limits e Tolerances e Other Parameters File names Index xfnbai xfnbao xfnips xfnlps xfnmps xfnmsg xfnsav xfnsta xfnlog xfnpro 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 67 xfnbai Specifies a filename of a basis saved in punch format from a previous run to restart the LP optimization with a simplex engine primal or dual but not IPM Type String 255 See also xstart Back to index xfnbao Specifies a filename of a basis to be saved saved in punch format at the end or after xfrbas iterations when using one of the simplex engines primal or dual Type String 255 See also xfrbas xbatyp Back to index xfnips File name optionally with path for the integer solution An IP solution file will be written if xouts gt 0 Type String 255 See also xoutsl Back to index xfnlog File name optionally with path for the log file Parameter xoutlv determines if a log file will be written and how detailed it is Type String 255 Back
45. or triplet The DAT file are not included automatically in the AMPL model It has to be included with the command include If the command solve is multiple called the LP IP solution and the static are only refer to the last optimization pass If the execution of an AMPL model produces a great amount of output the output buffer has to be increased see Options For the most models the default size of 2 MB has is adequate 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS STUDIO 64 e f the optimization has to be terminated before the end is reached the two processes ampl exe and mopsampl exe have to be stopped with the task manager Solution After the optimization of amodel MOPS Studio shows following output files e Statistic which includes all information about the model and the optimization e LP Solution and if existing an IP Solution e Solution Summary which includes solution values of each variable in the model It is only shown when AMPL models are executed 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter MOPS Parameter MOPS User Manual MOPS Parameter 66 6 6 1 6 2 6 2 1 6 2 2 MOPS Parameter MOPS Parameter MOPS uses a number of parameters The most important parameters are described in this manual e Input Parameter e Output Parameter Input Parameter Input Parameter MOPS Input Parameters can be set directly when using the static
46. rounding in branch and bound 4 total rounding at every xnlbab nodes 5 various rounding and diving heuristics at every xnlbab nodes Default 0 Type Long See also xnodse xnlbab xnlstr Back to index xlotst Determines the level of bound reduction for continuous variables 0 No bound reduction of continuous variables 1 all bounds of continuous variables are reduced 2 only the bounds of continuous variables with free integer variables in its rows are reduced 3 only the bounds of continuous variables with a change greater equal 0 05 are reduced Default 2 Type Long Back to index xipgap if xipbnd xinf and xlpgap lt xinf a tree bound xipbnd is computed after the first IP preprocessing xipbnd funct xlpgap funct if minimization and xipbnd funct xlpgap funct if maximization Note that a too small value for xlpgap might lead to a branch and bound cut search with no integer solution Range 0 xinf Default xinf Type Double 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 107 See also xipbnd xinf Back to index xipmip This parameter determines if an IP model will be solved as IP or if only its LP relaxation is solved Note that the LP preprocessing might be different in both cases Values 0 Only the LP relaxation of an IP model will be solved 1 IP model will be solved Default 1 Type Long Back to index xmirct Thi
47. runtimes for some integer models parameter xbndra A new heuristic for the initial solution of an IP model is available when setting parameters xnodse 3 xheutp 4 and setting parameter xmnheu for the number of nodes in the heuristic Saving and restoring of Branch and Bound trees is no longer supported Improved Gomory Mixed Integer Cuts may reduce solution times for some models Mixed Integer rounding xmirct and flow path cuts xflwct result in significant performance gains on some integer optimization problems A new DLL function Optimize combines and replaces OptimizeLP and OptimizelP The status of an IP solution returned by Get PSolution is now identical to the status returned by Optimize Modified return codes of DLL function MOPS Completely reworked IMR interface for when using the static MOPS LIB library from Fortran or C Additional DLL functions for building and modifying models 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter MOPS DLL MOPS User Manual MOPS DLL 6 2 2 1 MOPS DLL Using MOPS DLL The Dynamic Link Library MOPS DLL can be used under Windows from a variety of programming languages Any language that supports 32 bit DLL calls and features the data types listed below can callthe MOPS DLL The MOPS DLL can be used from Visual Basic C C Fortran Delphi as well as from any NET language such as VB NET CA Delphi NET etc There is also a 64 bit version of the MOPS DLL
48. systems Resource limits A number of MOPS parameters allows you to set resource limits that lead to a stop or a break of the optimization run when the respective value is reached There are resource limits for optimization time quality of the solution main memory and hard disk space If you don t know beforehand how the model will behave at run time you should set resource limits Particular large models might end up in sheer endless optimization runs if no resource limits have been set To stop such a running application you have to force a break which might lead to a crash and loss of data of the whole development environment this is especially in Visual Basic 6 0 the case Basic functions Basic functions Alphabetical list of MOPS DLL basic functions Index Initialize Finish GetIPSolution GetLPSolution GetModel GetParameter LoadModel MOPS Optimize 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 9 PutModel ReadMpsFile ReadProfile ReadTripletFile SetParameter WriteMpsFile WriteTripletFile Discontinued functions AllocateMemory FreeMemory InitModel OptimizelP OptimizeLP See Extended Functions for more functions Finish Finish frees all memory previously allocated for the model and closes all open files This is usually the last MOPS DLL function you will call in your model generator Input Output Re 14 0 OK lt gt 0 Error Example Re Finish Back to index G
49. upper lower bound of all waiting nodes when minimizing maximizing xzubnd is calculated from xipfun and xrimpr Type Double Back to index Error Message Every error has an explicit error code which is saved in the output parameter xertyp The following table includes the error codes with the corresponding error messages error code error message 0001 LP iteration limit xmiter reached xmiter is 0002 LP time limit xmxtlp reached xmxtlp is 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 119 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0050 0051 0054 0055 0058 0060 IP time limit xmxmin reached xmxmin is node LP iteration limit xmitip reached xmitip is insufficient space for LU factors increase xmxnen node limit xmxnod reached xmxnod is nodes buffer size to small increase xmxnin disk full optimization terminated granted disk space exhausted increase xmxdsk xmxnen must be larger than xnzero pivot element in LU factorization is too small disk capacity insufficient to restart IP optimization node memory insufficient to restart IP optimization required no IP solutions reached basis incorrect basis size is basis incorrect basic bit not set for basis incorrect duplicate index in basis list xh ba
50. values for row 17 Back to index GetRowBase Row index Row name max 64 characters Type of constraint 1 Unbounded 2 wea 3 z 4 5 Ranged Lower bound left hand side Upper bound right hand side Solution status of constraint 1 Basis 2 Lower bound 3 Upper bound 4 Fix Activity of constraint in solution Reduced cost dual values of constraint in solution 0 OK 1 Bad index 10 Model locked RowName RowType Lhs Rhs Status Activity RedCost GetRowBase StartRowIndex EndRowlndex Status gets the solution status of a constraint after optimization The array Status will be filled and must have sufficient size at least EndRowiIndex StartRowIndex 1 Input StartRowIndex 14 EndRowlndex 14 Output Status 14 Rc 14 Start index of rows End index of rows Solution status of constraint Basis Lower bound Upper bound Fix OK Start index greater than end index Start index less than 1 End index greater than number of rows 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 36 Example Fills array laStatus with reduced cost values for rows 3 4 and 5 Rc GetRowBase 3 5 laStatus Back to index GetRowDualValues GetRowDualValues StartRowIndex EndRowIndex Duals gets dual values of a number of rows after optimization The array Duals will be filled and must have sufficient size at least EndRowindex Star
51. xrtcod returncode Re GetParameter xipsta lpsta Re GetParameter xzbest zbest Back to index LoadModel LoadModel Intype inf m n nz ia ja a Ib ub rl ru c type fcpi transfers a complete LP IP model to the MOPS DLL Compared to PutModel this function can transfer IP models with extended integer types SC SI PI LI variable and SOS of Type 1 and 2 to the DLL A model with m constraints and n structural variables must be in the following form min max CIK bl lt Ax lt bu lt x lt u with xj being integer for every element j from set Jl The vectors x c I u are real vectors of size n A is a m x n matrix of type real bl and bu are real m vectors The vectors u bl bu can have elements that are plus or minus infinite inf to represent unbounded variables or constraints For equations the values b and bu must be identical 7 m and J 7 n are index sets for constraints and variables JI is a subset of J and contains all indices of integer variables If J is empty the model is pure LP Note The convexity constraints of special ordered sets S1 S3 should not be included in the above model They are generated automatically inside the function LoadModel However the size of the output 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 14 arrays to be passed to the functions GetLPSolution and GetlPSolution have to be increased to n m ns
52. 0 6 if P4 is realized 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Case Burma 143 9 2 In area D 1 2 if P5 is realized Investment costs in 1000 P1 5000 P2 10000 P3 2000 P4 2000 P5 5000 Water consumption in 1000 cubic meters sqkm Rice 0 25 Wheat 0 1 Profit in 1000 sqkm Area A Rice 1100 Wheat 1000 Area B Rice 1300 Wheat 1300 Area C Rice 1400 Wheat 1600 Area D Rice 1600 Wheat 1800 Task Build a linear mixed integer problem to maximize profit Solution Decision variables xga Area under cultivation for wheat in region A in sqkm xgb Area under cultivation for wheat in region B in sqkm xgc Area under cultivation for wheat in region C in sqkm i xgd Area under cultivation for wheat in region D in sqkm xra Area under cultivation for rice in region A in sqkm xrb Area under cultivation for rice in region B in sqkm xrc Area under cultivation for rice in region C in sqkm xrd Area under cultivation for rice in region D in sqkm y1 1 if area A is irrigated by a channel else y1 0 y2 1 if the embankment dam is build else y2 0 y3 1 if the channel to irrigate area B is build else y3 0 y4 1 if the channel to irrigate area C is build else y4 0 y5 1 if the hydro plant and pumping irrigation for region D is build else y5 0 Objective function Maximize z with z 1100 xra 1300 xrb 1400 xrc 1600 xrd
53. 0 Then Output Optimal LP Solution found Value 6 funct rc GetLPSolution stat funct Activity 1 RedCost 1 Status 1 Else If stat 1 Then Output LP is infeasible Else If stat 2 Then Output LP is unbounded Else Output LP not solved rc r End If Else Report results for IP phase LP was solved to optimality If stat 0 Then Output Optimal IP Solution found Value amp funct rc GetIPSolution stat funct Activity 1 RedCost 1 Status 1 Output index activity reduced costs status NoCols has been retrieved previously by GetDim For j 1 To NoCols Output j amp daActivity j daRedCost j amp amp laStatus j Next Elself stat 1 Then Output IP is infeasible Elself stat 3 Then Output IP Solution found search not completed Value amp funct Else Output No IP Solution found search not completed rc amp r End If End If Back to index PutModel 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 16 PutModel Intyp inf m n nz ia ja a lb ub c type transfers a complete LP IP model to the MOPS DLL A model with m constraints and n structural variables must be in the following form min max CIK bl lt Ax lt bu lt x lt u with Xj being integer for every element j from set JI The vectors x c I u are real vectors of size n A is a m x n matrix of type real
54. 007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS STUDIO 59 In Figure 1 you can see the Main Window of MOPS Studio Here you can find all useful control elements Menus Menus are located across the top ofthe screen just below the Title bar The main menu selections are File Edit View MOPS Tools Window and Help When you choose one ofthe menus a submenu drops down to show other options Fie Edit View MOPS Tools Help Figure 2 Menus bar File contains commands that apply to the entire model or file such as New Model Open Save and Close Model Edit contains commands for editing the model or file such as Undo Redo Cut Copy and Paste View contains commands for controlling the display of the model or file such as Show and Clear Output Window and Show Line Numbers MOPS contains commands as Check Model Syntax Optimize Model MOPS Parameters and Execute AMPL Tools contains functions such as Convert Model to Rename Variables Write Debug Model File Report Bug and Options Help contains links to the Help file and information about the version of MOPS Studio you have installed and automatic online check for updates Toolbar Fo Od Tl den Je Figure 3 Toolbar OB In Figure 3 displays the toolbar of MOPS Studio It is responsible for the fundamental functions H M for creating a new model Freely selectable possibilities are MPS AMPL Triplet or Lindo e to open a model I s M
55. 1 but the extended bound reduction is also executed when the model is an IP model Default 0 Type Long Back to index xbndrd Level of bound reduction during IP processing and branch and bound cut Values 0 Level 0 no bound reduction 1 Level 1 bound reduction of all variables during IP processing and branch and bound cut 2 Level 2 extended bound reduction during IP processing and branch and bound 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 97 cut Default 1 Type Long Back to index xbrheu Branching heuristic Determines how a branching variable will be chosen Values 0 When minimizing maximizing a fractional IP variable with maximal minimal objective function coefficient will be set to the down rounded value 1 When minimizing maximizing a fractional IP variable with minimal maximal objective function coefficient will be set to the up rounded value 2 Branch on most fractional IP variable Tie breaking rule is the best cost 3 Branch on IP variable with largest smallest costs if minimization maximization The variable will be set to the down rounded value Tie breaking rule is most fractional part 5 Branch on fractional integer variable with largest weighted pseudo costs Tie breaking rule is most fractional part If global gap is less than 0 02 change to xbrheu 3 6 Branch on fractional integer variable with the largest smallest pseudo costs Tie
56. 1StartIndex As Integer ByVal lEndIndex As Integer ByVal pdVal As IntPtr As Integer Declare Function GetRowLhs Lib mops d11 ByVal lRowIndex As Integer ByRef dLhs As Double As Integer Declare Function GetRowLPSolution Lib mops dl1 ByVal 1StartIndex As Integer ByVal lEndIndex As Integer ByVal pdVal As IntPtr As Integer Declare Function GetRowRhs Lib mops d11 ByVal lRowIndex As Integer ByRef dRhs As Double As Integer Declare Function GetRowType Lib mops dll ByVal lRowIndex As Integer ByRef lRowTyp As Integer As Integer Declare Function GetSolutionStatus Lib mops dl1 As Integer 2 5 4 Visual C C 6 0 Copy and paste these declarations into a C C header file name it for example mopsdll h and include this header into your C C code AAA A A A A A NS Sa KN mopsdll h PI 01 08 DH This header has to be included when the MOPS DLL is used from C C programs Wieser ee typedef long _ stdcall ALLOCATEMEMORY long typedef long __stdcall DELCOL long typedef long __stdcall DELROW long typedef long stdcall FINDNAME char long long typedef long __stdcall FINISH void typedef long __stdcall FREEMEMORY void typedef long stdcall GETCOL long char long long double double double long double double typedef long _ stdcall GETDIM long long long typedef long __stdcall GETIPSOLUTION long doub
