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ILOG CPLEX 10.1 Getting Started

1. 32 Using the Callable Library 2 eel xk lI ye f Xxx x RR x eee Ges a 33 Interactive Optimizer 35 Starting ILOG CPLEX cc ceva c i e ra I9 ee Rr 3 eee eee eee on hy Rx 36 Using Help Rc Reges Den cm 36 Entering a Problem cinta teed be xS e par ih RR RR ane QR ee eileen 38 Entering the Example Problem 38 Using the EP Format ITE a Ge Rea ee CP 39 Entering EMEN 41 Displaying a Problem eee hh hh hh mtn 42 Displaying Problem s 43 Specifying Item RangeS 0 0 0 eee e mr 44 Displaying Variable or Constraint Names 44 Ordering Variables 5 xi nop a Gp wan aden ed ain ed ee ee 45 Displaying Constraints 2 0 0 0 ms 46 Displaying the Objective 46 Displaying Bounds Gok gba eae wea pba dake dak 46 Displaying a Histogram of NonZero 47 Solving a Problem 2 1216 ace Rp ue ei Pes ral Eram RETE wee 48 Solving the Example Problem 48 Solutior Options rn ROI SEI e EU ERE ERREUR ERRARE RUNE 49 Disp
2. endl cplex getValues vals vars env out Values vals endl catch IloException amp e cerr Concert exception caught e endl catch cerr Unknown exception caught endl env end return 0 END main ILOG CPLEX 10 1 GETTING STARTED Using Concert Technology in Java Here is a Java application using ILOG CPLEX with Concert Technology to solve the example An expanded form of this example is discussed in detail in Chapter 5 Concert Technology Tutorial for Java Users import ilog concert import ilog cplex public class Example public static void main String args try IloCplex cplex new IloCplex double lb 0 0 0 0 0 0 double ub 40 0 Double MAX VALUE Double MAX VALUE IloNumVar x cplex numVarArray 3 lb ub double objvals 1 0 2 0 3 0 cplex addMaximize cplex scalProd x objvals cplex addLe cplex sum cplex prod 1 0 x 0 cplex prod 1 0 x 1 cplex prod 1 0 x 2 20 0 cplex addLe cplex sum cplex prod 1 0 x 0 cplex prod 3 0 1 cplex prod 1 0 x 2 30 0 if cplex solve cplex output println Solution status cplex getStatus cplex output println Solution value cplex getObjValue double val cplex getValues x int ncols cplex getNcols for int j 0 j ncols cplex output println Column j Value
3. val jl cplex end catch IloException e System err println Concert exception e caught ILOG CPLEX 10 1 GETTING STARTED 31 Using Concert Technology in NET There is an interactive tutorial based on that same example for NET users of ILOG CPLEX in Chapter 6 Concert Technology Tutorial for NET Users 32 ILOG CPLEX 10 1 GETTING STARTED Using the Callable Library Here is a C application using the CPLEX Callable Library to solve the example An expanded form of this example is discussed in detail in Chapter 7 Callable Library Tutorial include lt ilcplex cplex h gt include lt stdlib h gt include lt string h gt define NUMROWS 2 define NUMCOLS 3 define NUMNZ 6 int main int argc char argv int status 0 CPXENVptr env NULL CPXLPptr lp NULL double obj NUMCOLS double 1b NUMCOLS double ub NUMCOLS double x NUMCOLS int rmatbeg NUMROWS int rmatind NUMNZ double rmatval NUMNZ double rhs NUMROWS char sense NUMROWS int solstat double objval env CPXopenCPLEX amp status if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE 1 CPXcreateprob env amp status 1 1 if lp NULL fprintf stderr Failed to create LP n goto TERMINATE
4. de dT aetna aren e RERUM RR d eus 79 Modeling by Columns ks eck Se ee eee oa a UM doe Aa 79 Modeling by Nonzero Elements 80 Complete Program ast uite Dx ERES ER Gore 4a E toe et E ear 80 Writing and Reading Models and Files 80 Selecting an Optimizer eseeeeeeeeseeeeeeeee n n n nnn 81 Reading a Problem from a File Example 1 2 82 Reading the Model from a 83 Selecting the 83 Accessing Basis Information 83 Querying Quality eee 83 Gomplete Progtatm t eroe D EP ede Deelah eee gale EE LEBEN dake 84 Modifying and 1 2 84 Modifying an Optimization Problem Example 84 Setting ILOG CPLEX Parameters 85 Modifying an Optimization 86 Starting from a Previous BaSiS 1 0 0 0 ccna 86 Complete Programas ied ee emt RR eka oe eR Peek eer 86 Concert Technology Tutorial for Java 87 Compiling ILOG CPLE
5. With this setting the command display problem stats shows this additional information Variables Min LB 0 000000 Max UB 40 00000 Objective nonzeros Min 1 000000 Max 3 000000 Linear constraints Nonzeros Min 1 000000 Max 3 000000 RHS nonzeros Min 20 00000 Max 30 00000 Another way to avoid displaying an entire problem is to display a specific part of it by using one of the following three options of the display problem command names documented in Displaying Variable or Constraint Names on page 44 can be used to display a specified set of variable or constraint names constraints documented in Displaying Constraints on page 46 can be used to display a specified set of constraints bounds documented in Displaying Bounds on page 46 can be used to display a specified set of bounds Specifying Item Ranges For some options of the display command you must specify the item or range of items you want to see Whenever input defining a range of items is required ILOG CPLEX expects two indices separated by a hyphen the range character The indices can be names or matrix index numbers You simply enter the starting name or index number a hyphen and finally the ending name or index number ILOG CPLEX automatically sets the default upper and lower limits defining any range to be the highest and lowest possible values Therefore you have the option of leaving out either the upper or lower name
6. CPXchgobjsen env lp CPX MAX obj 0 1 0 obj 1 2 0 obj 2 3 0 lb 0 0 0 lb 1 0 0 lb 2 0 0 ub 0 40 0 ub 1 CPX INFBOUND ub 2 CPX INFBOUND status CPXnewcols env lp NUMCOLS obj lb ub NULL NULL if status ILOG CPLEX 10 1 GETTING STARTED 33 34 fprintf stderr Failed t goto TERMINATE rmatbeg 0 0 rmatind 0 0 rmatind 1 rmatval 0 1 0 rmatval i rmatbeg 1 3 rmatind 3 0 rmatind 4 rmatval 3 1 0 rmatval 4 status CPXaddrows env lp rmatind if status fprintf stderr Failed t goto TERMINATE status CPXlpopt env lp if status fprintf stderr Failed t goto TERMINATE status CPXsolution env lp if status fprintf stderr Failed t goto TERMINATE printf nSolution status printf Solution value f printf Solution zr TERMINATE if lp NULL status CPXfreeprob env if status fprintf stderr CPXfr if env NULL Status CPXcloseCPLEX amp e if status char errmsg 1024 o populate problem in 1 rmatind 2 2 sense 0 L 1 0 rmatval 2 1 0 rhs 0 20 0 1 rmatind 5 2 sense 1 L 3 0 rmatval 5 1 0 rhs 1 30 0 0 NUMROWS NUMNZ rhs sense rmatbeg rmatval NULL NULL o populate problem n optimize LP n amp solstat amp objval x NULL NULL NULL obtain so
7. Changing the rules of business ILOG CPLEX 10 1 Getting Started July 2006 COPYRIGHT NOTICE ILOG CPLEX 10 1 Copyright 1997 2006 by ILOG S A 9 Rue de Verdun 94253 Gentilly Cedex France and ILOG Inc 1080 Linda Vista Ave Mountain View California 94043 USA All rights reserved General Use Restrictions This document and the software described in this document are the property of ILOG and are protected as ILOG trade secrets They are furnished under a license or nondisclosure agreement and may be used or copied only within the terms of such license or nondisclosure agreement No part of this work may be reproduced or disseminated in any form or by any means without the prior written permission of ILOG S A or ILOG Inc Trademarks ILOG the ILOG design CPLEX and all other logos and product and service names of ILOG are registered trademarks or trademarks of ILOG in France the U S and or other countries All other company and product names are trademarks or registered trademarks of their respective holders Java and all Java based marks are either trademarks or registered trademarks of Sun Microsystems Inc in the United States and other countries Microsoft and Windows are either trademarks or registered trademarks of Microsoft Corporation in the United States and other countries document version 10 1 Preface Part Chapter 1 Part Il Table of Contents Introducing ILOG CPLEX
8. Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src ilolpex2 cpp Modifying and Reoptimizing In many situations the solution to a model is only the first step One of the important features of Concert Technology is the ability to modify and then re solve the model even after it has been extracted and solved one or more times A look back to examples ilolpex1 cpp and ilolpex2 cpp reveals that models have been modified all along Each time an extractable is added to a model it changes the model However those examples made all such changes before the model was extracted to ILOG CPLEX Concert Technology maintains a link between the model and all IloCplex objects that may have extracted it This link is known as notification Each time a modification of the model or one of its extractables occurs the change is notified to the IloCplex objects that extracted the model They then track the modification in their internal representations Moreover IloCplex tries to maintain as much information from a previous solution as is possible and reasonable when the model is modified in order to have a better start when solving the modified model In particular when solving LPs or QPs with a simplex method IloCplex attempts to maintain a basis which will be used the next time the method solve is invoked with the aim of making subsequent solves go faster Modi