57. 2 End If Back to index SetParameter SetParameter s sets MOPS parameters All parameters are initialized to defaults when calling InitModel and can be set individually afterwards Several parameters can be specified if they fit into the input string s Input s C255 Parameter and value Syntax lt Parameter gt lt Valuet gt Output Re 14 0 OK lt gt 0 Error Example Set parameter xoutlv to 1 so that no log messages are written to the logfile Set parameter xoutsl 0 implies that no solution file is written s xoutlv 1 xoutsl 0 Re SetParameter s Back to index WriteMpsFile 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 19 WriteMpsFile FileName saves the model in main memory as MPS file to the hard disk Input FileName C255 Name of the MPS file optionally with path Output Re 14 0 OK lt gt 0 Error 10 Model locked Example Rc WriteMpsFile c mops models myfile mps Back to index WriteTripletFile Write TripletFile FileName saves the current model as a triplet file to the hard disk Input FileName C255 Name of the triplet file optionally with path Output Re 14 0 OK lt gt 0 Error 10 Model locked Example Re WriteTripletFil c mops models myfile tri Back to index AllocateMemory This function is discontinued and only for backward compatibility Use nitialize instead AllocateMemory Memory
58. 2Varl 0 0 il isp SC 27 20 29074 SL k 10 9 1000 7 55 HEH K 300 The variables LIVar1 LIVar3 belong to a linearized function The integer type has to be less than zero The variables SOS2Var1 SOS2Var3 are from the Special Ordered Set Type 2 The weights of these variables are included in the reference row number four The integer type has to be greater than 2 xm 5 The SC variable has the threshold value 1 and fixed charge cost 30 The SI variable has the threshold value 2 and the fix charge cost are 10 The threshold value of the Pl variable is 300 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter MOPS Output Files MOPS User Manual MOPS Output Files 138 8 8 1 8 2 MOPS Output Files MOPS Output Files MOPS does a considerable part of output via files The files written by MOPS are plain text files which can be edited with almost any text editor See the following sections for more information about MOPS files e Solution Files e Log Files e fort xxx Files Solution Files If parameter xouts has been set accordingly the LP and if existing an IP solution will be written to files xfnlps and xfnips Solution files consist of tree sections 1 Identification Gives information about status optimal infeasible unbounded and the objective function value 2 Row Section For each row the following information is given Internal index xn 1 xn xm Status BS Variable is in
59. 7 typedef long __stdcall READPROFILE char typedef long _ stdcall READTRIPLETFILE char typedef long _ stdcall SETMAXIPDIM long long long long typedef long __stdcall SETMAXLPDIM long long long long long long long long typedef long stdcall SETPARAMETER char typedef long stdcall WRITEMPSFILE char typedef long _ stdcall WRITETRIPLETFILE char typedef double stdcall GETIPOBJVALUE typedef double stdcall GETLPOBJVALUE typedef long __stdcall CHANGECOLLB long double typedef long __stdcall CHANGECOLTYPE long long typedef long __stdcall CHANGECOLUB long double ap SS loine sree sCRANETCOST doner KOS a ke A typedef long _ stdcall CHANGENONZEROS long long long double typedef long _ stdcall CHANGELHS int double typedef long _ stdcall CHANGERHS int double typedef long stdcall GENFILENAMES char typedef long _ stdcall GETCOLBASE long long long typedef long __stdcall GETCOLIPSOLUTION long long double typedef long stdcall GETCOLLB long double typedef long __stdcall GETCOLLPSOLUTION long long double typedef long stdcall GETCOLTYPE long long typedef long _ stdcall GETCOLUB long double ode leone ikal ENG GS Lemmer Sea a s typedef long _ stdcall GETNUMBEROFCOLUMNS long typedef long _ stdcall GETNUMBEROFNZ long typedef long _ stdcall GETNUMBEROFROWS long typedef long
60. AAA EE SECHER ES u BA A E MPA an AAA E pe a Ak Kawa a IA AAA Aa E EA AA a E EA AA AA cm A ma ee ee e MPS File MPS file for the Burma model NAME BURMAA ROWS OBJECTIV OGISCH1 OGISCH3 1 OGISCH4 G LOGISCHS WASSERA WASSERB WASSERC WASSERD ANBAUA ANBAUB L ANBAUC A M BAUD REISA OBJECTIV 1100 000 WASSERA s250 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Case Burma 146 REISA ANBAUA 1 000 XGETREI NONO REISB OBJECTIV 1300 000 WASSERB sa REISB ANBAUB 1 000 XGETREI gt IOC REISC OBJECTIV 1400 000 WASSERC SO REISC ANBAUC 1 000 XGETREI 31010 REISD OBJECTIV 1600 000 WASSERD 230 REISD ANBAUD 1 000 XGETREI 306 GETREIDA OBJECTIV 1000 000 WASSERA 100 GETREIDA ANBAUA 1 000 XGETREI 700 GETREIDB OBJECTIV 1300 000 WASSERB a LOC GETREIDB ANBAUB 1 000 XGETREI o HOC GETREIDC OBJECTIV 1600 000 WASSERC o LOG GETREIDC ANBAUC 1 000 XGETREI 700 GETREIDD OBJECTIV 1800 000 WASSERD 100 GETREIDD ANBAUD 1 000 XGETREI OO ISTO0001 MARKER INTORG EIKANALA OBJECTIV 5000 000 WASSERA 1 800 EIKANALA OGISCHl 1 000 LOGISCH5 1 000 STAUDAMM OBJECTIV 10000 000 LOGTSCHT 1 0106 STAUDAMM
61. Activity RedCost Back to index GetColBase GetColBase StartCollndex EndCollndex Status gets the variable status after optimization The array Status will be filled and must have sufficient size at least EndCollndex StartCollndex 1 Input StartCollndex 14 Start index of columns EndCollndex 14 End index of columns Output Status 14 Array of variable status in solution 1 basic 2 lower bound 3 upper bound 4 fixed Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of columns 10 Model locked 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 29 Example Fills array iaColBase with status indicators of columns 3 4 and 5 Re GetColBase 3 5 iaColBase Back to index GetCollPSolution GetCollPSolution StartCollndex EndCollndex IPSol gets the IP solution for a number of columns after successful optimization The array IPSol will be filled and must have sufficient size at least EndCollndex StartCollndex 1 Input StartCollndex 14 Start index of columns EndCollndex 14 End index of columns Output IPSol R8 Array of IP solution values Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of columns 4 No IP solution present Example Fills array daIPSo1 with IP solution values for columns 3 4 and 5 Re GetColIPSolution 3 5 dal
62. B or the DLL in most cases the answer will be to use the MOPS DLL Nevertheless there are cases when utilizing the static library can be appropriate MOPS LIB resp MOPS64 LIB offers you full access to all MOPS routines When using a DLL you can only call functions that are explicitly exported by the dynamic link library any other routine is hidden in the DLL The static library on the other hand allows you to call these hidden routines The Fortran MOPS LIB demo sample for instance calls xcordr to reorder the IMR a function that would not be accessible in the DLL Using such MOPS internal routines of course requires that you have expert knowledge of the MOPS architecture since internal functions are not publicly documented MOPS LIB allows furthermore full access to all MOPS internal data structures You can manipulate all common block variables even those not supported by SetParameter and all global arrays This enables you to write very efficient though in most cases very intricate model generators which build optimization models directly on the IMR arrays See the MOPS White Paper for a description of the IMR Again working with internal data structures requires profound knowledge of MOPS Using LIB functions bypasses the DLL Layer Internally all MOPS DLL functions go down to call LIB functions after performing DLL specific checks and transformations Thus using MOPS LIB is more direct since the DLL Layer overload is stripped In
63. Branching 3 Relaxation Induced Neighborhood Search RINS heuristic Relaxation based Search Space RSS heuristic with LIFO If xhfinb 1 a part of the nonbasic variables will be fixed and all basic integer variables with a fractional part less than xhrdlb will be fixed to the next lower integer value Basic integer variables with a fractional part larger than xhrdub will be fixed to the next larger integer value 5 RSS heuristic with xnodse 3 6 RSS heuristic with xnodse 3 and total rounding xlocs 4 every xnlbab 5 nodes 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 102 Default 6 Type Long See also xmnheu xhtlim xhgap Back to index xhfinb Determine whether a subset of the nonbasic integer variables are fixed before the heuristic will start This parameter is only valid for Local Branching RINS and RSS heuristic xheutp gt 1 Values 0 no none basics are fixed 1 a subset of nonbasic integer variables are fixed before the heuristic will start Default 1 Type Long See also xheutp Back to index xhgap If the global relative gap in the heuristic is smaller than xhgap the heuristic will be terminated This parameter is only relevant if a heuristic is used xheutp gt 0 Default 0 05 Type Double See also xheutp xmnheu xhtlim Back to index xhrdlb A fractional integer variable will be rounded down if its fractional part is smaller than xhrdl
64. Co KG MOPS User Manual MOPS Input Files 132 7 3 4 7 3 4 1 X lt 2 X22 0 X3 lt 20 Ka lt 30 and integer kkkkkkkkkkkkkkkkkkkkkk kk AAA KA KK AH KH A A example of an IP model KAKAK KKN KK NK KKN KK KE NK AAA AAA KA AAA DA Ny 221 10420 1E 20 2 0 0 X1 0 1E 20 0 0 X2 20 20 0 0 30 1E 20 1E 20 1 1 X4 1 1 RI 0 0 R2 151059 L 1 341 Another example for an Triplet file can be found in the Burma case study Extended Integer Types Extended Integer Types The new Branch and Bound xnewbb 1 in MOPS supports the following integer types Name Type Number binary variables for linearized functions Ll variable lt 0 continuous variables binary variables integer variables semi continuous variables SC variable semi integer variables Sl variable partial integer variables Pl variable SOS of type 3 5 and lt 5 xm 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 133 7 3 4 2 SOS of type 1 gt 5 xm and lt 5 2 xm SOS of type 2 gt 5 2 xm All variables of the same SOS or the same linearized function must have the same unique type number The extended integer types can require additional information Variable Information Required semi continuous variables fix charge cost no threshold value yes semi integer variables fix charge cost no threshold value yes
65. Default 0 Type Long Back to index xrimpr This value determines the relative improvement required for the next integer solution Range 0 xinf Default 1 d 4 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 113 6 3 6 3 1 Type Double See also xglgap xabgap xnogap Back to index xusepl This value determines if a cut pool is derived and stored Note that a cut pool requires a significant amount of additional main memory Values 0 do not derive a cut pool Le all violated cuts during IP preprocessing are included into the model 1 derive a cut pool all violated cuts are stored in a cut pool Finally a subset of the cuts are included into the model according some sophisticated selection algorithms Default 0 Type Integer Back to index Output Parameters OutputParameters The following MOPS parameters can be retrieved with GetParameter when using MOPS DLL or directly when using the IMR interface Index xcmgap xctime xertyp xipfun xipsta xiptim xiter xline1 xline2 xlpfun xlpsta xIptim xm xmorig xmxj xmxj1 xn xnints xnodes xnzero xrtcod xversn xzlbnd xzubnd 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 114 xcmgap Global gap in if IP optimization has been stopped before an optimal solution was found Type Double Back to index xctime Total optimization time in minutes Type Double Back
66. Default 1 Type Long Back to index xfrlog Sets LP logging frequency After xfrlog LP Simplex iterations a line will be written to the log file if xoutlv Logging is very time consuming and should only be activated during debugging Default 0 Type Long See also xoutlv Back to index ximrrw If ximrrw is 1 the model in main memory will be written to the hard disk and retrieved after the optimization run If you would like to make changes to the original model or read model information after O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 91 the optimization for example to modify the model for a new optimization run you have to activate this parameter Values 0 No model will be saved before optimization 1 Model will be saved before optimization for later changes Default 0 Type Long Back to index xinf Represents an infinite value This value is used for specifying infinite bounds on variables and constraints xinf is an internal parameter and cannot be changed in profiles or via SetParameter Range 1 0E10 1 0E30 Default 1 0E20 Type Double Back to index xinfor Sets input format of model data Values 0 Internal format 1 MPS format 2 Triplet format Default 1 Type Long See also xfnmps Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 92 xminmx Sets optimization direction
67. E C Programme MOPS MOPSStudio mopsampl exe m Size of AMPL output buffer in bytes 20971 52 Default 2 MB Figure 6 AMPL Options Parameters In order to change some parameters access Menu MOPS gt MOPS Parameters or simply click on 8 this S button 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS STUDIO 63 We recommend you not to change any of this options Eigenschaften von MOPS Control x Parameter Optimization Direction xminmx Minimize O Maximize Ressource Limits E E Miscellaneous Switches and Yalues E File Names and File Switches El Tolerances DI MPS Vector Names xbound xdata xobj xrange xrhs Optimization Direction Abbrechen bernehmen Figure 7 MOPS Parameters Execute AMPL The feature Execute AMPL E is available in Mops Studio 1 1 5 and above This feature is necessary to execute AMPL models with procedural AMPL commands i e to optimize a slightly updated AMPL model multiple times in one run The optimization is started as soon as the command solve is called Results or additional information are displayed in the Output Window with the command display The following points are important for using Execute AMPL e The whole AMPL output is shown in the Solution Summary window All models executed by Execute AMPL cannot be converted to other formats like LINDO MPS
68. ELER AE 84 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Table of Contents Il Other Parameters ss shes bedi and akuan abawa cadet Gots doa ati Basted ate ended ede de na aan A ead case Eed 89 IP Parameter ii anana aha kaen en a aaa anan aaa b aa dang daa A a anan a aaa saka ak dana ag da aa sa dang aas kaa 95 3 Output Parameters u 4 2 0 113 Output Parameters ee Age ee deidad lacio 113 Error Message ii 118 Chapter VII MOPS Input Files 124 1 MOPS Input Files citada 124 2 Profiles iia aa 124 3 Data N UN a A a kg a kag aana bapan ai naun 125 Data lnputi a EE E EE EE 125 MPSFiless nee a a a ag A Laa an aaa eee 125 MPS EIS eegener ENEE 125 Example e da aa KA a AND ITA a eae ANA RAN 126 SECONS EE 127 Meger ENEE 129 T eletrtileg A A o 130 Bel lu A A a 130 E Lu 131 Extended Integer Types e adn 132 Extended Integer Types ui A AA ENEE 132 Enhanced MPS FOMA aana a ANG ode io esos se anne end eno Bates le helle 133 Enhanced Triplet Formats akasara a aca id 136 Chapter VIIIMOPS Output Files 138 1 MOPS Output Files Se 138 2 Solution A A ege 138 DA MOG MS 2 os ccccecacsqctcccesetsaseccstaeeeseeacsdcuaerdsashssecetevsesuccsneraeivtcuacccsesasueuceceieaersassaneraesuesuspenecs 139 4 TOrtdooc EE 139 Chapter IX Case Burma 142 1 Ae RE 142 ET BEE 143 3 MPS File oia ii aida 145 A Triplet File ii aa 146 AMP Re EES ee 148 Chapter X References 151 TI EE 151
69. MOPS LIB can also be linked against C C programs but peculiarities of the C Fortran inter language interface make this approach somewhat more intricate The Fortran Common Block must be mapped to an exactly corresponding C structure pointers to the internal MOPS arrays must be obtained and different calling sequences and name decorations must be considered In general the dynamic link library is the easiest and most stable way of using MOPS from a C C application You should consider a C Fortran inter language architecture with MOPS LIB only if there are very good reasons for it If necessary contact the MOPS development team for more information about this subject 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter MOPS EKE MOPS User Manual MOPS EKE 56 4 4 1 MOPS EKE Using MOPS EKE MOPS is also available as a command line executable for Windows The advantage of the command line executable MOPS EXE is that MOPS can be run without any programming effort independent of any development environment and with no previous installation process However the model has to be passed to MOPS as an mps or triplet file The LP and IP solution are also stored as files on disk MOPS EXE carries out a complete LP IP optimization run as specified in a MOPS Profile To start MOPS from the command line use the following Syntax assuming that MOPS EXE is located in the current directory c gt mops myprofile If no profi
70. N1102 5 00000 Y2N1103 RTN1103 5 00000 Y2N1104 KSN1104 1 00000 Y2N1105 RTN1105 2 00000 Y2N1106 KSN1106 1 00008 SEN1999 MARKER SOSEND 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 130 7 3 3 7 3 3 1 IONW999 MARKER GENEE XXNW100 GGNW100 2500 00000 XXNW100 GONW100 90000 00000 IENW999 MARKER INTEND The names that precede in field 2 the MARKER tokens are irrelevant for MOPS 2 Integer variables can also be specified in the BOUNDS section by the respective type keywords BV defines a binary variable and LI LU define lower and upper bound of a variable that becomes implicitly integer Triplet Files Triplet Format Triplet files are a MOPS specific file format for LP and IP models The Triplet file format has several advantages against MPS files e Fast to read e Free of redundancies e Names can be longer than 8 characters up to 64 The five Sections of the Triplet Format Section 1 contains comments All lines at the beginning of a Triplet file that start with are treated as comments they are read over by the MOPS parser Section 2 holds model dimensions This section consists of only one line which holds the following information in the given order e Number of constraints xm e Number of variables xn e Max Number of nonzeros xnzmax e Max number of 1 byte characters used for variable and constraints names xrcmax e Floating poi
71. OPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 31 LB R8 Upper bound Re 14 0 OK 1 Bad column index 10 Model locked Example Get upper bound of column 1 Re GetColUB 1 dUB Back to index GetCost GetCost Collndex Cost gets the objective function coefficient of a variable Input Collndex 14 Column index Output Cost R8 Objective function coefficient Re 14 0 OK 1 Bad column index 10 Model locked Example Get cost coefficient of column 1 Rr GetCost 1 dCost Back to index GetDim GetDim NRows NCols NNz returns current model dimensions Input Output NRows 14 Number of rows NCols 14 Number of columns NNZ 14 Number of nonzero elements Re 14 0 OK lt gt 0 Error Example Re GetDim NoRows NoCols NoNz Back to index O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 32 GetlPObjValue GetIPObjValue returns the IP objective function value after optimization Input Output GetIPObjValue R8 IP objective function value Example dObj GetIPObjValue Back to index GetLPObjValue GetLPObjValue returns the LP objective function value after optimization Input Output GetLPObjValue R8 LP objective function value Example dObj GetLPObjValue Back to index GetMaxDim GetMaxDim MaxRows MaxCols MaxNz returns the maximal model dimensions You can change these values with SetMaxLPDim
72. PS Parameters for a list of the most important parameters 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 12 Input Parameter C6 Name of the parameter Output Value C80 Current value ofthe parameter Re 14 0 OK lt gt 0 Error Example Re GetParameter xmxmin sValue returns the current value of parameter xmxmin Back to index Initialize Initialize replaces in MOPS v 9 x the former functions AllocateMemory and InitModel The function must be called before a model is passed to the MOPS DLL PutModel LoadModel ReadMPSFile ReadTripletFile All parameters are set to default values Parameters can be changed after a call to Initialize by reading a MOPS profile ReadProfile or by SetParameter Input Output Re 14 0 OK lt gt 0 Error Example Re Initialize Back to index MOPS MOPS FileName carries out a complete standard optimization run The passed variable FileName contains the file name optionally with path of a MOPS profile in which any MOPS parameter can be set The function MOPS allocates memory carries out all initializations sets parameters specified in the profile reads the model from an MPS or triplet file runs LP and IP optimization and writes solutions to files if xouts gt 0 See chapter MOPS Parameters for a description of the most important parameters In case of an error you can use GetParameter to retrieve xertyp xline1 and x
73. PS Profile A profile is a plain ASCII file where you can set any MOPS parameters See section Profiles for an example Input FileName C255 Filename of the profile optionally with path Output Re 14 0 OK lt gt 0 Error I O or syntactical Example Rc ReadProfile c mops xmops pro If Re lt gt 0 Then Rc GetParameter xertyp Errortype Rc GetParameter xlinel ErrorDescriptionl Rc GetParameter xline2 ErrorDescription2 End If Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 18 ReadTripletFile ReadTripletFile FileName reads triplet file into the main memory Before calling this function you have to call AllocateMemory and InitModel See section Triplet Files for an example lf an error occurs check parameter xertyp for further information Input FileName C255 Name of the triplet file optionally with path Output Re 14 0 OK lt gt 0 Error I O or syntactical Errortypes 1 File O error 2 Max model dimensions xmmax xnmax xnzmax xrcmax exceeded 3 Syntax error Bad integer or floating point value token longer than 64 characters wrong row index or column index 4 Logical error e g Ib gt ub Example Re ReadTripletFile d mops models myfile tri If RC lt gt 0 Then Rc GetParameter xertyp Errortype Rc GetParameter xlinel ErrorDescriptionl Rc GetParameter xline2 ErrorDescription
74. PSol Back to index GetColLB GetCoILB Collndex LB gets the lower bound of a column Input Collndex 14 Column index Output LB R8 Lower bound Rc 14 0 OK 1 Bad column index 10 Model locked Example Get lower bound of column 1 Re GetColLB 1 dLB Back to index GetColLPSolution 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 30 GetColLPSolution StartCollndex EndCollndex LPSol gets the LP solution for a number of columns after successful optimization The array LPSol will be filled and must have sufficient size at least EndCollndex StartCollndex 1 Input StartCollndex 14 Start index of columns EndCollndex 14 End index of columns Output LPSol R8 Array of LP solution values Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of columns Example Fills array daLPSo1 with IP solution values for columns 3 4 and 5 Re GetColLPSolution 3 5 daLPSol Back to index GetColType GetColType Collndex ColType gets the type of a column Input Collndex 14 Column index Output ColType 14 Type of variable 0 continuous 1 integer Re 14 0 OK 1 Bad column index 10 Model locked Example Get type of column 1 r GetColType 1 l1ColType Back to index GetColUB GetColUB Collndex UB gets the upper bound of a column Input Collndex 14 Column index Output 2007 M
75. R1 1 0000 X3 R1 1 0000 X4 OBJ FUNC 1 0000 R2 1 0000 KA R1 1 0000 RHS RHS R1 1 0000 BOUNDS UP BOUND x1 2 00 UP BOUND X3 20 00 UI BOUND X4 30 00 ENDDATA The first line is not part of the MPS file it is only to show column positions Another example for an MPS file can be found in the Burma case study Sections NAME Section The NAME section contains the keyword NAME in column 1 Starting from column 15 the name of the model is specified as a string that may not contain blanks Only the first 32 characters of this string are significant ROWS Section The ROWS section starts with a line that contains the keyword ROWS in column 1 In the following rows the constraints of the model are specified Field 1 contains the type of the constraint L or LE for less or equal G or GE for greater or equal E or EQ for equal and N for unrestricted The objective function is always specified as N Types must be in capital letters In field 2 follows the name of the constraint as a 8 character string with leading and trailing blanks being significant COLUMNS Section O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Input Files 128 The COLUMNS section starts with the keyword COLUMNS in column 1 The following rows contain variable names and nonzero elements of the matrix A nonzero element is specified by the respective row name same as in ROWS section and the column name Again leading and trail
76. ackward compatibility Use Finish instead FreeMemory is called to free the memory block allocated by AllocateMemory All model data in main memory is lost if you call this function Input Output Re 14 0 OK lt gt 0 Error Example Re FreeMemory Back to index OptimizelP This function is discontinued and only for backward compatibility Use Optimize instead OptimizelP FrNod Nodes NintSol Errtype ObjFunc LpBouna starts an IP optimization run Before O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 21 calling OpitimizelP the model has to be solved successfully as an LP by calling OptimizeLP The IP optimization will be stopped after having processed FrNod nodes or when an optimal solution has been found You can use a loop to call this solution until the problem will be solved within the loop you can analyze the results found so far or stop the optimization if appropriate Input FrNod 14 Number of nodes until next break Output Nodes 14 Current number of nodes in Branch amp Bound tree NintSol 14 number of found IP solutions Errtype 14 Error code for problems during optimization e g resource problems 0 OK lt gt 0 Error ObjFunc R8 Best objective function value found so far LpBound R8 Best possible objective function value of the IP solution Re 14 0 Optimization successfully terminated 1 LP is infeasible unbounded or could not be solved because of a
77. after the value of xfrinv unless there are numerical problems or a significant amount of fill which makes it more efficient to recompute the LU factors Range 0 maxint Default determined automatically by the size of the model dual Type Long See also xluctr Back to index xipmem Specifies how the memory for the Cholesky factorization of the IPM engine is allocated 1 default means the memory is allocated dynamically outside of the MOPS memory block 0 means it is allocated form the MOPS memory block Note that the value of xipmem is only relevant if the IPM engine is used to solve the initial LP xlptyp 4 Furthermore if xipmen is set to O memory has to be allocated explicitly i e xmreal has to specify the amount of megabytes for the total amount of memory allocated including the Cholesky factorization Default 1 Type Long See also xmreal Back to index xipxov Values 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 73 0 No x over after solving the initial LP with IPM 1 Only primal part of x over 2 Primal and dual part of x over and primal simplex to finish 3 Primal and dual part of x over and dual simplex to finish Default 2 Type Long See also xIptyp Back to index xipdua specifies a percent value If the ratio of the number of active rows and columns after LP preprocessing is larger than xipdua percent then the IPM engine solves the dual LP
78. aint can be defined as GE or LE hence in the RHS section it will hold either or u if not 0 as its coefficient Be r u J with r gt 0 Then the RANGES section contains for this constraint r as coefficient A RANGES element can also be used to specify an equation Generally speaking if b is the coefficient of a constraint defined in the RHS section ris the coefficient specified in the RANGES section and if and u are the lower and upper bound of the constraint the following relationship applies Type Sign of r I u G or b b r L or b r b E b b rl E b r b BOUNDS Section The BOUNDS section starts with keyword BOUNDS in column 1 In the following datasets individual bounds for the structural variables can be defined if these bound differ from the default bounds Default is O as lower bound and infinite as upper bound Each vector must have an unique name in field 2 Field 3 contains the name of the structural variable and field 1 holds the type of the variable Some types require field 4 to hold a numeric value for the respective bound The following types are possible Type Meaning Intervall Value required Y N LO Lower Bound Y UP Upper Bound Y FX Fixed Value Y 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 129 7 3 2 4 FR Free Variable N PL 0 0 N MI oo 0 N BV Binary Variable N LI Integer Variable Lower Bound Y UI Integer Variable Upper Bound Y Some
79. ake on any real value in a SC variable specified positive range It can also have a fixed charge cost K associated with it if the variable is nonzero Semi integer variable Sl variable This variable is either zero or has an integer value in a specified positive range It can also have a fixed charge cost K associated with it if the variable is nonzero Partial integer variables Pl variable An integer variable which can only take integer values in a small user defined range Outside this range the variable can take on any real value in a specified range Special Ordered Set of type 1 SOS1 A set of variables where at most one variable of this set may be nonzero These variables are not necessarily integer variables Special Ordered Set of type 2 SOS2 A set of continuous variables where at most two variables of this set may be nonzero and they have to be adjacent Special Ordered Set of type 3 SOS3 A set of 0 1 variables which sum up to 1 Ll variables A set of 0 1 variables to linearize a separable function of nonlinear continuous variables The formulation of Ll variables is an alternative modeling technique of SOS2 The input format of the extended integer types in the new branch and cut code is described in Extended Integer Types The MOPS libraries are primarily designed for use under Windows operating systems but versions for other platforms are also available Under Windows the following interfaces are supported
80. al Basic 6 0 43 Visual C C 6 0 46 We WriteMpsFile 8 51 8 8 WriteTripletFile 8 51 X xabgap 79 xadcol 79 xadnon 79 xadrow 79 xallocm 51 xbatyp 69 xbndha 69 xbound 77 xchksw 89 xcmgap 113 xctime 113 xdata 77 xdecol 51 xderow 51 xdimen 89 xdjscl 69 xdropf 69 xdropm 69 84 xertyp 113 xfiltl 69 xfname 51 xfnbai 66 xfnbao 66 xfnips 66 xfnlog 66 xfnips 66 xfnmps 66 xfnmsg 66 xfnpro 66 xfnsav 66 xfnsta 66 xfrbas 69 xfreem 51 xfrinv 69 xfrlog 89 xfrnod 95 xglgap 79 xgtcol 51 xgtips 51 xgtlps 51 xgtmod 51 xgtnz 51 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Index 154 xgtrow 51 ximrrw 89 xinf 89 xinfor 89 xinitm 51 xipdua 69 xipfun 113 xipmem 69 xipsta 113 xiptim 113 xipxov 69 xiter 113 xline1 113 xline2 113 xIpfun 113 xlpsta 113 xlptim 113 xlptyp 69 xluctr 69 xm 113 xmaxel 89 xminmx 89 xmiter 79 xmitip 79 xmmax 79 xmorig 113 xmreal 79 xmxdsk 79 xmxj 113 xmxj1 113 xmxmin 79 xmxnod 79 xmxtlp 79 xn 113 xnenmx 79 xnif 113 xnints 113 xnmax 79 xnodes 113 xnproc 69 xnwcon 89 xnwluf 69 xnwluu 69 xnzero 113 xnzmax 79 xobj 77 xoptim 51 xoptip 51 xoptlp 51 xoripm 69 xoutlv 89 xoutsi 89 xpreme 69 xptcol 51 xptmod 51 xptnzs 51 xptrow 51 xrange 77 xrcmax 89 xrdmps 51 xrdtri 51 xrduce 69 xrhs 77 xrimpr 84 xrprof 51 xrtcod 113 xscale 89 xsif 113 xstart 69 xstmps 51 xstorn 89 xsttri 51 xtold1 84 xtold2 84 xtoli
81. allocates a block of continuous main memory and initializes internal default values You must call AllocateMemory before you use any other functions to build the model If amemory block has already been allocated by a previous call to AllocateMemory re invoking the functions frees this memory and allocates a new block all data in the previous block will be lost SetMaxLPDim and SetMaxIPDim change the default maximal dimensions of a model set by AllocateMemory Input Memory 14 Size of the memory block in megabyte MB If Mem 0 the default value of 300 MB will be used Output Re 14 0 OK lt gt 0 Not enough memory available 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 20 Example Rc AllocateMemory 0 Allocates 300 MB default of main memory Re AllocateMemory 800 Allocates 800 MB of main memory Back to index InitModel This function is discontinued and only for backward compatibility Use nitialize instead InitModel initializes a memory block and sets default values for parameters and internal variables This function must be called after AllocateMemory For maximal model dimensions default values are used or the dimensions previously set by SetMaxLPDim and SetMaxIPDim if these functions have been called Input Output Re 14 0 OK lt gt 0 Error Example Re InitModel Back to index FreeMemory This function is discontinued and only for b
82. ation if it is less or equal xdropf multiplied by a value of an element with the largest magnitude of a row or column Range 0 1 0E 9 Default 1 0E 11 Type Double 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 71 Back to index xdropm A matrix coefficient with a smaller magnitude than xdropm will be set to 0 0 Range 0 0 1 0E 4 Default 1 0E 7 Type Double Back to index xfiltl Determines how much fill is tolerated when using the aggregator during LP preprocessing If xfiltl is set to a higher value more fill is allowed As a consequence the preprocessed matrix and its factorizations may have more nonzeros but fewer constraints Range 0 0 inf Default 4 0 Type Double See also xrduce Back to index xfrbas Iteration frequency for saving the current basis in punch format or internal format if one of the simplex engines is used If the IPM engine is used on optimal basis can be saved after the cross over if xfrbas gt 0 This allows a warm start with one of the simplex engines Values 1 Basis is never saved 0 Basis is saved after termination p Basis is saved after p iterations p gt 0 Default 1 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 72 Type Long See also xbatyp xfnbao xfnsav Back to index xfrinv A new LU factorization in one of the simplex engines is computed