9. all display entire problem binaries display binary variables bounds display a set of bounds constraints display a set of constraints or node supply demand values generals display general integer variables histogram display a histogram of row or column counts integers display integer variables names display names of variables or constraints qpvariables display quadratic variables semi continuous display semi continuous and semi integer variables sos display special ordered sets stats display problem statistics variable display a column of the constraint matrix Display which problem characteristic Enter the option a11 to display the entire problem Maximize obj 1 2 x2 3 x3 Subject To cl xl 2 x3 lt 20 2 3 2 x3 lt 30 Bounds 0 lt xl lt 40 All other variables are gt 0 ILOG CPLEX 10 1 GETTING STARTED The default names obj c1 c2 are provided by ILOG CPLEX If that is what you want you are ready to solve the problem If there is a mistake you must use the change command to modify the problem The change command is documented in Changing a Problem on page 61 Summary Display problem characteristics by entering the command display problem Displaying Problem Statistics When the problem is as small as our example it is easy to display it on the screen however many real problems are far too large to display For these problems the stats option of the display
10. 63 Removing Bounds s ues lata VER fiancee deeded es She cae 63 Changing Coefficients liiis 64 Deleting ii ike RETE SEGURA G Se EE eee s 64 Executing Operating System 66 Quitting ILOG CPLEX 0 0 ccc eee eee eee eens 66 Concert Technology Tutorial for C Users 69 The Design of CPLEX in Concert Technology 70 Compiling and Linking ILOG CPLEX in Concert Technology Applications 71 Testing Your Installation on UNIX 0 0 0 71 Testing Your Installation on Windows 71 Gase of Problems ote eU a a a ae i ies 72 The Anatomy of an ILOG Concert Technology Application 72 Constructing the Environment lloEnv 72 Creating a Model 73 Solving the Model lloCplex 1 0 0 0 cette teeta 76 Querying Results aw Sea ee eee Oe ea eae ey 76 eile ae ie ee SE Aa perder CREE 77 ILOG CPLEX 10 1 GETTING STARTED 5 Chapter 5 Building and Solving a Small LP Model 78 General Structure of an ILOG CPLEX Concert Technology Application 78 Modelingiby ROWS
11. APIs and the Interactive Optimizer ILOG CPLEX 10 1 GETTING STARTED Part Setting Up This part shows you how to set up ILOG CPLEX and how to check your installation It includes information for users of Microsoft and UNIX platforms Setting Up ILOG CPLEX You install ILOG CPLEX in two steps first install the files from the distribution medium a CD or an FTP site into a directory on your local file system then activate your license At that point all of the features of CPLEX become functional and are available to you The chapters that follow this one provide tutorials in the use of each of the Technologies that ILOG CPLEX provides the ILOG Concert Technology Tutorials for C Java and NET users and the Callable Library Tutorial for C and other languages This chapter provides guidelines for Installing ILOG CPLEX on page 20 Setting Up Licensing on page 22 Using the Component Libraries on page 23 Important Please read these instructions in their entirety before you begin the installation Remember that most ILOG CPLEX distributions will operate correctly only on the specific platform and operating system for which they are designed If you upgrade your operating system you may need to obtain a new ILOG CPLEX distribution ILOG CPLEX 10 1 GETTING STARTED 19 Installing ILOG CPLEX The steps to install ILOG CPLEX involve identifying the correct distribution file for your particular platform
12. Solve 108 After you have declared the decision variables and added the constraints and objective function to the model your application is ready to search for a solution Search for a solution Go to Step 9 in the file and add this line to make your application search for a solution if cplex Solve Display the solution Go to the comment Step 10 in the file and add these lines to enable your application to display any solution found in Step 9 double x cplex GetValues var 01 double dj cplex GetReducedCosts var 01 double pi cplex GetDuals rng 0 double slack cplex GetSlacks rng 01 cplex Output WriteLine Solution status cplex GetStatus cplex Output WriteLine Solution value cplex ObjValue int ncols cplex Ncols for int j 0 j ncols cplex Output WriteLine Column J Value x jl Reduced cost 5 151 int nrows cplex Nrows for int i 0 i lt nrows i cplex Output WriteLine Row 1 Slack slack i pilil ILOG CPLEX 10 1 GETTING STARTED Save the model to a file If you want to save your model to a file in LP format go to the comment Step 11 in your application file and add this line cplex ExportModel 1 1 1 If you have followed the steps in this tutorial interactively you now have a complete application that you can compile a
13. eseeseeseeeeee nnn 9 WhatlIs ILOG CPLEX ER REL Re ERR Re mede RE dd 10 ILOG CPLEX Comiponerls 54 i e RR RR e ke UGS Bane aa eae 11 Optimizer Options 1 2 A aed Oy ald OL RAGA Ae e bil 12 Data Entry Options 2 asd oe ee Gree Ak eee Soe 13 What You Need to Know 2 cece eee eee eee eee hh 13 What s in This Manual eee eee IIR hn 13 Notation in this Manual 0 0 0 cece eee eee eee eee eee 14 Related Documentation lese hn n nnn 15 Setting setts ous wee x eae ia e ERA EE E Setting Up ILOG CPLEX 52 2 ime E ERE 19 Installing ILOG CPLEX 2 seed oa nece tad eee enc eue xc Are cn RE e vede tae cm es 20 Setting Up Licensing Sov lE DeL a A is we e E UN Rare Ex aes 22 Using the Component 23 aad win ee kd et EG xD uus rad od 08 ILOG CPLEX 10 1 GETTING STARTED 3 Chapter 2 Chapter 3 Solving an LP with LOG CPLEX 27 Problem Statement 0 0 eee cece eee eh n nnn 28 Using the Interactive Optimizer 29 Using Concert Technology C 30 Using Concert Technology in Java 31 Using Concert Technology in NET
14. optimizer baropt command and the network optimizer netopt command Many problems can be solved faster using these alternative optimizers which are documented in more detail in the LOG CPLEX User s Manual If you want to solve a mixed integer programming problem the optimize command is equivalent to the mipopt command Interrupting the Optimization Process Our short example was solved very quickly However larger problems particularly mixed integer problems can take much longer Occasionally it may be useful to interrupt the optimization process ILOG CPLEX allows such interruptions if you use cont rol c The control and c keys must be pressed simultaneously Optimization is interrupted and ILOG CPLEX issues a message indicating that the process was stopped and displays progress information If you issue another optimization command in the same session ILOG CPLEX will resume optimization from where it was interrupted Displaying Post Solution Information After an optimal solution is found ILOG CPLEX can provide many different kinds of information for viewing and analyzing the results This information is accessed via the display command and via some write commands Information about the following is available with the display solution command objective function value solution values numerical quality of the solution slack values reduced costs ILOG CPLEX 10 1 GETTING STARTED dual values shad
15. unbounded Java API 93 UNIX building Callable Library C APT applications 113 executing commands in Interactive Optimizer 66 installation directory 20 installing CPLEX 20 testing CPLEX C API 71 verifying installation 23 UnsatisfiedLinkError Java API 89 V variable Boolean C API 74 box in Interactive Optimizer 43 changing bounds in Interactive Optimizer 63 changing names in Interactive Optimizer 62 continuous C API 74 creating C API 81 deleting in Interactive Optimizer 64 displaying in Interactive Optimizer 43 displaying names in Interactive Optimizer 44 entering bounds in Interactive Optimizer 40 entering names in Interactive Optimizer 39 integer C API 74 modeling Java APT 92 name limitations in Interactive Optimizer 39 ordering in Interactive Optimizer 45 removing bounds in Interactive Optimizer 63 representing in model C API 74 W warning method Java API 95 wildcard displaying ranges of items in Interactive Optimizer 44 solution information in Interactive Optimizer 52 wildcard in Interactive Optimizer 44 Windows building Callable Library C APT applications 113 dynamic loading C API 114 installing CPLEX 20 Microsoft Visual C compiler C API 114 ILOG CPLEX 10 1 Microsoft Visual C IDE C API 113 testing CPLEX C API 71 verifying installation 24 write Interactive Optimizer command 53 54 file type options 53 syntax 55 writing basis files in Interactive Optimizer 54 fi
16. 1 GETTING STARTED Identify the Routines to be Called By separating the application into smaller parts you can easily identify the tools needed to complete the application Part of this process consists of identifying the Callable Library routines that will be called In some applications the Callable Library is a small part of a larger program In that case the only ILOG CPLEX routines needed may be for problem creation optimizing obtaining results In other cases the Callable Library is used extensively in the application If so Callable Library routines may also be needed to modify the problem set parameters determine input and output messages and files query problem data Test Procedures in the Application Itis often possible to test the procedures of an application in the ILOG CPLEX Interactive Optimizer with a small prototype of the model Doing so will help identify the Callable Library routines required The test may also uncover any flaws in procedure logic before you invest significant development effort Trying the ILOG CPLEX Interactive Optimizer is an easy way to determine the best optimization procedure and parameter settings Assemble the Data You must decide which approach to populating the problem object is best for your application Reading an MPS or LP file may reduce the coding effort but can increase the run time and disk space requirements of the program Buil