83. b This parameter is only relevant for the RINS and RSS heuristic xheutp 3 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 103 Range b o 1 0 Default depends on heuristic and size of the problem Type Double See also xheutp xhrdub Back to index xhrdub A fractional integer variable will be rounded up if its fractional part is larger than xhrdub This parameter is only relevant for the RSS heuristic xheutp gt 4 Range b o 1 0 Default depends on heuristic and size of the problem Type Double See also xheutp xhrdlb Back to index xhtlim Time limit in the heuristic This parameter is only relevant if a heuristic is used xheutp gt 0 Range 0 xmxmin Default 10 d0 Type Double See also xhgap xheutp xmnheu Back to index O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 104 ximbnd Determines the use of conditional bound implications only mixed integer models during IP preprocessing and branch and bound cut Values 0 Bound Implications are not derived and not used 1 Bound Implications are only used during IP preprocessing 2 Bound implications are also used during the branch and bound cut Default 2 Type Long Back to index ximpli Determines how implications that have been derived by probing will be used during IP preprocessing Values 0 No implications will be derived
84. basis UL Variable is at upper limit LL Variable is at lower limit EQ Variable ist fixed UL LL IN Restriktion is inactive Row name If the name is longer than 8 characters only the leading 8 characters will be written Activity Value of the constraint when solution values are put in e Slack Difference between the value of the constraint and the RHS bound Lower limit LHS Upper limit RHS Dual Activity Indicates the marginal change of the objective function value if the right hand side would be changed with 1 unit Gei Column section Internal index 1 xn Status like in Row Section In IP models integer variables have status IV e Column name If the name is longer than 8 characters only the leading 8 characters will be written Activity Solution values of variables Objective function coefficient Lower limit of variable O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Output Files 139 8 3 8 4 e Upper limit of variable e Reduced Cost Indicates that the objective function will change with the value of the reduced cost if the constraint is changed with 1 unit Note The preprocessor xrduce 7 might change the bounds of structural variables but this does of course not change the LP solution If you want the bounds to remain unchanged keep the default xbndha 0 Log Files If parameter xoutlv gt 2 a log file will be opend and all major MOPS routines
85. ck to index xtold2 Dual feasibility tolerance in phase 2 of the Simplex Reduced costs must be greater than xtold2 to be taken into the basis Range 1 0E 10 1 0E 1 Default 1 0E 7 Type Double Back to index xtolin A solution value will be regarded as integer if it is not more than xtolin away from the next integer value Range 1 0E 3 1 0E 6 Default 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 86 1 0E 5 Type Double Back to index xtolpv Minimum pivot value in Simplex Tolerance for the determination of the pivot element Range 1 0E 8 1 0E 3 Default 1 0E 7 Type Double Back to index xtolqi A solution value will be regarded as quasi integer to the controlling of the Branch amp Bound Heuristic if it is not more than xtolgi away from the next integer value Range 1 0E 3 1 0E 6 Default 0 05 Type Double See also xheutp Back to index xtolr1 Primal relative feasibility tolerance in phase 1 of the Simplex A variable x with lower bound b and upper bound ub will only be regarded as feasible if Ib xtolx1 xtolr1 Ib lt x lt ub xtolx1 xtolr1 ub This rule is also applied to logical variables Range 0 0 1 0E 7 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 87 Default 1 0E 12 Type Double See also xtolx1 Back to index xtolr2 Primal rela
86. cultivated We have to decide how many sqkm rice and how many sqkm wheat to cultivate The most important factor is the construction of irrigation facilities The following investments in irrigation facilities are possible projects P1 to P5 P1 Area A can be irrigated by a canal from the river M see sketch river M is flowing from north to south P2 Building an embankment dam so other regions can also be irrigated P3 If projects P1 and P2 are realized the canal can be extended to bring water to area B P4 Area C can be irrigated to another channel starting from the P3 channel P5 Additionally to the embankment dam but independently from P1 P3 and P4 a hydro power plant can be constructed to irrigate region D with electrical pumps This project will not have any effect on the other areas P2 Staudamm dal Krattwerk The government intends to realize at least one of the projects P1 to P5 The cultivation of rice and wheat differs in the consumption of water and in yield see data below Because of certain market constraints the area to cultivate wheat on may not exceed 30 of the total area used for agriculture The planning period are 12 years and 2 years are needed to realize a project We are looking for the solution with maximal profit Data Amount of water in 1000 cubic meter In area A 1 5 if P1 is realized In area A 1 4 and in area B 1 0 if P3 is realized In area A 1 0 in area B 0 8 and in area C
87. during the Interior Point Engine which is critically for its performance is determined automatically See also the parameter xoripm Another outstanding feature of the Interior Point Engine is that it can use multiprocessing On the Intel Core Duo architecture a 40 speed improvement can be obtained by specifying xnproc 2 number of processors to be used A new Branch and Bound Cut algorithm with extended integer types is available See parameter xnewbb The new algorithms include different heuristic xheutp branching xbrheu and node selection xnodse strategies Additionally local search strategies x ocs can be executed This algorithm is the default and leads to large performance gains on many integer optimization problems The old branch and bound algorithm can be used by setting xnewbb 0 The simplex engines and the crossover algorithm of the IPM engine use a newly implemented LU factorization and a new LU update which use memory more efficiently The old LU factorization and the old LU update are possible See the parameters xnwluf and xnwluu If the model contains range constraints the IP Preprocessing can be more efficient in many cases if 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Introduction 4 these constraints are split into a pair of constraints parameter xranha An extended bound reduction technique is used during the IP preprocessing This technique sometimes leads to shorter
88. e Change 2 nonzero elements 1 1 1 and 1 2 5 ia 1 1 ja 1 1 a 1 1 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 26 ia 2 1 ja 2 Re ChangeNonzeros eg IND Eu E Back to index ChangeRhs ChangeRhs RowiIndex Rhs changes the upper bound right hand side of the constraint with index Rowindex Input Rowindex 14 Row index Rhs R8 Upper bound right hand side Output Re 14 0 OK 1 Bad row index 2 Lower bound is greater than upper bound 10 Model locked Example Sets the upper bound of row 1 to 0 r ChangeRhs 1 0 Back to index DelCol DeICol Collndex deletes a column of the model Input Collndex 14 Column index Output Re 14 0 OK 1 Bad column index 6 Matrix is in false internal format 10 Model locked Example Re DelCol 8 Back to index DelRow DelRow RowIndex deletes a row of the model Input Rowindex 14 Row index Output 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 27 Rc 14 0 OK 1 Bas row index 6 Matrix is in false internal format 10 Model locked Example Re DelRow 8 Back to index FindName FindName Name Mode Index searches for row and column names and returns the corresponding index if available Input Name C64 Row name or column name to be searched for Mode 14 0 if looking for a row name else column names Output Index 14 Ind
89. e the usage of DLL and LIB more alike Most MOPS DLL functions have a MOPS LIB function as counterpart which is called with exactly the same parameters Refer to the description of the MOPS DLL function if you need information about the analog static library function O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS LIB 52 Some DLL functions have no counterparts because in IMR context when using the LIB you have direct access to allMOPS variables and information like for example model dimensions can be retrieved directly from the variables in that case xm xn xnzero One important difference between DLL and LIB functions is that when passing a string the LIB functions require that as additional parameter the length of the string is passed just behind the string itself So DLL function FindName is called FindName name mode index and the corresponding LIB function xfname is called xfname name length mode index The following table shows MOPS DLL functions and the corresponding LIB functions See also the MOPS LIB demonstrator for samples how to call most LIB functions MOPS DLL functions and their MOPS LIB counterparts AllocateMemory DelCol DelRow FindName FreeMemory GetCol GetDim GetIPSolution GetLPSolution GetMaxDim GetModel GetNonzero GetParameter GetRow Initialize InitModel LoadModel Mops Optimize OptimizelP OptimizeLP xallocm xdecol xderow xfname xfreem xgtcol xgtips
90. ed it is set to xinf The lower bound has to be greater or equal zero and the upper bound has to be greater than the threshold value A special order of the types LO UP and SC is not necessary BOUNDS 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 135 LO BND SCT 2 000 UP BND SCT 9 000 SC BND sei 20 00 LO BND SEZ 2 000 UP BND sc2 9 000 SC BND SCZ LO BND SICH 5 000 SC BND SES The SC Variable SC2 and SC3 have no fix charge costs The upper Bound of variable SC3 is xinf Semi integer variable This variable is marked with the type SI The threshold value and the upper bound are labeled with the types LO and UP or with LI and UI If LO LI is set to zero or is not defined then the threshold value is set to one If the upper bound is not defined it is set to xinf The threshold value has to be greater or equal zero and the upper bound has to be greater than the threshold value A special order of the types LO LI UP UI and SI is not necessary BOUNDS LO BND stil 2 000 UP BND sti 9 000 SENENI STIL 20 00 LI BND SE 2 000 UI BND St 9 000 SC BND SZ UP BND SS 20 00 SC BND SS The SI Variable SI2 and SI3 have no fix charge costs The threshold value of variable SI3 is one Partial integer variable This variable is marked with the type PI The lower and upper bound are labeled with the types LO LI and UP UI The threshold value of this variable has to be greater than
91. embed MOPS DLL and how to call functions Visual Basic 6 0 Copy and paste these declarations to your VB 6 0 module Names of functions are case sensitive you should not modify them Eventually the location of the MOPS DLL must be adapted Declare Function AllocateMemory Lib mops dl1 ByVal 1lMemory amp As Long Declare Function DelCol Lib mops dl1 ByVal 1ColIndex amp As Long Declare Function DelRow Lib mops dl1 ByVal lRowIndex amp As Long Declare Function FindName Lib mops dl1 ByVal sName ByVal 1Mode amp lIndex8 As Long Declare Function Finish Lib mops dl1 As Long Declare Function FreeMemory Lib mops dl1 As Long Declare Function GetCol Lib mops dll ByVal 1ColIndex amp ByVal sColName l1ColTypes 1NElements amp dCost dLB dUB 1Status amp dActivity dRedCost As Long Declare Function GetDim Lib mops dl1 1NRows amp 1NCols amp 1NNz amp As Long Declare Function GetIPSolution Lib mops d11 1IPStas amp dIPFunct daActivity daDj laSta As Long Declare Function GetLPSolution Lib mops d11 1LPStas amp dLPFunct daActivity daDj laSta amp As Long Declare Function GetMaxDim Lib mops dl1 1MaxRows amp 1MaxCols amp 1MaxNz amp As Long Declare Function GetModel Lib mops dl1 ByVal lIntypes INF 1NRows amp 1NCols amp 1NNZ amp laRowIndices amp laColIndices amp daNZs daLBs daUBs daCosts laColTypes As Long Declare Function GetNonzero Lib mops dl1
92. er cuts are not used Simple generalized flow cover inequalities SGFCIs Extended generalized flow cover inequalities EGFCls more violated of SGFCI and EGFCI Lifted simple generalized flow cover inequalities LSGFCIs Lifted flow cover inequalities LFCIs more violated of LSGFCI and LFCI oak Go MM O Default 4 Type Long Back to index xflwpa This parameter determines if flow path cuts should be derived Values 0 flow path cuts are not used 1 simple flow path cuts 2 extended flow path cuts Default 0 Default 0 Type Long Back to index xfrnod 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 100 Determines if the branch and bound cut process of xoptim Optimize will be interrupted if xfrnod gt 0 Usage example in pseudo code do call xoptim dir status phase funct or optimize dir status phase funct if xrtcod 5then interrupted after xfrnod nodes or integer solution write IP value funct cycle else if xrtcod gt O then fatal error exit exit else normal exit exit end if enddo Values 1 no interrupt of the branch amp bound cut process 0 an interrupt occurs after an automatically computed number of nodes or an integer solution was found gt 0 an interrupt occurs after xfrnod nodes or an integer solution was found Default 1 Type Long Back to index xfrtre Re starting an IP optimization from a saved branch and bo
93. erations Ninfeas 14 Number of infeasibilities LPStatus 14 Optimization status 0 Optimal 1 Infeasible 2 Unbounded ObjFunc R8 Current objective function value Suminfeas R8 Sum of infeasibilities Re 14 0 Model optimally solved 1 Resource limit reached memory iterations time 2 Input error 3 Output error 4 Numerical problem 6 System error 8 Error while reading or writing IMR to file 999 Breakpoint reached optimization can be continued Example The optimization of the LP is stopped after each 100 iterations xfrlog 100 Do rc OptimizeLP xfrlog xiter xnif xlpsta xfunct xsif If rc 0 Then MsgBox LP optimization successfully finished Else If rc 1 Then MsgBox Resource limit e g iteration limit Else If rc 2 Then MsgBox Input error occurred Else If rc 3 Then MsgBox Output error occurred End If Loop Until rc lt gt 999 Back to index Extended functions Extended functions Alphabetical list of MOPS DLL extended functions Many of the following DLL functions have been added to MOPS DLL since v8 x Index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 23 ChangeColLB Change ost ChangeRhs FindName GetColBase GetColLPSolution GetCost GetLPObjValue GetNumberOfColumns GetRedCost GetRowDualValues GetRowLhs GetSolutionStatus PutRow ChangeColLB ChangeColType ChangeLhs DelCol GenFileNames GetCol
94. ern int GetNonzero int iRowIndex int iColIndex ref double dElement D11Import mopsFile public static extern int GetParameter string sParameter StringBuilder sValue D11Import mopsFile public static extern int GetRow int iRowIndex StringBuilder sRowName ref int iRowType ref double dLhs ref double dRhs ref int iStatus ref double dActivity ref double dRedCost D11Import mopsFile public static extern int Initialize D11Import mopsFile public static extern int InitModel D11Import mopsFile public static extern int MOPS string sFileName D11Import mopsFile public static extern int Optimize int iDirection ref int iStatus ref int iPhase ref double dObjFunc D11Import mopsFile public static extern int OptimizelP int iFrNod ref int iNodes ref int iNIntSol ref int iErrtype ref double dObjFunc ref double dLpBound D11Import mopsFile public static extern int OptimizeLP int iFrLog ref int ilter ref int iNInfeas ref int iLpStatus ref double dObjFunc ref double dSumInfeas D11Import mopsFile public static extern int PutCol int iColIndex int iMode string sColName int iColType ref double dCost ref double dLB ref double dUB D11Import mopsFile public static extern int PutModel int ilntype double dINF int iNRows int iNCols int iNNz IntPtr iaRowIndices IntPtr iaColIndices IntPtr daNZzs IntPtr dalBs IntPtr daUBs IntPtr daCosts IntPtr 1acolTypes D11Import mopsFile
95. es All MOPS input parameters can be set in a Profile Profiles are regular text files with the following structure e Ifa line starts with C or c it contains a comment and will be ignored e After an exclamation mark the rest of the line will be treated as a comment e All characters are converted to uppercase if they are not part of a string enclosed by or So MOPS parameter names are not case sensitive xStart and XSTARt are the same e Values are assigned to MOPS parameters by the equal sign Between parameter name equal sign and value blanks can be set optionally Profiles can be read by the DLL function ReadProfile Example of a MOPS Profile Filename could be myProfile pro xfnmps optilproblimops mps xminmx max optimization direction min or max default min sasi nara i orare Teme Cresi Josisals Xfnsta statist file name for statistic file xmreal 100 xnzmax 50000 xadnon 40000 xstorn 0 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 125 7 3 7 3 1 7 3 2 7 3 2 1 Data Input Data Input The data input files pass model data to MOPS The new branch and bound supports extended Integer Types which need a special handling in the MPS and Triplet format e MPS Files e Triplet Files e Extended Integer Types MPS Files MPS Files The MPS file format is can be processed by almost all commercial solver systems Therefore MPS models
96. essary because MOPS transforms great parts ofthe model notably during preprocessing See parameter ximrrw which controls the saving of locked models Datatypes MOPS DLL requires in its interface exclusively the following data types Make sure that your program uses the same types when calling MOPS DLL functions if not errors and crashes might occur Name used in this manual Fortran C C VB 14 integer integer 4 long Long R8 floating point real 8 double Double Cien string of length len character len char mystring len String len For brevity this manual uses the following variables mor xm Number of constraints nor xn Number of structural variables xp xn xm Total number of variables structural logical Avoiding errors Errors when passing variables A correct calling sequence for the MOPS DLL functions is essential for the stability of our application Mismatches of declaration or passed variables will result in errors or might even lead to a crash of you development environment including loss of data It is important that the correct number of variables is passed to a function that the type of these variables is correct and that the necessary calling conventions are respected Observe the following hints for a stable application O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 8 2 3 2 3 1 Numerical values are passed either as 4 byte integers long or as 8 byte reals
97. etlPSolution GetIPSolution IPStatus IPFunct Activity RedCost Status returns the best found integer solution If a feasible solution has been found the arrays Activity RedCost and Status will be filled with the corresponding solution values Note integer variables always get the status 0 Only non integer variables get their original status in the LP solution Input Output IPStatus 14 Status of the IP solution 0 Optimal search completed 1 Optimality not proved IPFunct R8 Objective function value of the IP solution Activity 1 xj R8 Activities of variables and constraints RedCost 1 xj R8 Reduced costs of variables and dual values of constraints Status 1 xj 14 Status of variables in solution 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 10 O Integer variable 1 Basic 2 LB 3 UB 4 Fixed 5 Superbasic 6 below LB 7 above UB Re 14 0 OK lt gt 0 Error Example Solution values for all variables continuous or integer gt O will be written if xnints gt 0 then Re GetIPSolution IpStatus ipFunct Activity RedCost Status do j 1 to xn if dActivity j gt 0 001 then Output values End if Enddo End if Where xnints is the number of integer variables previously returned by MOPS and xn is the number of structural variables Back to index GetLPSolution GetLPSolution LPStatus LPFunct Activity RedCost Status returns the values o
98. ex of row or column Zero if name could not be found Re 14 0 OK lt gt 0 Error 10 Model locked Example Re FindName Constraint Berlin 0 Index Back to index GenFileNames GenFileNames FileName generates names for all MOPS output files solution files statistic files etc from a template Input FileName C64 Name of the file that serves as a template Output Re 14 0 OK 1 Empty or invalid file name Example Generates names like for example demomodel Ips LP solution file demomodel sta statistic file etc Re GenFileNames demomodel mps Back to index GetCol O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 28 GetCol Collndex ColName ColType NElements Cost LB UB Status Activity RedCost returns data of a structural variable Input Collndex 14 Column index Output ColName C64 Name of the variable max 64 characters ColType 14 Type of the Variable 0 continuous 1 integer NElements 14 Number of nonzero elements in the column Cost R8 Objective function coefficient LB R8 Lower bound UB R8 Upper bound Status 14 Status of the variable in solution 1 basic 2 lower bound 3 upper bound 4 fixed Activity R8 Activity solution value of the variable RedCost R8 Reduced cost of variable in solution Re 14 0 OK 1 Bad index 10 Model locked Example Re GetCol 17 ColName ColType NoElements Cost LB UB Status
99. f an optimal LP solution If a solution has been found the arrays Activity RedCost und Status will be filled with the respective values Note if the LP is detected as infeasible during LP preprocessing the values of the returned solution is meaningless If you turn off LP preprocessing xrduce 0 and use one of the simplex engines then the values of the array Status indicates the infeasible variables Input Output LPStatus 14 Status of the LP solution 0 optimal 1 infeasible 2 unbounded 3 not optimal LPFunct R8 Objective value of the LP solution Activity 1 xj R8 Activities of variables and constraints RedCost 1 xj R8 Reduced costs of variables and dual values of constraints Status 1 xj 14 Status of variables in solution 1 Basic 2 LB 3 UB 4 Fixed 5 Superbasic 6 below LB 7 above UB Re 14 0 OK lt gt 0 Error Example Return the activities of all basic variables if they are gt 0 Re GetLPSolution LpStatus LpFunct Activity RedCost Status 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 11 If LpStatus 0 then doj 1 to xj if Status j 1 and Activity j gt 0 001 then Qutput of values End if Enddo End if Back to index GetModel GetModel Intype inf m n nz ia ja a Ib ub c type returns a complete model to MOPS DLL See PutModel for a detailed description of the arrays All arrays must be dimensioned sufficiently
100. for reached IP time limit xmxmin for B amp B reached Node LP iteration limit xmitip reached Insufficient space xmxnen for LU factors Node limit xmxnod reached Nodes buffer size too small 10 Disk full 11 Granted disk space xmxdsk exhausted OO JO Om P GO A CH 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 39 12 xmxnen must be larger than xnzero 13 Input error in IMR or basis 14 Output error 15 Numerical problem 16 frlog limit reached 17 Internal system error 18 Matrix singular 19 B amp B finished optimal solution found 20 B amp B finished no solution found 21 Node iteration or time limit in b amp b reached 22 Input error in b amp b tree or IMR 23 Output error in IP optimization 24 Numerical problem in IP optimization 25 Not enough memory for LU matrices 26 Internal system error in IP optimization Example 1Stat GetSolutionStatus PutCol PutCol Collndex Mode ColName ColType Cost LB UB adds a new column to the model when Mode 0 or updates an existing column when Mode lt gt 0 A new column will be inserted before the passed index Collndex i e if a new column 17 is inserted the present column 17 becomes column 18 18 becomes 19 and so on Input Collndex 14 Column index values from 1 to number of columns 1 Mode 14 0 Insert 1 Update ColName Column name max 64 characters ColType 14 Type of variable 0 continuous 1
101. ile will be taken Type 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 78 String 64 See also xfnmps Back to index xdata Sets the name of the data deck to be processed in an MPS file If xdata is empty the first data deck encountered in the MPS file will be taken else the data deck specified by xdata will be searched for Type String 64 See also xfnmps Back to index xobj Vector name of objective function in MPS file This line of the file must be of type N unrestricted If no name is given MOPS takes the first N row in the data deck as objective function Type String 64 See also xfnmps Back to index xrange Name of the Range Vector in MPS files If xrange is empty the first vector in the RANGES section of the data deck will be chosen Type String 64 See also xfnmps Back to index xrhs Name of the right hand side vector in MPS file If xrhs is empty the first vector in the RHS section of the MPS file will be taken Type String 64 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 79 6 2 5 See also xfnmps Back to index Ressource limits Index xabgap xadcol xadnon xadrow xglgap xmiter xmitip xmmax xmreal xmxdsk xmxint xmxmin xmxnod xmxpsu xmxtlp xabgap Absolute gap The Branch and Bound search will be stopped if xz bnd xzubnd lt xabgap Default 0 0 Type Double
102. inated when the value of xmxint is reached independent of any other search limitation such as CP time xmxmin node limit xmxnod disk space xmxdsk or global gap xglgap Range 0 maxint Default maxint Type Long Back to index xmxmin Maximum CPU time in minutes for the initial LP and the Branch and Bound process The IP optimization will be stopped if xmxmin has been reached Note Previous versions of MOPS saved the B amp B tree if xfrtre gt 0 so that a restart of the IP optimization was possible Current MOPS versions do not support this functionality anymore Range 0 xinf Default 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 83 120 Type Double See also xmxnod xfrtre xipbeg Back to index xmxnod Maximum number of nodes in Branch and Bound process The IP optimization will be stopped after xmxnod nodes Note Previous versions of MOPS saved the B amp B tree if xfrtre gt 0 so that a restart of the IP optimization was possible Current MOPS versions do not support this functionality anymore Range 0 maxint Default 9 999 999 Type Long See also xmxmin xipbeg Back to index xmxpsu Max number of passes in IP preprocessing for improving the strength ofthe LP Relaxation The IP preprocessing will be terminated after xmxpsu passes or if the objective function value does not change anymore Range 0 maxint Default
103. ing blanks are significant Field 2 contains the column name field 3 holds the row name and field 4 stores the value of the nonzero element Values must be in US number format e g 1000 1 Exponents are denoted by D or E and optionally a sign Examples of valid numbers are 1 1E 2 27 0 27 0 27 2 27 E 5 Fields 5 and 6 can optionally contain another nonzero element of the same column All nonzero elements of a column must be grouped together their order within this group is irrelevant RHS Section The RHS section starts with keyword RHS in column 1 In the following datasets the nonzero elements of the right hand side vector are specified several vectors are possible but usually only one vector is specified Each vector must have an unique name in field 2 In fields 3 to 6 the nonzero elements are stored like in the COLUMNS section The same rules like in the COLUMNS section apply RANGES Section The RANGES section starts with keyword RANGES in column 1 The following datasets hold the nonzero elements of the RANGES vector Each vector must have an unique name in field 2 In fields 3 to 6 the nonzero elements are stored like in the COLUMNS section The same rules like in the COLUMNS section apply A RANGES vector defines upper and lower bound of a constraint The bounded constraint lt a x lt u with a and x being real vectors and and u being real scalars can be defined by a RANGES vector In the ROWS section this constr
104. ise or column wise Lower bound for structural variables and constraints Upper bound for structural variables and constraints Objective function coefficient Type of structural variable 0 continuous lt gt 0 integer 0 OK 1 The size of model passed is to large for the available memory 2 Input data error The following little model will be passed to MOPS DLL in triplet form intyp 0 Max 3x1 5x2 x1 20x2 lt 0 x1 10x22 2 x1 gt 0 x2 is a binary variable Parameter for PutModel 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 17 m 2 n 2 nz 4 inf 1 e20 ee 330 2 05 typ 0 1 lb 0 0 0 0 1 e20 2 0 ub 1 e20 1 0 0 0 1 e20 ia 1 1 2 2 ja 1 2 1 2 a 120 20 0 1 0 10 0 Back to index ReadMpsFile ReadMpsFile FileName reads an MPS model into the main memory A path can be optionally specified in FileName Before calling this function you have to call AllocateMemory and InitModel Input FileName C255 Name of the MPS file optionally with path Output Re 14 0 OK lt gt 0 Error I O or syntactical error in MPS file Example Rc ReadMpsFile c mops models myfile mps If Re lt gt 0 Then Rc GetParameter xertyp Errortype Rc GetParameter xlinel ErrorDescriptionl Rc GetParameter xline2 ErrorDescription2 End If Back to index ReadProfile ReadProfile FileName reads a MO
105. l 10 1 LL 2 2 AL a DD Se 3 13 i AO al 4 10 1 Al Alal Al a 12 AL Aber il 5 1 0 25 5 3 0 1 5 NS By ade AO ga By Lb OE 2 0 23 1 Li i 12 0 2 7 3 0 23 Y a Oell Y 12 0 6 8 4 0 25 SS 0 1 Sek Seale al YS il Romane es cane oa SS 00 lt a gony Om ISS DE oor ps lt lt a O ven INO iS Ee 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Case Burma 148 9 5 AMPL AMPL files for the Burma model Model file sets set REGION the four parts of the 20 square kilometer region set PROD wheat and rice set PROJ the five possible projects parameter param water REGION PROJ default 0 0 the amount of water param costs PROJ gt 0 the investment costs param wateruse PROD gt 0 0 the water consumption param profit REGION PROD gt 0 profit param maxarea REGION default 5 max size of each area param percent default 0 3 percent of the whole region to cultivate wheat variables var project PROJ binary var area PROD REGION gt 0 objective function maximize ProfitBurma sum r in REGION p in PROD profit r p area p r Sp a BROW Cosics 3 I peogecez j Logical constraints Sib O SES O SAA ES project RIY gt project p2 EU S E Projaeeds s piojece Pal project Ron lt 03 Sf Projects project 25 project P2 lt Of Soto Alle
106. lDirection As Integer ByRef 1Status As Integer ByRef 1Phase As Integer ByRef dZf As Double As Integer OptimizeIP Lib mops d11 ByVal 1FrNod As Integer ByRef lNodes As Integer ByRef 1NIntSol As Integer ByRef lResou As Integer ByRef dZf As Double ByRef dLpBound As Double As Integer OptimizeLP Lib mops d11 ByVal lFrLog As Integer ByRef Liter As Integer ByRef 1NoInfeas As Integer ByRef 1LPStatus As Integer ByRef dZf As Double ByRef dSumInfeas As Double As Integer PutCol Lib mops dl1 ByVal 1ColIndex As Integer ByVal 1Mode As Integer ByVal sColName As String ByVal 1ColTyp As Integer ByRef dCost As Double ByRef dLB As Double ByRef dUB As Double As Integer PutModel Lib mops dl1 ByVal lIntyp As Integer ByVal dInf As Double ByVal 1 NRows As Integer ByVal 1NCols As Integer ByVal 1NNz As Integer ByVal plRowIndices As IntPtr ByVal plColIndices As IntPtr ByVal pdAij As IntPtr ByVal pdLBs As IntPtr ByVal pdUBs As IntPtr ByVal pdCosts As IntPtr ByVal plColTyps As IntPtr As Integer PutNonzeros Lib mops dll ByVal 1NElements As Integer ByVal plRowIndices As IntPtr ByVal plColIndices As IntPtr ByVal pdAij As IntPtr As Integer PutRow Lib mops dll ByVal iRowIndex As Integer ByVal 1Mode As Integer ByVal sRowName As String ByRef dLoRhs As Double ByRef dUpRhs As Double As Integer ReadMpsFile Lib mops dl11 ByVal sFileName As String As Integer ReadProfile Lib mops dl11 ByVal sFileName As String As Integer
107. lPSolution GetColType GetDim GetMaxDim GetNumberOfNZ GetRow GetRowIPSolution GetRowRhs PutCol SetMalPDim ChangeColUB ChangeNonzeros DelRow GetCol GetColLB GetColUB GetlPObjValue GetNonzero GetNumberOfRows GetRowBase GetRowLPSolution GetRowType PutNonzeros SetMaxLPDim ChangeCoILB Collndex LB changes the lower bound of the structural variable with index Collndex Input Collndex 14 LB R8 Output Re 14 Example Column index Lower bound 0 OK 1 Bad column index 2 Lower bound is greater than upper bound 10 Model locked Change lower bound of column 2 to 0 Re ChangeColLB 2 Back to index ChangeColType 0 ChangeCoILB Collndex LB changes the lower bound of the structural variable with index Collndex Input O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS DLL 24 Collndex 14 Column index LB R8 Lower bound Output Re 14 0 OK 1 Bad column index 2 Lower bound is greater than upper bound 10 Model locked Example Change lower bound of column 2 to 0 Re ChangeColLB 2 0 Back to index ChangeColUB ChangeColType Collndex ColType changes the type of a variable specified by Collndex Input Collndex 14 Column index ColType 14 Type of variable 0 continuous 1 integer Output Rc 14 0 OK 1 Bad column index 10 Model locked Example Change type of column 3 to integer Re ChangeColType 3 1 Back t