17. 77 testing installation 24 testing installation C API 72 ILOG CPLEX 10 1 example adding rows to a problem C API 123 entering a problem in Interactive Optimizer 38 entering and optimizing a problem C API 119 entering and optimizing a problem in C 103 ilolpex2 cpp C API 82 ilolpex3 cpp C API 84 1 1 C API 119 lpexi cs 103 lpex2 c API 121 lpex3 c API 123 modifying an optimization problem C 84 reading a problem file C API 121 reading a problem from a file C API 82 running C API 71 running Callable Library C API 113 running Component Libraries 23 running from standard distribution C API 113 solving a problem in Interactive Optimizer 48 exception handling C API 77 executing operating system commands in Interactive Optimizer 66 exportModel method IloCplex class C API 80 expression column 79 F false return value of IoCplex solve 93 feasible solution Java API 93 file format read options in Interactive Optimizer 56 write options in Interactive Optimizer 53 file name extension 81 extension in Interactive Optimizer 54 57 G getCplexStatus method IloCplex class C API 76 getCplexStatus method Java API 93 getDuals method GETTING STARTED Java 133 IloCplex class C API 79 getObj Value method IloCplex class C API 77 getReducedCosts method IloCplex class C API 79 getSlacks method IloCplex class C API 79
18. C API 78 extracting C API 78 modifying C API 84 reading from file C API 81 83 solving C API 83 writing to file C API 81 modeling by columns C API 79 by columns Java API 95 by nonzeros C API 80 by nonzeros Java API 97 by rows Java API 95 objects C API 70 variables Java API 92 modeling by rows C API 79 modifying problem object C API 116 monitoring iteration log in Interactive Optimizer 48 MPS file format in Interactive Optimizer 57 multiple algorithms C API 82 N netopt Interactive Optimizer command 50 network description 10 network flow C API 85 network optimizer availability in Interactive Optimizer 50 selecting C API 82 solving with C APD 85 Nmake Java API 88 no license found Java API 89 NoClassDefFoundError Java API 89 node LP solving C API 82 nonzeros modeling C API 80 modeling Java API 97 notation in this manual 14 notification C API 84 numeric parameter C API 86 136 ILOG CPLEX 10 1 numVarArray method Java API 95 objective function accessing value in Interactive Optimizer 50 adding to model C API 75 changing coefficient in Interactive Optimizer 64 changing sense in Interactive Optimizer 63 creating C API 79 81 default name in Interactive Optimizer 40 displaying in Interactive Optimizer 46 entering in Interactive Optimizer 40 entering in LP format in Interactive Optimizer 39 name in Interactiv
19. CPLEX 10 1 GETTING STARTED x 0 x 1 x 2 lt 20 0 can be added by calling cplex addLe cplex sum cplex negative x 0 x 1 x 2 20 Again many methods are provided for adding other constraint types including equality constraints greater than or equal to constraints and ranged constraints Internally they are all represented as IloRange objects with appropriate choices of bounds which is why all these methods return IloRange objects Also note that the expressions above could have been created in many different ways including the use of I1oLinearNumExpr Solve the Model So far you have seen some methods of IloCplex for creating models All such methods are defined in the interfaces 110Modeler and its extension IloMPModeler and IloCplexModeler However I1oCplex not only implements these interfaces but also provides additional methods for solving a model and querying its results After you have created a model as explained in Create the Model on page 91 the 110Cplex object cplex is ready to solve the problem which consists of the model and all the modeling objects that have been added to it Invoking the optimizer then is as simple as calling the method solve The method solve returns a Boolean value indicating whether the optimization succeeded in finding a solution If no solution was found false is returned If true is returned then ILOG CPLEX found a feasible solution though it is not necessarily an optimal
20. CPLEX 10 1 GETTING STARTED 51 52 objective function righthand side values bounds To view the sensitivity analysis of the objective function enter the command display sensitivity obj You can also use a wildcard to query solution information like this display sensitivity obj For our example ILOG CPLEX displays the following ranges for sensitivity analysis of the objective function OBJ Sensitivity Ranges Variable Name Reduced Cost Down Current Up 1 3 5000 2 5000 1 0000 infinity x2 zero 5 0000 2 0000 3 0000 x3 zero 2 0000 3 0000 t infinity ILOG CPLEX displays each variable its reduced cost and the range over which its objective function coefficient can vary without forcing a change in the optimal basis The current value of each objective coefficient is also displayed for reference Objective function sensitivity analysis is useful to determine how sensitive the optimal solution is to the cost or profit associated with each variable Similarly to view sensitivity analysis of the righthand side type the command display sensitivity rhs For our example ILOG CPLEX displays the following ranges for sensitivity analysis of the righthand side RHS RHS Sensitivity Ranges Constraint Name Dual Price Down Current Up c1 2 7500 36 6667 20 0000 t infinity c2 0 2500 140 0000 30 0000 100 0000 ILOG CPLEX displays each constraint its dual price and a range over which its righthand side coefficient c
21. added by CPXaddrows For convenience the total number of nonzeros in the rows being added is stored in an extra element of the array rmatbeg and this element is passed for the parameter nzcnt The name arguments to CPXaddrows are NULL since no variable or constraint names were defined for this problem After the CPXaddrows call the parameter LPMETHOD is set to CPX_ALG DUAL and the routine CPX1popt is called to re optimize the problem using the dual simplex optimizer After re optimization CPXsolution is called to determine the solution status the objective value and the primal solution NULL is passed for the other solution values since the information they provide is not needed in this example At the end the problem is written as a SAV file by CPXwriteprob This file can then be read into the ILOG CPLEX Interactive Optimizer to analyze whether the problem was correctly generated Using a SAV file is recommended over MPS and LP files as SAV files preserve the full numeric precision of the problem After the TERMINATE label CPX reeprob releases the problem object and CPXcloseCPLEX releases the ILOG CPLEX environment Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src lpex3 c ILOG CPLEX 10 1 GETTING STARTED Performing Sensitivity Analysis In Performing Sensitivity Analysis on page 51 there is a discussion of how
22. an Optimizer on page 81 Reading a Problem from a File Example ilolpex2 cpp on page 82 Modifying and Reoptimizing on page 84 9 9 9 9 9 0 Modifying an Optimization Problem Example ilolpex3 cpp on page 84 ILOG CPLEX 10 1 GETTING STARTED 69 The Design of CPLEX in Concert Technology 70 A clear understanding of C objects is fundamental to using ILOG Concert Technology with ILOG CPLEX to build and solve optimization models These objects can be divided into two categories 1 Modeling objects are used to define the optimization problem Generally an application creates multiple modeling objects to specify one optimization problem Those objects are grouped into an IloModel object representing the complete optimization problem 2 IloCplex objects are used to solve the problems that have been created with the modeling objects An IloCplex object reads a model and extracts its data to the appropriate representation for the ILOG CPLEX optimizer Then the 11oCplex object is ready to solve the model it extracted and be queried for solution information Thus the modeling and optimization parts of a user written application program are represented by a group of interacting C objects created and controlled within the application Figure 4 1 shows a picture of an application using ILOG CPLEX with ILOG Concert Technology to solve optimization problems User Written Application lloCplex object Concert Tech
23. and then executing a command that uses that distribution file The identification step is explained in the booklet that comes with the CD ROM or is provided with the FTP instructions for download After the correct distribution file is at hand the installation proceeds as follows Installation on UNIX On UNIX systems ILOG CPLEX 10 1 is installed in a subdirectory named cplex101 under the current working directory where you perform the installation Use the cd command to move to the top level directory into which you want to install the cplex subdirectory Then type this command gzip dc lt path cplex tgz tar xf where path is the full path name pointing to the location of the ILOG CPLEX distribution file either on the CD ROM or on a disk where you performed the FTP download On UNIX systems both ILOG CPLEX and ILOG Concert Technology are installed when you execute that command Installation on Windows Before you install ILOG CPLEX you need to identify the correct distribution file for your platform There are instructions on how to identify your distribution in the booklet that comes with the CD ROM or with the FTP instructions for download This booklet also tells how to start the ILOG CPLEX installation on your platform Directory Structure After completing the installation you will have a directory structure like the one in Figure 1 1 and Figure 1 2 Be sure to read the readme htm1 carefully for the most recent informat