108. large model generators there might be a very very small performance gain from this though in most cases you would notice no significant performance difference in using the DLL or the LIB The MOPS LIB resp MOPS64 LIB must not be explicitly loaded during run time But since the MOPS DLL isa very small footprint library of about 2 MB and since loading is done quickly and efficiently by Windows there is no measurable performance gain from not having to load anything when using the LIB When linking statically the used functions from the MOPS LIB become part of the application executable This has advantages for application deployment since you do not need to distribute an additional DLL Furthermore it becomes impossible to rip the MOPS DLL from you application and use it independently Summarizing it makes only sense to use the MOPS LIB if you need full access to MOPS internal functions and data structures In the vast majority of cases the DLL is the more appropriate way to employ MOPS in your application See section MOPS LIB Functions for a list of the most important functions available in the static library MOPS LIB Functions The functions of the static MOPS library can be called with no further ado from any Fortran program under Windows Library versions for HP Visual Fortran formerly Compaq Digital and for Intel Fortran are available The MOPS LIB functions and their calling sequences have been re designed in MOPS v8 x to mak
109. le double double long typedef long __ stdcall GETLPSOLUTION long double double double long typedef long __stdcall GETMAXDIM long long long typedef long __stdcall GETMODEL long double long long long long long double double double double long typedef long _ stdcall GETNONZERO long long double typedef long stdcall GETPARAMETER char char yace ome NT herek CREO Moni meras Jeer clomlol ory rlomiglss mon City comio Teke hp typedef long __stdcall INITIALIZE void typedef long __stdcall INITMODEL void typedef long stdcall MOPS char typedef long stdcall OPTIMIZEIP long long long long double double typedef long stdcall OPTIMIZELP long long long long double double typedef long stdcall OPTIMIZE iome Lenes Jeer clenmoles y ass loma sieclesilal PURECO Kerney Ong michar deney SISKS eleh teure typedef long stdcall PUTMODEL long double long long long long long double double double double long typedef long _ stdcall PUTNONZEROS long long long double typedef long _ stdcall PUTOBJ long double typedef long __ stdcall PUTROW long long char double double typedef long _ stdcall READMPSFILE char 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 4
110. le name is specified the default name xmops pro will be taken In the profile all mops parameters can be set and the model will be read from an MPS or Triplet file depending on the values specified in xinfor and xfnmps Profiles can be edited with any text editor After optimization statistics and solutions can be loaded into your favorite editor See chapter MOPS Files for further details 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter MOPS STUDIO MOPS User Manual MOPS STUDIO 58 5 5 1 MOPS STUDIO Using MOPS STUDIO MOPS Studio MOPS Studio is an interactive front end to MOPS which supports the creation of models in the modeling languages AMPL MathProg Lindo and MPL combined with MOPS The version of AMPL implemented in MOPS Studio is identical to the original version with an additional graphic user surface Furthermore models in standard MPS format or in the MOPS specific triplet format can be loaded and solved with MOPS Index Main Window Menus Toolbar Input Window Output Window Options Parameters Execute AMPL SEN Solution Main Window EEE Dis TEBENG GET Be I EN WA diet Xx set NUTR a set FOOD param cost FOOD gt 0 param min FOOD gt 0 param max j in FOOD gt f_min j param n min NUTR gt 0 param n max i in NUTR gt n min i param amt NUTR FOOD gt 0 Figure 1 Main Window 2
111. lic static extern public static extern static extern ic static extern ic static extern ref int iColType public publ publ hungarian notation a array st be static int AllocateMemory int iMemory int DelCol int iColIndex int DelRow int iRowIndex int FindName string sName int iMode dais int FreeMemory int GetCol int iColIndex ref int iNElements ref double dCost int 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 48 ref double dLB ref double dUB ref int iStatus ref double dActivity ref double dRedCost D11Import mopsFile public static extern int GetDim ref int iNRows ref int iNCols ref int iNNz D11Import mopsFile public static extern int GetIPSolution ref int ilpSta ref double dTpFunet IntPtr daXs IntPtr daD IntPtr iaSta D11Import mopsFile public static extern int GetLPSolution ref int iLpSta ref double dLpFunct IntPtr daXs IntPtr daDj IntPtr iaSta D11Import mopsFile public static extern int GetMaxDim ref int iMaxRows ref int iMaxCols ref int iMaxNz D11Import mopsFile public static extern int GenFileNames string sFileName D11Import mopsFile public static extern int GetModel int ilIntype ref double dINF ref int iNRows ref int iNCols ref int iNNz IntPtr iaRowIndices IntPtr iaColIndices IntPtr daNZs IntPtr dalBs IntPtr daUBs IntPtr daCosts IntPtr jacolTypes D11Import mopsFile public static ext
112. line2 to get a more specific error description Input FileName C255 Name of profile to use optionally with path max 255 characters Output Re 14 0 OK 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 13 Error while reading the profile Generating default file names caused an error Bad MOPS parameter wrong name or value Error while reading MPS or triplet file Error in model generator Error in LP optimization see OptimizeLP for details Error while writing solution files Error in IP optimization see OptimizelP for details OO JO Om P GO LP Example A maximization problem is solved with MOPS parameters taken from c mops xmops pro After the optimization the return code of the LP run and the objective function value is retrieved fnpro c mops xmops pro Re MOPS fnpro Re GetParameter xrtcod returncode If returncode 0 Then Rc GetParameter xlpsta lpsta If lpsta 0 Then Rc GetParameter xfunct funct End if End if IP Example The profile contains all relevant optimization parameters If the profile lies in the current working directory you can only pass the filename of the profile or else the filename must be preceded by a relative or absolute path After the optimization return code IP status and objective function value are retrieved fnpro c mops xmops pro Rc Mops fnpro Re GetParameter
113. mbH amp Co KG MOPS User Manual MOPS Input Files 134 SOs3 MARKER SOSORG SOS3END MARKER SOSEND st sosi MARKER SOSORG SOSIEND MARKER SOSEND S2 910 MARKER SOSORG SOS2END MARKER SOSEND When a variable and its type are defined as a SOS variable with type x then it is not necessary to define the nonzero elements of the SOS row and there bounds in the bound section exception weights in the lower bound see Extended Integer Types Linearized functions The LI variables of linearized functions are integer variables and each group of Ll variables are marked with the keywords INTORG and INTEND To identify the groups they are indicated with a LI in the first field of the record COLUMNS EL eral MARKER INTORG I LEND MARKER IT INTEND These variables are saved as binary variables and so it is not necessary to define their bounds in the bound section Bound section The extended integer types require new types in the bound section Type Meaning Value required Y N SC fix charge costs for SC variables N SI fix charge costs for Sl variables N PI threshold value for Pl variables Y Semi continuous variable This variable is marked with the type SC The threshold value and the upper bound are labeled with the types LO and UP If no threshold value is defined or it is set to zero then the threshold value is set to xtolin If the upper bound is not defin
114. ments in LU factorization rcnx 14 Max number of characters for storing row and column names 0 No names will be stored 1 mx nx xdfnal gt 1 Actual number passed adm 14 Max number of additional constraints e g for cuts adn 14 Max number of additional rows adnz 14 Max number of additional nonzeros e g for cuts Output Re 14 0 OK lt gt 0 Error Example Set number of nonzeros to 600000 and use defaults for all other parameters Re SetMaxLPDim 0 0 600000 0 1 0 0 0 Back to index Embedding the DLL Declarations You can use MOPS DLL from a almost any programming language available under Windows but most languages require that you declare the functions you are about to use Usually these declaration are done before the actual program for example in headers or in declaration sections We used Hungarian Notation for the names of the function parameters with the following abbreviations indicating the type of the variable expected by MOPS DLL d double long i integer s string a array So the variable 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 43 2 5 2 aMyVariable is an array of integers Declarations of all MOPS DLL functions are available for the most popular programming languages Simply copy and paste them into your code Visual Basic 6 0 Visual C C 6 0 Visual Basic NET e C See also the demos that are distributed with MOPS DLL for examples how to
115. mines whether an MPS file is written from the internal model representation before LP preprocessing Values 0 mps file is not written 1 mps file is written before LP preprocessing Default 0 Type Long Back to index IP Parameters Index xadrow xbckpa xbndha xbndrd xbrheu xclict xcored xcovct xeucrd xflwct xflwpa xfrtre xfrnod xgomct xgommc xheutp xhfinb xhgap xhrdlb xhrdub xhtlim ximbnd ximpli xipbnd xiplpt xlifo xlocs xlotst xlpgap xlpmip xmnheu xmirct xnewbb xnibab xnistr xnodbf xnodse xnoitb xnopre xnogap xparnd xpcini xprlev xranha xrimpr xusepl xadrow Maximum number of additional constraints which can be added during IP preprocessing Default 2000 Type Long 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 96 Back to index xbckpa Backtracking parameter for mixed lifo node selection strategy xnodse lt O and xlifo 2 Range 0 0 1 0 Default 0 999 Type Double See also xnodse xlifo Back to index xbndha The dual simplex engine xIptyp 2 benefits from tight bounds derived during the LP preprocessing LPP xbndha determines the level of bound reduction and bound retaining after LP preprocessing Values 0 Level 0 tight bounds from LPP are retained if the initial LP is solved by the dual simplex and the model is a pure LP model 1 Level 1 as 0 but in addition an extended bound reduction is used to further tighten the bounds 2 Level 2 as
116. mpr and xglgap are relative values Therefore we compute rimpr min xrimpr 1 1 zlb and glgap min xglgap 1 1 zlb where zlb is the functional value after IP preprocessing If one the values rimpr or glgap are smaller then the corresponding value of xrimpr or xglgap the value is replaced Values 0 dynamic computation of xrimpr and xglgap after IP preprocessing and possible reduction of these values if the LP objective function zlb is sufficiently large 1 no dynamic computation xrimpr and xglgap are unchanged Default 0 Type Long See also xrimpr xglgap Back to index xnoitb Indicate whether integer table is build The integer table is automatically built if extended integer types are present In all other cases there is no need to built an integer table where various information about integer variables are stored Values 0 integer table can be build 1 no integer table Default 1 Type Long Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 111 xnopre Allows to turn off IP preprocessing Values 0 no IP preprocessing gt 0 IP preprocessing with individual settings Default 1 Type Long Back to index xparnd Set the partitioning type for the node table The node table is partitioned in two sets of nodes those which are immediate candidates and those which are waiting If the IP model still has a bad LP relaxation after IP preprocessing xpa
117. n 84 xtolpv 84 xtolqi 84 xtolr1 84 xtolr2 84 xtolre 84 xtolx 84 xtolx1 84 xtolx2 84 xtolzr 84 xversn 113 xwrmps 89 xzbest 113 xzlond 113 xzubnd 113 2007 MOPS Optimierungssysteme GmbH amp Co KG
118. n ReadMpsFile Lib mops dll ByVal sFileName As Long Declare Function ReadProfile Lib mops dll ByVal sFileName As Long 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 44 2 5 3 Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Declare Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function Function ReadTripletFile Lib mops dl1 ByVal sFileName As Long SetMaxIPDim Lib mops dll INNo amp As Long SetMaxLPDim Lib mops dll ByVal 1NC1i amp ByVal 1NImp8 ByVal 1NZc18 ByVal ByVal 1NRowsg ByVal 1NCols amp ByVal 1NNz8 ByVal lNLunz amp ByVal lRcn ByVal 1NAdRows amp ByVal 1NAdCols amp ByVal 1INAdNz amp As Long SetParameter Lib mops dl WriteMpsFile Lib mops dl 1 1 ByVal sParameter As Long ByVal sFileName As Long WriteTripletFile Lib
119. n int ChangeNonzeros int iNElements IntPtr iaRowIndices IntPtr iaCollndices IntPtr daNZs D11Import mopsFile public static extern int ChangeRhs int iRowIndex double dRhs D11Import mopsFile public static extern int GetColBase int iStartColIndex int iEndColIndex IntPtr iaStatus D11Import mopsFile public static extern int GetCollPSolution int iStartColIndex int iEndColIndex IntPtr daIPSol D11Import mopsFile public static extern int GetColLB int iColIndex ref double dLB D11Import mopsFile public static extern int 7 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 49 2 6 2 6 1 GetColLPSolution int iStartColIndex int iEndColIndex IntPtr daLPSol DllImport mopsFile public static extern int GetColType int iCollndex ref int iColType D11Import mopsFile public static extern int GetColUB int iColIndex ref double dUB D11Import mopsFile public static extern int GetCost int iColIndex ref double dCost D11Import mopsFile public static extern double GetIPObjValue D11Import mopsFile public static extern double GetLPObjValue D11Import mopsFile public static extern int GetNumberOfColumns ref int iNCols D11Import mopsFile public static extern int GetNumberOfNZ ref int iNNz D11Import mopsFile public static extern int GetNumberOfRows ref int iNRows D11Import mopsFile public static extern in
120. ng GetNumberOfRows Lib mops dl1 1NRows amp As Long ByVal 1StartCollndex amp ByVal 1EndColIndex GetRedCost Lib mops dll daRedCost As Long GetRowBase Lib mops dl1 As Long ByVal 1StartRowIndex ByVal lEndRowIndex laStatus amp GetRowDualValues Lib mops dl1 ByVal 1StartRowIndex8 ByVal lEndRowIndex amp daDuals As Long GetRowIPSolution Lib mops dl1 ByVal 1StartRowIndex8 ByVal lEndRowIndex amp daIPSol As Long GetRowLPSolution Lib mops dl1 ByVal 1StartRowIndex8 ByVal lEndRowIndex amp daLPSol As Long GetRowLhs Lib mops dll GetRowRhs Lib mops dll GetRowType Lib mops dll Visual Basic NET Copy and paste these declarations to your VB NET module Names of functions are case sensitive you should not modify them Eventually the location of the MOPS DLL must be adapted See Samples and VB NET documentation for usage of IntPtr for passing Arrays to the unmanaged MOPS DLL Declare Declare Declare Declare Declare Declare Declare Declare Declare Function Function Function Function Function Function Function Function Function ByVal lRowIndex amp dLhs As Long ByVal lRowIndex amp dRhs As Long ByVal lRowIndex amp lRowType amp As Long GetSolutionStatus Lib mops dl1 As Long AllocateMemory Lib mops dl1 ByVal lMemory As Integer As Integer DelCol Lib mops dl1 ByVal 1ColIndex As Integer As Integer DelRow Lib
121. nt value to represent infinity e g 1 0E 20 The first four values are integer If xrcmax 0 no names will be processed even if there are names present in the Triplet file If xremax 1 then xrcmax will be calculated as xrcmax xn xm xdfnal where xdfnal specifies the maximum length of names default xdfnal 8 If xrcmax gt 1 its actual value will be taken Section 3 contains xn datasets with information for all structural variables Each line holds the following values in the given order e Lower bound e Upper bound e Cost coefficient 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 131 7 3 3 2 e Type 0 continuous 1 integer e Name of variable optionally max 64 characters The name may be enclosed in quotation marks Inverted commas or quotation marks are treated as delimiters and will not be stored with the name Section 4 contains xm datasets with information for all constraints Each line holds the following values in the given order e Costcoefficient e MOPS internal ower bound internal LHS e MOPS internal upper bound internal RHS e Name of constraint optionally max 64 characters The name may be enclosed in quotation marks Inverted commas or quotation marks are treated as delimiters and will not be stored with the name The internal bounds are defined as MOPS internal ower bound external upper bound MOPS internal upper bound