24. application using Visual C first create or open a project in the Visual C Integrated Development Environment IDE Project files are provided for each of the examples found in the directory or folder examples msvc format For details about the build process refer to the information file msvc html which is found in the top of the installed ILOG CPLEX directory structure Note The distributed application must be able to locate CPLEX101 d11 at run time ILOG CPLEX 10 1 GETTING STARTED 113 Microsoft Visual C Command Line Compiler If the Visual C command line compiler is used outside of the IDE the command should resemble the following example The example command assumes that the file cplex101 lib is in the current directory with the source file 1pex1 c and that the line in the source file include ilcplex cplex h correctly points to the location of the include file or else has been modified to do so or that the directories containing these files have been added to the environment variables LIB and INCLUDE respectively cl 1 1 cplex101 1lib This command will create the executable file 1pex1 exe Using Dynamic Loading Some projects require more precise control over the loading and unloading of DLLs For information on loading and unloading DLLs without using static linking please refer to the compiler documentation or to a book such as Advanced Windows by Jeffrey Richter from Microsoft Press If this is n
25. by columns is a more natural or more efficient approach to implement For example problems with network structure typically lend themselves well to modeling by column Readers familiar with matrix algebra may view the method populateByColumn as producing the transpose of what is produced by the method populateByRow In contrast to modeling by rows modeling by columns means that the ILOG CPLEX 10 1 GETTING STARTED 95 96 coefficients of the constraint matrix are given in a column wise way As each column represents the constraint coefficients for a given variable in the linear program this modeling approach is most natural where it is easy to access the matrix coefficients by iterating through all the variables such as in network flow problems Range objects are created for modeling by column with only their lower and upper bound No expressions are given building them at this point would be impossible since the variables have not been created yet Similarly the objective function is created only with its intended optimization sense and without any expression Next the variables are created and installed in the existing ranges and objective These newly created variables are introduced into the ranges and the objective by means of column objects which are implemented in the class IloColumn Objects of this class are created with the methods 11oCplex column and can be linked together with the method IloColumn and to form aggregate IloCo
26. call to CPXgetbase are dependent on the solution type returned by CPXsolninfo The primal solution values of the variables are obtained by a call to CPXgetx and then these values along with the basis statuses if available are printed in a loop for each variable After that a call to CPXgetdbl1quality provides a measure of the numerical roundoff error ILOG CPLEX 10 1 GETTING STARTED present in the solution by obtaining the maximum amount by which any variable s lower or upper bound is violated After the TERMINATE label the data for the solution x cstat and rstat are freed Then the problem object is freed by CPX reeprob After the problem is freed the ILOG CPLEX environment is freed by CPXcloseCPLEX Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src lpex2 c Adding Rows to a Problem Example Ipex3 c This example illustrates how to develop your own solution algorithms with routines from the Callable Library It also shows you how to add rows to a problem object Here is the problem that 1pex3 solves Minimize subject to Ax d b Ax I lt xsu where 310101000 d 3 1 1010000 1 0 1 1001 1 0 4 000 1 0 101 3 0000 10 1 1 5 A 2 1 2 1 2 1 2 3 b 4 1 3 23 121 1 2 c 9 14 2 8 2 812 l 00000000 u 50 50 50 50 50 50 50 50 The constraints Hx d represent the flow conservat
27. conflict Set parameters for finding conflicts defaults set all parameter values to defaults emphasis set optimization emphasis feasopt set parameters for feasopt logfile set file to which results are printed lpmethod set method for linear optimization mip Set parameters for mixed integer optimization network Set parameters for network optimizations output Set extent and destinations of outputs preprocessing Set parameters for preprocessing qpmethod set method for quadratic optimization read set problem read parameters sifting Set parameters for sifting optimization simplex Set parameters for primal and dual simplex optimizations threads set default parallel thread count timelimit Set time limit in seconds workdir set directory for working files workmem Set memory available for working storage in megabytes Parameter to set If you press the return key without entering a parameter name the following message is displayed No parameters changed Resetting Defaults After making parameter changes it is possible to reset all parameters to default values by issuing one command set defaults This resets all parameters to their default values except for the name of the log file Summary The general syntax for the set command is set parameter option new value Displaying Parameter Settings The current values of the parameters can be displayed with the command display settings all A list of parameters with settin
28. enter the constraint or objective function The final thing to remember when you are entering a problem is that after you have pressed return you can no longer directly edit the characters that precede the lt return gt As long as you have not pressed the return key you can use lt backspace gt key to go back and change what you typed on that line After return has been pressed the change command must be used to modify the problem The change command is documented in Changing a Problem on page 61 ILOG CPLEX 10 1 GETTING STARTED 41 Displaying a Problem 42 Now that you have entered a problem using ILOG CPLEX you must verify that the problem was entered correctly To do so use the display command At the CPLEX gt prompt type display A list of the items that can be displayed then appears Some of the options display parts of the problem description while others display parts of the problem solution Options about the problem solution are not available until after the problem has been solved The list looks like this Display Options conflict display conflict that demonstrates model infeasibility problem display problem characteristics sensitivity display sensitivity analysis settings display parameter settings solution display existing solution Display what If you type problem in reply to that prompt that option will list a set of problem characteristics like this Display Problem Options
29. format problem file mst MIP start file net CPLEX network format of embedded network ord Integer priority order file ppe Binary format for primal perturbed problem pre Binary format for presolved problem prm Non default parameter settings rlp LP format problem with generic names rew MPS format problem with generic names sav Binary matrix and basis file sol Solution file File type ILOG CPLEX 10 1 GETTING STARTED 53 54 The BAS format is used for storing basis information and is introduced in Writing Basis Files on page 54 See also Reading Basis Files on page 57 The LP format was discussed in Using the LP Format on page 39 Using this format is explained in Writing LP Files on page 54 and Reading LP Files on page 56 The MPS format is covered in Reading MPS Files on page 57 Reminder All these file formats are documented in more detail in the reference manual ILOG CPLEX File Formats Writing LP Files When you enter the write command the following message appears Name of file to write Enter the problem name example and ILOG CPLEX will ask you to select a type from a list of options For this example choose LP ILOG CPLEX displays a confirmation message like this Problem written to file example If you would like to save the file with a different name you can simply use the write command with the new file name as an argument Try this using the name 1 2 This time you can avoi
30. in va11 Other methods are available for querying other solution information For example the objective function value of the solution can be accessed using IloNum objval cplex getObjValue Handling Errors Concert Technology provides two lines of defense for dealing with error conditions suited for addressing two kinds of errors The first kind covers simple programming errors Examples of this kind are trying to use empty handle objects or passing arrays of incompatible lengths to functions This kind of error is usually an oversight and should not occur in a correct program In order not to pay any runtime cost for correct programs asserting such conditions the conditions are checked using assert statements The checking is disabled for production runs if compiled with the DNDEBUG compiler option The second kind of error is more complex and cannot generally be avoided by correct programming An example is memory exhaustion The data may simply require too much memory even when the program is correct This kind of error is always checked at runtime In cases where such an error occurs Concert Technology throws a C exception In fact Concert Technology provides a hierarchy of exception classes that all derive from the common base class IloExcept ion Exceptions derived from this class are the only kind of exceptions that are thrown by Concert Technology The exceptions thrown by 11oCplex objects all derive from class TloAlgo
31. monitoring the rate of progress The iteration log display can be modified by the set simplex display command to display differing amounts of data while the problem is being solved Reporting the Solution After it finds the optimal solution ILOG CPLEX reports the objective function value ILOG CPLEX 10 1 GETTING STARTED the problem solution time in seconds the total iteration count the Phase I iteration count in parentheses Optimizing our example problem produces a report like the following one although the solution times vary with each computer Tried aggregator 1 time No presolve or aggregator reductions Presolve Time 0 00 sec Iteration Log Iteration 1 Dual infeasibility 0 000000 Iteration 2 Dual objective 202 500000 Dual simplex Optimal Objective 2 0250000000e 02 Solution Time 0 00 sec Iterations 2 1 CPLEX gt In our example ILOG CPLEX finds an optimal solution with an objective value of 202 5 in two iterations For this simple problem 1 Phase I iteration was required Summary To solve an LP problem use the command optimize Solution Options Here are some of the basic options in solving linear programming problems Although the tutorial example does not make use of these options you will find them useful when handling larger more realistic problems Filing Iteration Logs on page 49 Re Solving on page 50 Using Alternative Optimizers on page 50
32. or index number on either side of the hyphen To see every possible item you would simply enter Another way to specify a range of items is to use a wildcard ILOG CPLEX accepts these wildcards in place of the hyphen to specify a range of items question mark for a single character asterisk for zero or more characters For example to specify all items you could enter instead of if you want The sequence of characters c1 matches the name of every constraint in the range from c10 to c19 for example Displaying Variable or Constraint Names You can display a variable name by using the display command with the options problem names variables If you do not enter the word variables CPLEX prompts you to specify whether you wish to see a constraint or variable name ILOG CPLEX 10 1 GETTING STARTED Type the following command display problem names variables In response ILOG CPLEX prompts you to specify a set of variable names to be displayed like this Display which variable name s Specify these variables by entering the names of the variables or the numbers corresponding to the columns of those variables A single number can be used or a range such as 1 2 All of the names can be displayed at after if you type a hyphen the character Try this by entering a hyphen at the prompt and pressing the return key Display which variable name s You could also use a wildcard to disp
33. order corresponding to their internal ordering All of the options of the display command can be entered directly after the word display to eliminate intermediate steps The following command is correct for example display problem names variables 2 3 Displaying Constraints To view a single constraint within the matrix use the command and the constraint number For example type the following display problem constraints 2 The second constraint appears C2 3 x2 x3 lt 30 You can also use a wildcard to display a range of constraints like this display problem constraints Displaying the Objective Function When you want to display only the objective function you must enter its name obj by default or an index number of 0 display problem constraints Display which constraint name s 0 Maximize obj x1 2 2 3 x3 Displaying Bounds To see only the bounds for the problem type the following command don t forget the hyphen or wildcard display problem bounds or try a wildcard like this display problem bounds The result is 0 lt 1 lt 40 ILOG CPLEX 10 1 GETTING STARTED All other variables are O0 Summary The general syntax of the display command is display option option2 identifier identifier2 Displaying a Histogram of NonZero Counts For large models it can sometimes be helpful to see summaries of nonzero counts of the columns or
34. problem command is helpful When you select stats information about the attributes of the problem appears but not the entire problem itself These attributes include the number and type of constraints variables nonzero constraint coefficients Try this feature by typing display problem stats For our example the following information appears Problem name example Variables 3 Nneg 2 1 Objective nonzeros 3 Linear constraints 2 Less 2 Nonzeros E 6 RHS nonzeros 2 This information tells us that in the example there are two constraints three variables and six nonzero constraint coefficients The two constraints are both of the type less than or equal to Two of the three variables have the default nonnegativity bounds x and one is restricted to a certain range box variable In addition to a constraint matrix nonzero count there is a count of nonzero coefficients in the objective function and on the righthand side Such statistics can help to identify errors in a problem without displaying it in its entirety You can see more information about the values of the input data in your problem if you set the datacheck parameter before you type the comman display problem stats Parameters are explained Setting ILOG CPLEX Parameters on page 58 later in this tutorial To set the datacheck parameter type the following for now Set read datacheck yes ILOG CPLEX 10 1 GETTING STARTED 43 44
35. solution More precise information about the outcome of the last call to the method solve can be obtained by calling IloCplex getStatus The returned value tells you what ILOG CPLEX found out about the model whether it found the optimal solution or only a feasible solution whether it proved the model to be unbounded or infeasible or whether nothing at all has been determined at this point Even more detailed information about the termination of the optimizer call is available through the method I1oCplex getCplexStatus Query the Results If the solve method succeeded in finding a solution you will then want to access that solution The objective value of that solution can be queried using a statement like this double objval cplex getObjValue Similarly solution values for all the variables in the array x can be queried by calling double xval cplex getValues x More solution information can be queried from IloCplex including slacks and depending on the algorithm that was applied for solving the model duals reduced cost information and basis information ILOG CPLEX 10 1 GETTING STARTED 93 Building and Solving a Small LP Model in Java 94 The example LPex1 java part of the standard distribution of ILOG CPLEX is a program that builds a specific small LP model and then solves it This example follows the general structure found in many ILOG CPLEX Concert Technology applications and demonstrates three main wa
36. standard distribution of the product at yourCPLEXinstallation examples src lpexl c Reading a Problem from a File Example 2 The previous example 1pex1 c shows a way to copy problem data into a problem object as part of an application that calls routines from the ILOG CPLEX Callable Library Frequently however a file already exists containing a linear programming problem in the industry standard MPS format the ILOG CPLEX LP format or the ILOG CPLEX binary SAV format In example 1pex2 c ILOG CPLEX file reading and optimization routines read such a file to solve the problem Example 1pex2 c uses command line arguments to determine the name of the input file and the optimizer to call Usage lpex2 filename optimizer Where ilename is a file with extension MPS SAV or LP lower case is allowed and optimizer is one of the following letters ILOG CPLEX 10 1 GETTING STARTED 121 122 default primal simplex dual simplex network with dual simplex cleanup barrier with crossover barrier without crossover sifting oO 00252 5 Q O concurrent For example this command lpex2 example mps d reads the file example mps and solves the problem with the dual simplex optimizer To illustrate the ease of reading a problem the example uses the routine CPXreadcopyprob This routine detects the type of the file reads the file and copies the data into the ILOG CPLEX problem object that is created with a call
37. the default bounds there is no need to enter them You have finished entering the problem so to indicate that the problem is complete type end on the last line The CPLEX gt prompt returns indicating that you can again enter a ILOG CPLEX command Summary Entering a problem in ILOG CPLEX is straightforward provided that you observe a few simple rules The terms maximize or minimize must precede the objective function the term subject to must precede the constraints section both must be separated from the beginning of each section by at least one space The word bounds must be alone on a line preceding the bounds section On the final line of the problem end must appear Entering Data You can use the return key to split long constraints and ILOG CPLEX still interprets the multiple lines as a single constraint When you split a constraint in this way do not press return in the middle of a variable name or coefficient The following is acceptable time x1 x2 return X3 20 return labor 3x2 x3 lt 30 return The entry below however is incorrect since the lt return gt key splits a variable name time x1 x2 x return 3 lt 20 return labor 3x2 x3 lt 30 return If you type a line that ILOG CPLEX cannot interpret a message indicating the problem will appear and the entire constraint or objective function will be ignored You must then re