122. ntents Table of Contents Chapter Introduction 2 1 WACO e It Le EE 2 2 What s new in MOPS EE 3 Chapter Il MOPS DLL 6 1 Using MOPS DLU cios indica ga as kin aati 6 2 Avoiding KE EE 7 3 Basic FUNCTIONS alesana ta aar NG a AN Tag EN 8 BASIC FUNCTIONS EEN 8 A Extended TUNCHONS ses nssiccssscececteasssackeceaseaunccatssavducedecebensuavaaasucnisaveuscdvectwocausedaeecbvasssecdacvaie 22 Extended functions ieee ee GENEE A cee ab anana adadi 22 5 Embedding the DLL 2 22 42 Declarations sasur ana aana AR Ag Reade a as aa NEEN ea wo da aa Ka NE abu ceed abane ngena aan 42 Visual BASIC 6 0 EE 43 Visual Basic TN WEE 44 Visual e EEN 46 e GE 47 6 64 Bit Version a aaa ga Ta GENE EE NENNEN ENEE geen 49 G4 Bit Versi n nat Ee da ag aa E Nah ndan aa a be e 49 Chapter III MOPS LIB 51 1 Using MOPS LIB aan Ga anang Aga KANAAN NB nennen 51 2 MOPS LIB TITTEN 51 3 Calling MOPS LIB from C C unuuussssannnanannnnnannnnnnnnnnnnnnnnnnnnnannnnnnnnnnnnnnnannnnnnnnnnnnnnnnnnnnn 54 Chapter IV MOPS EXE 56 1 Using MOPS EKE un Ein 56 Chapter V MOPS STUDIO 58 1 Using MOPS STUDIO diante 58 Chapter VI MOPS Parameter 66 1 MOPS Parameter e dete ae anaa NEG ENEE AE aa aaa e 66 2 Input P rameter 2 4 aaa aka A A 66 InputParameter cio 2ER EES 66 BMG d TC 66 LP Param ters EE 69 IST TEEN 77 E ET EE 79 Leleratesg ge DN EE ee a KG aga EDA Nn BG ANG E
123. o index ChangeCost ChangeCost Collndex Cost changes the objective function coefficient of the structural variable with index Collndex Input Collndex 14 Column index Cost R8 Objective function coefficient Output Re 14 0 OK 1 Bad column index 10 Model locked Example 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 25 Changes cost of column 3 to 0 Re ChangeCost 3 0 Back to index ChangeLhs ChangeLhs Rowindex Lhs changes the lower bound left hand side of the constraint with index Rowindex Input Rowindex 14 Row index Lhs R8 Lower bound left hand side Output Re 14 0 OK 1 Bad row index 2 Lower bound is greater than upper bound 10 Model locked Example Sets the lower bound of row 1t0 0 r Changelhs 1 0 Back to index ChangeNonzeros ChangeNonzeros NElements RowIndices Collndices NZs changes a number of nonzero elements The last three parameters are arrays that contain the nonzero elements with their row and column indices triplet wise Input NElements 14 Number of elements to be changed Rowindices 14 Array of row indices Collndices 14 Array of column indices NZs R8 Array of nonzero elements Output Re 14 0 OK 1 Bad row index 2 Bad column index 3 One or more nonzero elements is 0 4 Nonzero element to be changed does not exist in the model 5 No rows or columns present that can be changed 10 Model locked Exampl
124. odel are stored separately The entire window can be spilt horizontal or vertical and you can drag and drop files into the windows Also the tabs can be dragged and dropped Output Window Figure 4 Output Window The Output Window can be activated with View gt Show Output Window The Output Window displays all information about the optimization and the syntax errors The position of a syntax error is marked with the line number and with gt gt gt and lt lt lt around the error The relevant line can be found easier if the line numbers are shown View gt Show Line Numbers Like all other windows in the new MOPS Studio versions since v1 7 the output window can be docked and hidden Options K In order to change some settings access Menu Tools gt Options or simply click on this button 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS STUDIO 62 OOOO sl General AMPL Location of MOPS DLL je Programme MOPS MOPSStudio mops dil MOPS DLL Version MOPS 7 80 C Uwe H Suhl 03 03 2006 MOPS Control Version 1 0 48 2643 IV Create new separate directories for each model below the model default directory Model Default Directory je ProgrammeMOPSAMOPS Studio samples Se mes Figure 5 General Options 2 options aa General AMPL Location of AMPL EXE C Programme MO PSAMOPS Studios ampl exe amp Location of MOPSAMPL EX
125. os instead of m n where nsos represents the number of special ordered sets This is so because the model contains m nsos constraints of which only m constraints are generated by the user Input Intyp 14 inf R8 m 14 n 14 nz 14 ia 1 nz 14 ja 1 nz 14 a 1 nz R8 Ib 1 n R8 ub 1 n R8 rl 1 m R8 ru 1 m R8 c 1 n R8 type 1 n 14 fepi 1 n R8 Back to index Optimize Mode of storing the model in the arrays ia ja a O Triplets in ia ja a The triplets i j aij have no special order 1 Row wise storage where ia contains in positions 1 m the start position of the rows in arrays ja and a 2 Column wise storage where ja contains in positions 7 n the start positions of the columns in arrays ia und a Value that represents infinity e g 1 0E20 Number of rows Number of columns Number of nonzeros Row indices intyp 0 2 or start positions of rows intyp 1 Columns indices intyp 0 1 or start positions of columns intyp 2 Nonzero elements of the matrix triplets row wise or column wise Lower bound for structural variables Upper bound for structural variables Lower bound for constraints Upper bound for constraints Objective function coefficient Type of structural variable fix charge cost for SC and SI variables threshold values for Pl variables and zero for the rest Optimize Direction Status Phase ObjFunc optimizes the LP IP model presently in memory
126. rnd should be set to zero because the search in the first set most likely results in no integer solution As a consequence the search process for an initial integer solution takes longer than necessary Values 0 no partitioning 1 partition node table Default 1 Type Long Back to index xpcini Set the initialization type for the computation of pseudo costs Values 0 initialize pseudo costs to zero 1 initialize pseudo costs to variable cost 2 solve LP partially to compute pseudo costs not activated Default 1 Type Long O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 112 See also xnodse xbrheu xparnd Back to index xprlev Probing level Probing tries to set binary variables that are not fixed to O or 1 on a tentative basis and analyzes the resulting implications In pure 0 1 models this technique can be very effective For mixed integer models probing is usually less effective Values 0 Probing only on fractional 0 1 variables during IP preprocessing 1 Probing on all 0 1 variables but only at IP preprocessing 2 Probing on all 0 1 variables at IP preprocessing and at each node of the tree Default 1 Type Long Back to index xranha Sets conversion of Range constraints that contain integer variables Values 0 No conversion 1 Range constraints with integer variables are converted into two separate constraints to allow a better IP preprocessing
127. ry sparse models Default 1 Type Long 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 75 Back to index xnwluu A new LU fupdate can be used in conjunction with the new LU factorization and has the same advantage The old LU update of MOPS can be used by specifying xnwluu 0 The old LU update offers a small advantage on very sparse models Note that the new LU update requires the new LU factorization However the new LU factorization can be used in conjunction with the old LU update Default 1 Type Long Back to index xoripm Ordering strategy for the Cholesky factorization using the interior point method xIptyp 4 Values 0 Automatic ordering 1 Minimum degree 2 Minimum local fill in 3 Nested dissection 4 Multi section ordering Default 0 Type Long Back to index xpreme Presolve action control for LP preprocessing The bits of this value represent turning on or off individual presolve techniques To get a particular form of the presolve set xpreme to the sum of the values corresponding to the following presolve methods 1 Singleton row check Singleton rows are replaced by bounds on variables 2 Singleton column check Free or implied free singleton columns are eliminated from the problem 4 Primal feasibility check This process evaluates the possible minimum and maximum row 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User
128. rzojecess sum dia PROT moge al 12 Irrigation constraint s t Waterbalance r in REGION sum j in PROJ water r j project j gt sum p in PROD wateruse p arealp r constraint of the area under cultivation sie Maximal Area r in REGIONIS Sumo in PROD area lla 12 lt mettes Let un maximal wheat cultivation coto Mezimel Wicats sumir in REGION area wo z sumijo ia ZROD 1m EGION percent area p r lt 0 Wu Data file sets set REGION set PROD set PROJ AB De R WR iL p2 Ips BA P57 Loggt o parameter param water 3 Pil pS P4 P5 PAN iss O 0 4 B o 1 0 0 2 Gos ORG 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Case Burma 149 Do 5 5 1 27 param costs 3 PL 5000 22 10000 23 2000 21 2000 PS 50005 param wateruse W 0 1 R 0 25 param profit gt OW Ro E A 1000 1100 B 1300 1300 e 1600 1400 D 1800 1600 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter References MOPS User Manual References 151 10 References 10 1 References MOPS White Paper Mathematical OPtimization System Technical Description MOPS Optimierungssysteme GmbH amp Co KG Paderborn January 2007 available as download from the MOPS homepage mops optimizer com 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Index 152 GetColBase 22 n d ex GetCollPSolution 22 GetColLB 22 Ge
129. s improves numerical stability 4096 Extended dual test This procedure performs additional dual tests which may change the optimal solution The optimal objective value is not changed This procedure can therefore be turned on if only the optimal objective function value is important Note If you need an optimal dual solution corresponding to the original optimization problem you have to turn off methods 128 and 1024 Range 0 8191 Default 2047 for pure LP models 3903 for pure IP models 3583 for mixed integer models For IP models with a small amount of 0 1 variables the strategy 2047 may be more efficient Type Long Back to index xrduce Determines if LP preprocessing is executed 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 77 Values 0 No LP preprocessing 2 LP Preprocessing Default 2 Type Long See also xpreme Back to index xstart Specifies how the initial basis is created when using one of the simplex engines Values 0 The basis will be defined by all logical variables 1 A crash basis is produced 2 Re start from an external basis xfnbai 3 Re start from save basis xfnsav Default 1 Type Long See also xfnbai xfnsav Back to index 6 2 4 MPS vector names Index xbound xdata xobj xrange xrhs xbound Name of vector to be used as Bound Vector in MPS files If xbound is blank the first vector in the BOUNDS section of an MPS f
130. s parameter determines if mixed integer rounding cuts should be derived during IP preprocessing Values 0 MIR cuts are not used 1 MIR cuts are derived only at the first IP preprocessing and only from original constraints 2 MIR cuts are derived at every IP preprocessing but only from original constraints 3 MlR cuts are derived at every IP preprocessing and all active constraints are considered Default 3 Type Long Back to index xmnheu Sets number of nodes to be processed by the heuristics before the branch and bound process This parameter is only relevant if heuristics are used xheutp gt 0 Range 0 maxint 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 108 Default 50 Type Long See also xheutp Back to index xnewbb This parameter allows to activate the old branch and bound algorithm Values 0 old branch and bound 1 new branch and bound Default 1 Type Long Back to index xnlbab Node limit in branch and bound before the next local search or mixed LIFO iteration starts This parameter is relevantif xnodse lt O or xlocs gt 0 Range 0 xmxnod Default 1000 Type Long See also xnodse xlocs xnlstr xlifo Back to index xnistr Node limit during local search heuristic or mixed lifo strategy This parameter is only relevant if xnodse lt 0 or xlocs gt 0 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS U
131. ser Manual MOPS Parameter 109 Range 0 xmxnod Default 1000 Type Long See also xnodse xlocs xnlbab xlifo Back to index xnodbf Combine a node selection strategy xnodse gt 1 with best first selection Values 1 no best first selection 0 the frequency of the best first strategy is computed depending on the gap x gt 0 best first strategy is used every x node Default 0 Type Long See also xnodse Back to index xnodse Sets the node selection strategy in the branch and bound process lt 0 mixed LIFO strategy with a node selection xnodse 0 LIFO 1 Chose node with best objective function coefficient 2 Chose node with minimum sum of integer infeasibilities 3 Best Projection with xnodse 2 until the first IP solution 4 Best Projection original version 5 Chose node with best estimation based on pseudo costs 6 Chose node until first IP solution with xnodse 2 than with xnodse 5 until gap is smaller than 5 and finally chose node with percentage error 7 Best estimation based on pseudo costs with xnodse 2 until first IP solution Default 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 110 3 Type Long See also xlifo xnodbf Back to index xnogap xrimpr and xglgap are set to default values of 1 d 4 If the IP model has very large objective function values then it is possible that a true optimal IP solution may nit be found because xri
132. sis incorrect index in xh out of range insufficient main memory increase xmreal to insufficient main memory increase xmreal insufficient main memory during presolve insufficient space for triplets increase xnenmx Allocation of memory missing or unsuccessfull MOPS library invalid open error on file with unit read error on file with unit write error on file with unit rewind error on file with unit input file incorrect for your model unit error closing file with unit license typ invalid for this feature row limit exceeded limit is col limit exceeded limit is USB dongle not present or invalid imr is not written set ximrrw 1 more then 3 primal dual cycles name in profile unknown line apostrophe missing or character string too long double precision value in profile incorrect line integer value in profile incorrect line input record incomplete missing value s token in record exceeds 64 characters 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 120 0061 0062 0063 0110 0112 0113 0122 0123 0125 0126 0128 0129 0130 0131 0132 0152 0156 0157 0158 0159 0161 0162 0163 0164 0165 0166 0167 0170 0171 0172 0173 0180 0181 0182 0183 0184 0185 0186 0201 0202 invalid fc cost for sc si or invalid value for pi lb of sc si is less than zero si sc pi sos or li are used wrong first record premature end of input file name
133. sis will be saved Values 1 Internal basis format Basis will be saved to file xfnsav 2 External basis format MPS format Basis will be saved to file xfnbao 3 Both internal and external basis formats will be saved Default 1 Type Long See also xfrbas xfnbao xfnsav xstart Back to index xbndha 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 70 Determines how bounds are treated when solvong initial LPs IPM and primal simplex psx needs less restricted bounds Dual dsx needs restricted bounds for best performance The default is set to 0 if IPM or psx is used and to 1 if dsx is used Furthermore in case of a pure LP and use of dsx xbndha is setto 2 and an extended bound reduction is executed This is not the case for IP models To execute the extended bound reduction xbndha has to be set to 2 Values 0 reduced bounds during LP preprocessing are relaxed at the end of LPP default when IPM is used 1 reduced bounds during LP preprocessing are kept default id DSX is used 2 extended bound reduction is used Default 0 Type Long Back to index xdjscl Sets scaling of Reduced Costs Values 0 No scaling of Reduced Costs in Pricing 1 Reduced Costs of non basis variables are scaled modified Devex 2 Full Devex 3 steepest edge pricing Default 1 Type Long Back to index xdropf An element in a row or column will be set to 0 during the LU Factoriz
134. so applied to logical variables Range 1 0E 9 1 0E 3 Default 1 0E 6 Type Double See also xtolr1 Back to index xtolx2 Primal absolute feasibility tolerance in phase 2 of the Simplex A variable x with lower bound b and O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 89 6 2 7 upper bound ub will only be regarded as feasible if Ib xtolx2 xtolr2 Ib lt x lt ub x tolx2 xtolr2 ub This rule is also applied to logical variables Range 1 0E 9 1 0E 3 Default 1 0E 5 Type Double See also xtolr2 Back to index xtolzr The result of a floating point calculation will be set to zero if its absolute value is smaller than xtolzr Range 1 0E 13 1 0E 9 Default 1 0E 12 Type Double Back to index Other Parameters Index xchksw xdimen xfrlog xinf xinfor xminmx xoutsl xmaxel xremax xstorn xwrmps xnwcon xchksw ximrrw xoutlv xscale 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 90 Determines if a model will be checked syntactically before optimization Values 0 No syntax check 1 Checking if the model is syntactically correct Default 0 Type Long Back to index xdimen Sets the maximum model dimensions used when reading MPS files Values 0 Set the maximal model dimensions specified by xnmax xmmax xnzmax 1 MPS Convert sets the max dimensions automatically