38. this tutorial it is sufficient to know that this algorithm consists of solving a sequence of LPs QPs or QCPs that are generated in the course of the algorithm The first LP QP or QCP to be solved is known as the root while all the others are referred to as nodes and are derived from the root or from other nodes If the model extracted to the cplex object is a pure LP QP or QCP no integer variables then it will be fully solved at the root As mentioned in Optimizer Options on page 12 various optimizer options are provided for solving LPs QPs and QCPs Whie the default optimizer works well for a wide variety of models 11oCplex allows you to control which option to use for solving the root and for solving the nodes respectively by the following methods void IloCplex setParam IloCplex RootAlg alg void IloCplex setParam IloCplex NodeAlg alg where IloCplex Algorithm is an enumeration type It defines the following symbols with their meaning IloCplex AutoAlg allow ILOG CPLEX to choose the algorithm IloCplex Dual use the dual simplex algorithm IloCplex Primal use the primal simplex algorithm IloCplex Barrier use the barrier algorithm IloCplex Network use the network simplex algorithm for the embedded network IloCplex Sifting use the sifting algorithm IloCplex Concurrent allow ILOG CPLEX to use multiple algorithms on multiple computer processors For QP models only the AutoAlg Dual Primal Barrier and
39. variables equality delete range of equality constraints greater than delete range of greater than constraints less than delete range of less than constraints Deletion to make At the first prompt specify that you want to delete a constraint Deletion to make constraints At the next prompt enter a constraint name or number or a range as you did when you used the display command Since the constraint to be deleted is named new3 enter that name Delete which constraint new3 Constraint 3 deleted Check to be sure that the correct range or number is specified when you perform this operation since constraints are permanently removed from the problem Indices of any constraints that appeared after a deleted constraint will be decremented to reflect the removal of that constraint The last message indicates that the operation is complete The problem can now be checked to see if it has been changed back to its original form display problem all Maximize obj xl 2 2 3 x3 Subject To cl Xl 2 X3 20 C23 xl 3 x2 x3 lt 30 Bounds lt lt 40 All other variables are gt 0 When you remove a constraint with the delete option that constraint no longer exists in memory however variables that appear in the deleted constraint are not removed from memory If a variable from the deleted constraint appears in the objective function it may still influence the solution process If that is not wha
40. variables directly for modeling it should be pointed out that such expressions are themselves represented by yet another Concert Technology class IloExpr Like most Concert Technology objects IloExpr objects are handles Consequently the method end must be called when the object is no longer needed The only exceptions are implicit expressions where the user does not create an IloExpr object such as when writing for example x1 2 x2 For such implicit expressions the method end should not be called The importance of the class IloExpr becomes clear when expressions can no longer be fully spelled out in the source code but need instead to be built up in a loop Operators like provide an efficient way to do this ILOG CPLEX 10 1 GETTING STARTED 75 Solving the Model lloCplex After the optimization problem has been created in an IloMode1 object it is time to create the IloCplex object for solving the problem This is done by creating an instance of the class IloCplex For example to create an object named 1 do the following IloCplex cplex env again using the environment env as a parameter The ILOG CPLEX object can then be used to extract the model to be solved One way to extract the model is to call cplex extract model However experienced Concert users recommend a shortcut that performs the construction of the cplex object and the extraction of the model in one line IloCplex cplex model This shortcu
41. 1 Expr model Sum model Prod 1 0 x 01 model Prod 3 0 x 1 model Prod 1 0 x 21 ILOG CPLEX 10 1 GETTING STARTED In those lines you can see how to populate an empty model with data indicating the nonzeros of the constraint matrix Those lines first create objects for the objective and the ranges without expressions They also create variables without columns that is variables with only their bounds Then those lines create expressions over the objective ranges and variables and add the expressions to the model Add an interface Go to the comment Step 7 in the file and add these lines to create a method that tells a user how to invoke this application internal static void Usage System Console WriteLine usage LPexl option System Console WriteLine options r build model row by row System Console WriteLine options c build model column by column System Console WriteLine options n build model nonzero by nonzero Add a command evaluator Go to the comment Step 8 in the file and add these lines to create a switch statement that evaluates the command that a user of your application might enter switch args 0 ToCharArray 1 case r PopulateByRow cplex var rng break case c PopulateByColumn cplex var rng break case n PopulateByNonzero cplex var rng break default Usage return ILOG CPLEX 10 1 GETTING STARTED 107
42. 2 The elements that can be changed are displayed like this Change options bounds change bounds on a variable coefficient change a coefficient delete delete some part of the problem name change a constraint or variable name objective change objective function value problem change problem type qpterm change a quadratic objective term rhs change a right hand side or network supply demand value sense change objective function or a constraint sense type change variable type Change to make Changing Constraint or Variable Names Enter name at the Change to make prompt to change the name of a constraint Change to make name The present name of the constraint is c3 In the example you can change the name to new3 to differentiate it from the other constraints using the following entries Change a constraint or variable name c or v c Present name of constraint c3 New name of constraint new3 The constraint c3 now has name new3 The name of the constraint has been changed The problem can be checked with a display command for example display problem constraints new3 to confirm that the change was made This same technique can also be used to change the name of a variable Changing Sense Next change the sense of the new3 constraint from 2 to using the sense option of the change command At the CPLEX gt prompt type change sense ILOG CPLEX prompts you to specify a constraint There are tw
43. 2i e oi dele coed lw date hited E E IIT 104 Solve icc cerns mer bre d m 108 Complete 109 Callable Library Tutorial llle 111 The Design of the ILOG CPLEX Callable Library 111 Compiling and Linking Callable Library Applications 112 Building Callable Library Applications on UNIX Platforms 113 Building Callable Library Applications on Win32 113 Building Applications that Use the ILOG CPLEX Parallel Optimizers 114 How ILOG CPLEX Works eeeueeeeeese eee hh 114 Opening the ILOG CPLEX 114 Instantiating the Problem 115 Populating the Problem Object 115 Changing the Problem 116 Creating a Successful Callable Library 116 Prototype the Model copo ect wad CERE RGUCOC REX GG REX ERE ed ee a 116 Identify the Routines to be Called 117 Test Procedures in the Application 117 Assemble the Data eR
44. 6 IloEnv class C API 72 end method 73 IloException class C API 77 IloExpr class C API 75 TloExtractable class C API 74 ILOG License Manager ILM 22 ILOG LICENSE FILE environment variable 23 loLinearNumExpr class Java API 92 loMinimize function C API 75 loModel class C API add method 74 75 extractable 74 role 70 IloModel class Java API column method 96 numVar method 96 IloNumArray class C API 79 IloNumColumn class C API 79 IloNumExpr class Java API 91 92 IloNumVar class C API 80 columns and 80 reading files and 81 role 74 IloNumVar class Java API role in model 91 I I I GETTING STARTED IloObjective class C API 74 79 81 setLinearCoef method 80 IloObjective class Java API role in model 91 TloRange class C API casting operator for 79 example 75 reading from file 81 role 74 setLinearCoef method 80 TloRange class Java API role in model 91 setExpr method 97 TloSemiContVar class C API 81 1108081 class C API 81 IloSOS2 class C API 81 importModel method IloCplex class C API 81 83 infeasible Java API 93 installing CPLEX 19 to 24 testing installation 23 integer parameter C API 86 integer variable optimizer used C API 118 representing in model C API 74 Interactive Optimizer 35 to 67 command formats 36 commands 37 description 11 example model 29 quitting 66 starting 36 invalid encrypted key Java API 89
45. APT 73 74 problem files in Interactive Optimizer 53 problem object C API 115 124 SOS C 81 variable C API 81 D data entering in Interactive Optimizer 41 entry options 13 deleting constraints in Interactive Optimizer 64 132 ILOG CPLEX 10 1 problem options in Interactive Optimizer 65 variables in Interactive Optimizer 64 directory installation structure 20 display Interactive Optimizer command 42 62 options 42 problem 42 bounds 46 constraints 46 names 44 45 46 options 42 stats 43 syntax 43 sensitivity 52 syntax 53 settings 59 solution 50 syntax 51 specifying item ranges 44 syntax 47 displaying basic rows and columns in Interactive Optimizer 51 bounds in Interactive Optimizer 46 constraint names in Interactive Optimizer 44 constraints in Interactive Optimizer 46 nonzero constraint coefficients in Interactive Optimizer 43 number of constraints in Interactive Optimizer 43 objective function in Interactive Optimizer 46 optimal solution in Interactive Optimizer 48 parameter settings in Interactive Optimizer 59 post solution information in Interactive Optimizer 50 problem in Interactive Optimizer 42 problem options in Interactive Optimizer 42 problem part in Interactive Optimizer 44 problem statistics in Interactive Optimizer 43 sensitivity analysis C API 125 sensitivity analysis in Interactive Optimizer 51 slack values in Interactive Optimizer 51 solution values in Interactive Optimizer 51 type of c