135. status if optimization was successful 1 maximization 1 minimization Iphase 0 LP phase Iphase 1 IP phase Istatus 0 optimal solution 6 Get LP solution or IP solution if optimal or time limit reached with an integer solution if Iphase 0 and Istatus O then LP model optimal LP solution found store it in user arrays rc GetLPSolution xIpsta xfunct xs 1 dj 1 stat 1 else if Iphase 1 and Istatus 0 or Istatus 3 then optimal IP solution or feasible IP solution found time limit store it in user arrays rc GetlPSolution ipsta xzbest xs 1 dj 1 stat 1 else error or time limit and no integer solution 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 7 2 2 end if If rc lt gt 0 Then exit As a general principle a function returns an integer return code which is zero ifthe call was successful and nonzero in case of an error Declarations To use MOPS DLL its exported functions must be declared See chapter Embedding the DLL for information about how to declare DLL functions Modellocking Once the optimization has started the model will be locked for functions which retrieve model information or which change the model If you try to use such functions while the model is locked error code 10 will be returned After complete optimization the model will be unlocked and you can for example change parts of it for a new optimization run This mechanism is nec
136. t GetRedCost int iStartColIndex int iEndColIndex IntPtr daRedCost D11Import mopsFile public static extern int GetRowBase int iStartRowIndex int iEndRowIndex IntPtr iaStatus D11Import mopsFile public static extern int GetRowDualValues int iStartRowIndex int iEndRowIndex IntPtr daDuals D11Import mopsFile public static extern int GetRowIPSolution int iStartRowIndex int iEndRowIndex IntPtr daIPSol D11Import mopsFile public static extern int GetRowLPSolution int iStartRowIndex int iEndRowIndex IntPtr daLPSol D11Import mopsFile public static extern int GetRowLhs int iRowIndex ref double dLhs D11Import mopsFile public static extern int GetRowRhs int iRowIndex ref double dRhs D11Import mopsFile public static extern int GetRowType int iRowIndex ref int iRowType D11Import mopsFile public static extern int GetSolutionStatus O 64 Bit Version 64 Bit Version The 64 bit version of MOPS DLL MOPS64 DLL works exactly the same way the previously described 32 bit version does In a 32 bit operating system addresses are 4 bytes long so when a DLL function expects an address pointer like for example in PutModel a 4 byte pointer is passed In 64 bit operating systems addresses double to 8 bytes Since the compiler takes care of these operations the user of 64 bit MOPS DLL doesn t have to bother about this So the syntax for calling 64 bit functions is exactl
137. tColLPSolution 22 6 8 GetColType 22 GetColUB 22 GetCost 22 64 Bit 49 GetDim 22 51 2 A GetIPObjValue 22 GetlPSolution 8 51 GetLPObjValue 22 AllocateMemory 8 51 GetLPSolution 8 51 S H S GetMaxDim 22 51 GetModel 8 51 GetNonzero 22 51 Burma 142 GetNumberOfColumns 22 C GetNumberOfNZ 22 GetNumberOfRows 22 GetParameter 8 51 C 47 GetRedCost 22 Case 142 GetRow 8 51 ChangeColLB 22 GetRowBase 22 ChangeColType 22 GetRowDualValues 22 ChangeColUB 22 GetRowlPSolution 22 ChangeCost 22 GetRowLhs 22 ChangeLhs 22 GetRowLPSolution 22 ChangeNonzeros 22 GetRowRhs 22 ChangeRhs 22 GetRowType 22 C Sharp 47 GetSolutionStatus 22 DelCol 22 51 Initialize 8 DelRow 22 51 InitModel 8 51 7 E a Interlanguage Interface 54 FindName 22 51 Finish 8 LIB 51 FreeMemory 51 LoadModel 8 51 FreeMemory discontinued 8 G M Main Window 58 Mops 8 51 MOPS LIB 51 GenFileNames 22 GetCol 22 51 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual Index 153 MPS File 145 MPS file example 126 MPS Files 125 O Optimize 8 51 OptimizelP 51 OptimizelP discontinued OptimizeLP 51 OptimizeLP discontinued P PutCol 22 51 PutModel 8 51 PutNonzeros 22 51 PutRow 22 51 sR ReadMpsFile 8 51 ReadProfile 8 51 ReadTripletFile 8 51 Ressource Limits 79 ao SetMaxIPDim 22 51 SetMaxLPDim 22 51 SetParameter 8 51 Static Library 51 Triplet File 146 V Visual Basic NET 44 Visu
138. tRowIndex 1 Input StartRowIndex 14 Start index of rows EndRowlndex 14 End index of rows Output Duals R8 Array of dual values Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of rows Example Fills array daDuals with dual values values for rows 3 4 and 5 Re GetRowDualValues 3 5 daDuals Back to index GetRowIPSolution GetRowIPSolution StartRowIndex EndRowindex IPSol gets IP solution values of a number of rows after optimization The array IPSol will be filled and must have sufficient size at least EndRowiIndex StartRowIndex 1 Input StartRowIndex 14 Start index of rows EndRowlndex 14 End index of rows Output IPSol R8 Array of IP solution values Re 14 0 OK 1 Start index greater than end index 2 Start index less than 1 3 End index greater than number of rows 4 No IP solution present Example Fills array dalPSol with IP solution values for rows 3 4 and 5 Re GetRowIPSolution 3 5 dalPSol 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS DLL 37 Back to index GetRowLPSolution GetRowLPSolution StartRowIndex EndRowindex LPSol gets LP solution values of a number of rows after optimization The array LPSol will be filled and must have sufficient size at least EndRowindex StartRowIndex 1 Input StartRowIndex 14 Start index of rows EndRowlndex 14 End index of rows Output LPSol R8
139. the lower bound and less than the upper bound BOUNDS LO BND PILI 2 000 UP BND PILI 40 00 PAN STI 20 00 LI BND PI2 4 000 UI BND PIZ 9 000 PI BND PILZ 6 000 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Input Files 136 7 3 4 3 Enhanced Triplet Format The integer variables with a extended integer type needs an enhanced Triplet format The declaration of the model dimension in Section 2 gets an additional parameter If the value of this parameter is greater than zero the model contains variables with extended variable types The Section 3 has to be adapted to the new variable types In this section the variable is defined with its lower bound upper bound cost type and optional with its name The changes of the lower bound and the different variable types are already described The definition of the fix charge costs of SC and SI variables and the threshold value of the Pl variable need a new record The record follows the normal definition of the variable It is marked with a k or K at the beginning and includes the value for the fix charge costs or the threshold value kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk example with extended integer types KAKAK AKAK KA KK AKK AKK AKK KK KAKAK KK KK AK A LOO 200 S00 22 11 122107 211 pipO l Eve vk lk NAN aa D vk lk NABI a ebe EE V a2 LOCAS OS Ee SN 10 20 3 SC 0 0 0 4 1 0 406 SOS
140. times more than one line in a BOUNDS section is necessary to specify bounds 20 lt x lt 30 requires LO x 20 and UP x 30 inf lt x lt 10 requires MI x und UP x 10 Integer Variables The normal integer variables binary general integer and SOS Type 3 can be declared in MPS files in twoways 1 By enclosing the integer variables in MPS Marker Datasets A Marker Dataset contains blanks in field 1 a specific name in field 2 and field 3 contains the token MARKER with inverted comma Field 4 is empty and field 5 contains a one of the following keywords INTORG INTEND SOSORG or SOSEND All variables enclosed in Marker Datasets with the keywords INTORG and INTEND are integer If no further specification about these variables are made in the BOUNDS section they will be regarded as 0 1 variables For defining them as integers appropriate bounds must be set in the BOUNDS section Variables enclosed between the keywords SOSORG and SOSEND belong to a Special Ordered Set SOS MOPS will generate for SOS variables a constraint in which all variables of the set have the coefficient 1 0 and the value of the RHS is also 1 0 with all variables of the set being binary variables So in a feasible solution one of the SOS variables must have the value one all others must be zero ROWS E SON1102 COLUMNS SON1102 MARKER SOSORG Y2N1101 KSN1101 1 00000 Y2N1101 RTN1101 5 00000 Y2N1102 RT
141. tion will be written to a file 2 row and column information of an LP IP solution will be written to a file Default 1 Type Long See also xfnlps xfnips Back to index xmaxel Maximum value of matrix coefficient If it is greater than xmaxel an error will occur xmaxel cannot be changed in profiles or via SetParameter Default 1 0E 5 xinf Type Double See also xinf Back to index xrcmax Determines how the size of the character space for row and column names is computed Note if standard mps files are used there is no need to store names In case of the convert based on the free format xrcmax is computed automatically based on the problem size Values 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 94 0 no storage of names xn xm xdfnal gt 1 this value in bytes Default 0 Type Long See also xstorn Back to index xscale Determines ifthe model is scaled before optimization Values 0 No scaling 1 Row wise scaling 2 Row wise and column wise scaling Default 2 Type Long Back to index xstorn Determines if row and column names are to be stored Values 0 No storage of names 1 Storage of names from mps data and or in the context of DLL functions Default 1 Type Long See also xremax Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 95 6 2 8 xwrmps Deter
142. tive feasibility tolerance in phase 1 of the Simplex A variable x with lower bound b and upper bound ub will only be regarded as feasible if Ib xtolx2 xtolr2 Ib lt x lt ub xtolx2 xtolr2 ub This rule is also applied to logical variables Range 0 0 1 0E 7 Default 1 0E 14 Type Double See also xtolx2 Back to index xtolre Primal relative feasibility tolerance after termination of the LP run A variable x with lower bound b and upper bound ub will only be regarded as feasible if Ib xtolx xtolre Ib lt x lt ub xtolx xtolre ub This rule is also applied to logical variables Range 0 0 1 0E 7 Default 1 0E 10 Type Double See also O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 88 xtolx Back to index xtolx Primal absolute feasibility tolerance after termination of the LP run A variable x with lower bound b and upper bound ub will only be regarded as feasible if Ib xtolx xtolre Ib lt x lt ub xtolx xtolre ub This rule is also applied to logical variables Range 1 0E 9 1 0E 3 Default 1 0E 4 Type Double See also xtolre Back to index xtolx1 Primal absolute feasibility tolerance in phase 1 of the Simplex A variable x with lower bound b and upper bound ub will only be regarded as feasible if Ib xtolx1 xtolr1 Ib lt x lt ub xtolx1 xtolr1 ub This rule is al
143. to index xertyp Internal error number Type Long See also Error Message Back to index xipfun Objective function value of the best IP solutions found so far Type Double Back to index xipsta IP optimization status 0 Branch 8 Bound search terminated 1 Search not yet terminated Type Long Back to index O 2007 MOPS Optimierungssysteme GmbH 6 Co KG MOPS User Manual MOPS Parameter 115 xiptim IP optimization time in minutes without initial LP Type Double Back to index xiter Current number of Simplex iterations Type Long Back to index xline1 First line with context sensitive information max 72 characters Type C72 Back to index xline2 Second line with context sensitive information max 72 characters Type C72 Back to index xipfun Objective function value if the initial LP Type Double Back to index xipsta LP solution status 0 optimal solution found 1 the problem has no feasible solution 2 unbounded solution 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 116 Type Long Back to index xIptim Time consumed for solving the initial LP in seconds Type Double Back to index xm Current number of constraints of the internal model Type Long Back to index xmorig Number of constraints in the original model before LP preprocessing Type Long Back to index xmxj Current number of
144. to index xfnips 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 68 File name optionally with path for the LP solution Parameter xouts determines whether a solution file will be written or not Type String 255 Back to index xfnmps File name optionally with path ofthe MPS file Type String 255 See also xdata xobj xrhs xrange xbound Back to index xfnmsg File name optionally with path ofthe error message file Type String 255 Back to index xfnpro File name optionally with path of aMOPS profile A profile can be used to set MOPS parameters Default xmops pro Type String 255 Back to index xfnsav Specifies a filename of a basis to be saved saved in internal format at the end or after xfrbas iterations when using one of the simplex engines primal or dual Type String 255 See also xfrbas xbatyp Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 69 6 2 3 xfnsta File name optionally with path of the statistic file Parameter xoutlv determines if a statistics will be written during optimization Type Long Back to index LP Parameters Index xbatyp xbndha xdjscl xdropf xdropm xfrbas xfrinv xipxov xlptyp xluctr xoripm xpreme xrduce xstart xnproc xipmem xnwluf xnwluu xfiltl xipdua xbatyp If xfrbas gt 0 then xbatyp determines in which format the internal ba
145. und tree is a discontinued function not supported by recent MOPS versions Determines if the Branch and Bound tree will be saved for posterior re starts when reaching a resource limit Values 0 B amp B tree will not be saved 1 B amp B tree will be saved to file Default 0 Type Long See also xmxnod xmxmin xipbeg Back to index 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Parameter 101 xgomct Determines Determines if and how Gomory Mixed Integer Cuts will be derived during IP preprocessing Values 0 No Cuts will be derived 1 Cuts with a limited number of nonzero elements are derived gt 1 The higher the value max 4 the more cuts will be derived Note that cuts are relatively dense which slows down the LP optimization at nodes Default 2 Type Long Back to index xgommc Sets the density level for taking Gomory cuts into the matrix A violated Gomory cut will only be added to the matrix if the sum of all nonzeros in all columns of the cut is smaller than xgommc xn A smaller value of xgommc results in a smaller number of Gomory cuts and possibly weaker LP relaxation but faster LP reoptimization Default 6 Type Long Back to index xheutp Determines the IP heuristic to be used to obtain initial IP solutions Values 0 No heuristic is used 1 Total rounding integer variables will be rounded to the nearest integer value in several passes 2 Local
146. will write a log message to that file when they are called The name of the log file can be specified by parameter xfnlog If no name has been set the log file s name is for007 or fort 7 Logging especially with xoutlv gt 3 is very time consuming and should only be activated for debugging purposes during application development fort xxx Files MOPS creates a number of output files in the working directory during an optimization run If you don t specify file names explicitly the names of these files have formats like forxxx or fort xxx with xxx being an internal Fortran unit number The following table shows which parameters you have to set to give these files explicit names and which parameters impede the creation of the files When using MOPS DLL call SetParameter to make the appropriate settings fort 13 LP solution file xfnips myName lps fort 16 IP solution file xfnips myName ips A A ts A A Y e A A KE Beie RE EE 2007 MOPS Optimierungssysteme GmbH amp Co KG MOPS User Manual MOPS Output Files 140 See also xoutlv xoutsl xfrbas xfrtre 2007 MOPS Optimierungssysteme GmbH amp Co KG Chapter Case Burma MOPS User Manual Case Burma 142 9 9 1 Case Burma Problem The government of Burma plans the agricultural development of a 20 square kilometers sqkm region that can be divided into 4 parts each 5 sqkm large In each of these parts rice or wheat can be
147. y the same as for calling 32 bit functions You cannot use the 32 bit MOPS DLL in a 64 bit process and vice versa Windows XP x64 has a 32 bit compatibility mode WOW64 in which 32 bit applications run as if they were running on a native 32 bit machine Via WOW64 a 32 bit MOPS DLL can be used under Windows XP x64 Since the 32 bit MOPS DLL is limited to 2 Gigabytes of main memory which id independent of the amount of physical main memory there is a limit on the size of the models which can be solved since the model data and a large amount of working data has to be kept in main memory The key advantage of using 64 bit software is the extremely large address space which allows to solve much larger models Another advantage is that memory intensive algorithms such as interior point methods can be used where the storage of the Cholesky factorization alone can take several Gigabytes see also the MOPS White Paper For those models which can be solved with the 32 bit Versions of MOPS there is no speed advantage compared to the 64 bit versions of MOPS The samples include 64 bit projects for VB NET C and C O 2007 MOPS Optimierungssysteme GmbH 6 Co KG Chapter MOPS LIB MOPS User Manual MOPS LIB 51 3 3 1 3 2 MOPS LIB Using MOPS LIB In addition to the DLL version MOPS is also available as a static library the MOPS LIB Ifthe question arises which type of MOPS library you should use for your application the LI

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