46. Barrier optimizer MIP models are all solved by the Mixed Integer Optimizer which in turn may invoke any of the LP or QP optimizers in the course of its computation Table 2 summarizes these possible choices Table 2 Optimizers LP Network QP QCP MIP Dual Optimizer yes yes Primal Optimizer yes yes Barrier Optimizer yes yes yes Mixed Integer Optimizer yes Network Optimizer Note 1 yes Note 1 Note 1 The problem must contain an extractable network substructure The choice of optimizer or other parameter settings may have a very large effect on the solution speed of your particular class of problem The ILOG CPLEX User s Manual describes the optimizers provides suggestions for maximizing performance and notes the features and algorithmic parameters unique to each optimizer Using the Parallel Optimizers On a computer with multiple CPUs the Barrier Optimizer and the MIP Optimizer are each capable of running in parallel that is they can apply these additional CPUs to the task of optimizing the model The number of CPUs used by an optimizer is controlled by the user ILOG CPLEX 10 1 GETTING STARTED under default settings these optimizers run in serial single CPU mode When solving small models such as those in this document the effect of parallelism will generally be negligible On larger models the effect is ordinarily beneficial to solution speed See the section Using Parallel Opti
47. C API 124 purpose in C API 115 use in C API 115 CPXfreeprob routine file format example in C API 123 LP example in C API 121 network example in C API 124 purpose in C API 115 CPXgeterrorstring routine closing LP example in C API 120 opening LP example in C API 121 CPXgetobjval routine 124 CPXlpopt routine in sensitivity analysis in C API 125 LP example in C API 120 network example in C API 124 CPXmsg routine 115 CPXnewcols routine LP example in C API 120 modular data in C API 117 populating model in C API 115 GETTING STARTED 131 CPXnewrows routine 120 example in C API 120 modular data in C API 117 populating model in C API 115 CPXopenCPLEX routine file format example in C API 122 LP example in C API 120 network example in C API 124 purpose in C API 114 CPXreadcopyprob routine example in C API 122 formatted data files in C API 115 CPXsetintparam routine 120 CPXsolution routine LP example in C API 120 network example in C API 124 CPXwriteprob routine LP example in C API 121 network example in C API 124 sensitivity analysis in C API 125 testing in CAPI 119 creating algorithm object C API 76 78 automatic log file in Interactive Optimizer 49 binary problem representation C APT 119 constraint C API 79 environment C API 124 environment object C API 72 78 model I1oModel C API 73 model Java API 91 model objects C API 78 objective function C APD 79 81 optimization model C
48. CPXrhssa env lp 0 cur_numrows 1 lowerr upperr if status fprintf stderr Failed to obtain RHS sensitivity n goto TERMINATE printf nRight hand side coefficient sensitivity Wn for i 0 i cur numrows i printf Row d Lower 10g Upper 10g n i lowerr i upperr il This sample is familiarly known as throw away code For production purposes you probably want to observe good programming practices such as freeing these allocated arrays at the TERMINATE label in the application A bound value of 7e CPX INFBOUND is treated as infinity within ILOG CPLEX so this is the value printed by our sample code in cases where the upper or lower sensitivity range on a row or column is infinite a more sophisticated program might print a string such as inf or inf when negative or positive CPX INFBOUND is encountered as a value ILOG CPLEX 10 1 GETTING STARTED 125 Similar code could be added to perform sensitivity analysis with respect to bounds via CPXboundsa 126 ILOG CPLEX 10 1 GETTING STARTED Part 111 Index A accessing basic rows and columns of solution in Interactive Optimizer 51 basis information C API 83 dual values in Interactive Optimizer 51 dual values in Interactive Optimizer example 51 objective function value in Interactive Optimizer 50 quality of solution in Interactive Optimizer 50 reduced cost Java API 93 reduced costs in Int
49. E eh ek eee Bsp ti e eb be See 117 Choose ar Optlmizet Se LE ER xis ede Rp RR TEENS GER 118 ILOG CPLEX 10 1 GETTING STARTED 7 Part Ill Observe Good Programming 118 Debug Your Program e I Im 118 Test Your Applicatloh ue esee rey EE e pErqu ere ere x e ER oe 119 Use the RP GRUB dee ds ween ek ea ORE QUE 119 Building and Solving a Small LP Model in 119 Complete Programs Hp E E ke de poked ate Meee hha AT Moos 121 Reading a Problem from a File Example 2 121 Complete Program seira ee ee ee pee ee ee Re Rida eae 123 Adding Rows to a Problem Example 123 Complete Program us ct sted ee ee ete eet ep ce e enn es 124 Performing Sensitivity Analysis cece eee eee nnn 125 ete eee eee ee ee eee eee ILOG CPLEX 10 1 GETTING STARTED Introducing ILOG CPLEX This preface introduces ILOG CPLEX 10 1 It includes sections about 0 What Is ILOG CPLEX on page 10 What You Need to Know on page 13 What s in This Manual on page 13 Notation in this Manual on page 14 Related Documentation on page 15 ILOG CPLEX 10 1 GETTING STARTED 9 What Is ILOG CPLEX ILOG CPLEX is a tool
50. ILOG CPLEX 10 1 GETTING STARTED Callable Library routine except those such as CPXmsg which do not require an environment The application developer must make an independent decision as to whether the variable containing the environment pointer is a global or local variable Multiple environments are allowed but extensive opening and closing of environments may create significant overhead on the licensor and degrade performance typical applications make use of only one environment for the entire execution since a single environment may hold as many problem objects as the user wishes After all calls to the Callable Library are complete the environment is released by the routine CPXcloseCPLEX This routine indicates to ILOG CPLEX that all calls to the Callable Library are complete any memory allocated by ILOG CPLEX is returned to the operating system and the use of the ILOG CPLEX license is ended for this run Instantiating the Problem Object A problem object is instantiated created and initialized by ILOG CPLEX when you call the routine CPXcreateprob It is destroyed when you call CPX reeprob ILOG CPLEX allows you to create more than one problem object although typical applications will use only one Each problem object is referenced by a pointer returned by CPXcreateprob and represents one specific problem instance Most Callable Library functions except parameter setting functions and message handling functions require a poi
51. Interrupting the Optimization Process on page 50 For detailed information about performance options refer to the ILOG CPLEX User s Manual Filing Iteration Logs Every time ILOG CPLEX solves a problem much of the information appearing on the screen is also directed into a log file This file is automatically created by ILOG CPLEX with the name cplex 10g If there is an existing cplex 10g file in the directory where ILOG CPLEX is launched ILOG CPLEX will append the current session data to the ILOG CPLEX 10 1 GETTING STARTED 49 50 existing file If you want to keep a unique log file of a problem session you can change the default name with the set logfile command See the ILOG CPLEX User s Manual The log file is written in standard ASCII format and can be edited with any text editor Re Solving You may re solve the problem by reissuing the optimize command ILOG CPLEX restarts the solution process from the previous optimal basis and thus requires zero iterations If you do not wish to restart the problem from an advanced basis use the set advance command to turn off the advanced start indicator Remember that a problem must be present in memory entered via the enter command or read from a file before you issue the optimize command Using Alternative Optimizers In addition to the optimize command ILOG CPLEX can use the primal simplex optimizer primopt command the dual simplex optimizer tranopt command the barrier
52. NIX platform or the compiler and library format combination for Windows 2 Go to the subdirectory in the examples directory where ILOG CPLEX is installed on your machine On UNIX this will be machine libformat and on Windows it will be compiler libformat This subdirectory will contain a makefile or javamake appropriate for your platform 3 Then use this file to compile the examples that came in the standard distribution by calling make execute java UNIX or nmake f javamake execute Windows 4 Carefully note the locations of the needed files both during compilation and at run time and convert the relative path names to absolute path names for use in your own working environment ILOG CPLEX 10 1 GETTING STARTED In Case Problems Arise If a problem occurs in the compilation phase make sure your java compiler is correctly set up and that your classpath includes the cplex jar file If compilation is successful and the problem occurs when executing your application there are three likely causes 1 If you get a message like java lang NoClassDefFoundError your classpath is not correctly set up Make sure you use classpath path to cplex jar in your java command If you get a message like java lang UnsatisfiedLinkError you need to set up the path correctly so that the JVM can locate the ILOG CPLEX shared library Make sure you use the following option in your java command Djava library path path to shared li
53. Network algorithms are applicable The optimizer option used for solving pure LPs and QPs is controlled by setting the root algorithm parameter This is demonstrated next in example ilolpex2 cpp Reading a Problem from a File Example ilolpex2 cpp 82 This example shows how to read an optimization problem from a file and solve it with a specified optimizer option It prints solution information including a Simplex basis if available Finally it prints the maximum infeasibility of any variable of the solution The file to read and the optimizer choice are passed to the program via command line parameters For example this command ilolpex2 example mps d ILOG CPLEX 10 1 GETTING STARTED reads the file example mps and solves the problem with the dual simplex optimizer Example ilolpex2 demonstrates Reading the Model from a File Selecting the Optimizer Accessing Basis Information Querying Quality Measures The general structure of this example is the same as for example ilolpex1 cpp It starts by creating the environment and terminates with destroying it by calling the end method The code in between is enclosed in try catch statements for error handling Reading the Model from a File The model is created by reading it from the file specified as the first command line argument argv 1 This is done using the method importModel of an IloCplex object Here the IloCplex object is used as a model reader rather
54. PLEX API Reference Manual documents the C API of the Concert Technology classes methods and functions It is available online as HTML and Microsoft compiled HTML help CHM The ILOG CPLEX Java API Reference Manual supplies detailed definitions of the Concert Technology interfaces and CPLEX Java classes It is available online as HTML and Microsoft compiled HTML help CHM The ILOG CPLEX NET Reference Manual documents the NET API for CPLEX It is available online as HTML and Microsoft compiled HTML help CHM The reference manual ILOG CPLEX Parameters contains a table of parameters that can be modified by parameter routines It is the definitive reference manual for the purpose and allowable settings of CPLEX parameters The reference manual ILOG CPLEX File Formats contains a list of file formats that ILOG CPLEX supports as well as details about using them in your applications ILOG CPLEX 10 1 GETTING STARTED 15 16 The reference manual ILOG CPLEX Interactive Optimizer contains the commands of the Interactive Optimizer along with the command options and links to examples of their use in the ILOG CPLEX User s Manual As you work with ILOG CPLEX on a long term basis you should read the complete User s Manual to learn how to design models and implement solutions to your own problems Consult the reference manuals for authoritative documentation of the Component Libraries their application programming interfaces
55. PLEX can be used to solve it This example continues with the following topics Solving the Example Problem on page 48 Solution Options on page 49 Displaying Post Solution Information on page 50 Solving the Example Problem The optimize command tells ILOG CPLEX to solve the LP problem ILOG CPLEX uses the dual simplex optimizer unless another method has been specified by setting the LPMETHOD parameter explained more fully in the LOG CPLEX User s Manual Entering the Optimize Command At the CPLEX gt prompt type the command optimize Preprocessing First ILOG CPLEX tries to simplify or reduce the problem using its presolver and aggregator If any reductions are made a message will appear However in our small example no reductions are possible Monitoring the Iteration Log Next an iteration log appears on the screen ILOG CPLEX reports its progress as it solves the problem The solution process involves two stages during Phase I ILOG CPLEX searches for a feasible solution in Phase II ILOG CPLEX searches for the optimal feasible solution The iteration log periodically displays the current iteration number and either the current scaled infeasibility during Phase I or the objective function value during Phase II After the optimal solution has been found the objective function value solution time and iteration count total with Phase I in parentheses are displayed This information can be useful for
56. RTED Those lines populate the model with data specific to this particular example However you can see from its use of the interface IMPModeler how to add ranged constraints to a model IMPModeler is the Concert Technology interface typically used to build math programming MP matrix models You will see its use again in Step 5 and Step 6 Populate the model by columns Go to the comment Step 5 in the file and add these lines to create a method to populate the empty model with data by columns internal static void PopulateByColumn IMPModeler model INumVar var IRange rng IObjective obj model AddMaximize rng 0 new IRange 2 rng 0 0 model AddRange System Double MaxValue 20 0 rng 0 1 model AddRange System Double MaxValue 30 0 IRange r0 rng 0 0 IRange r1 rng 0 1 var 0 new INumVar 3 var 0 0 model NumVar model Column obj 1 0 And model Column rO0 1 0 And model Column r1 1 0 0 0 40 0 var 0 1 model NumVar model Column obj 2 0 And model Column rO0 1 0 And model Column r1 3 0 0 0 System Double MaxValue var 0 2 model NumVar model Column obj 3 0 And model Column rO0 1 0 And model Column r1 1z0 0 0 System Double MaxValue Again those lines populate the model with data specific to this problem From them you can see how to use the interface IMPModeler to add columns to an empty model While for many e
57. STARTED 129 starting from previous C API 86 basis file reading in Interactive Optimizer 57 writing in Interactive Optimizer 54 Boolean parameter C API 86 Boolean variable representing in model C API 74 bound adding in Interactive Optimizer 60 changing in Interactive Optimizer 63 default values in Interactive Optimizer 40 displaying in Interactive Optimizer 46 entering in LP format in Interactive Optimizer 40 removing in Interactive Optimizer 63 sensitivity analysis C API 126 sensitivity analysis in Interactive Optimizer 52 box variable in Interactive Optimizer 43 branch amp bound C API 82 branch amp cut C API 81 C Callable Library description 11 example model 33 Callable Library C API 111 to 126 application development steps 116 compiling and linking applications 112 conceptual design 111 CPLEX operation 114 distribution file 112 error handling 118 opening CPLEX 114 change Interactive Optimizer command 61 bounds 63 change options 61 coefficient 64 delete 64 delete options 65 objective 64 rhs 64 sense 62 syntax 65 changing bounds in Interactive Optimizer 63 130 ILOG CPLEX 10 1 coefficients in Interactive Optimizer 64 constraint names in Interactive Optimizer 62 objective in Interactive Optimizer 64 parameters C API 85 parameters in Interactive Optimizer 58 problem in Interactive Optimizer 61 righthand side rhs in Interactive Optimizer 64 sense in Interactive Optimizer 62 v
58. X Applications in ILOG Concert Technology 88 In Case Problems 89 The Design of ILOG CPLEX in ILOG Concert 90 The Anatomy of an ILOG Concert Technology 90 Create the Model 0 0 2 0 cette hh 91 solveithe Model irs pene 93 Query the Res lts teh Paced ee gee ae 93 Building and Solving a Small LP Model Java 94 Modeling by ROWS eo REC Re EV DEPT bebe vero eds 95 Modeling by Col mris med ge AG eu exe Re eg age due Tur vested a 95 ILOG CPLEX 10 1 GETTING STARTED Chapter 6 Chapter 7 Modeling by 2 e I m 97 Complete Programi sceo ric icd ld eb be See Ih Palo eet RM E 97 Concert Technology Tutorial for NET Users 99 What You Need to Know Prerequisites cece eee eee eee eee eee 100 What You Will Be Doing 0 0 101 a citi b beri ELEME end 101 fee els carted one LE oet baba Bu Aoc tact od ae IN RE feci e e E 102 SOVE rU 102 Desctlbe eua ata Re IRR ROPA ee ele Saale SUR Ts 102 Building a Small LP Problem in 103 Model 5
59. ables var and range constraints rng respectively the methods will write to var 0 and rng 0 an array of all the variables and constraints in the model for later access ILOG CPLEX 10 1 GETTING STARTED After the model has been created in the cplex object it is ready to be solved by a call to cplex solve The solution log will be output to the screen this is because IloCplex prints all logging information to the OutputStream cplex output which by default is initialized to System out You can change this by calling the method cplex setout In particular you can turn off logging by setting the output stream to nu11 that is by calling cplex setOut null Similarly 11oCplex issues warning messages to cplex warning and cplex setWarning can be used to change or turn off the OutputStream that will be used If the solve method finds a feasible solution for the active model it returns t rue The next section of code accesses the solution The method cplex getValues var 0 returns an array of primal solution values for all the variables This array is stored as double x The values in are ordered such that 5 is the primal solution value for variable var 0 j Similarly the reduced costs duals and slack values are queried and stored in arrays dj pi and slack respectively Finally the solution status of the active model and the objective value of the solution are queried with the methods IloCplex getStatus and IloCp
60. ad Interactive Optimizer command 56 57 avoiding prompts for options 57 basis files and 57 file type options 56 syntax 58 reading file format in Interactive Optimizer 56 LP files in Interactive Optimizer 56 model from file C API 81 83 MPS files in Interactive Optimizer 57 problem files C API 121 problem files in Interactive Optimizer 55 reduced cost accessing Java API 93 accessing in Interactive Optimizer 50 GETTING STARTED 137 removing bounds in Interactive Optimizer 63 representing optimization problem C APT 78 re solving in Interactive Optimizer 50 righthand side RHS changing coefficient in Interactive Optimizer 64 sensitivity analysis C API 125 sensitivity analysis in Interactive Optimizer 52 root LP solving C API 82 S SAV file format C API 124 saving problem files in Interactive Optimizer 53 solution files in Interactive Optimizer 53 scalProd method Java API 95 sense changing in Interactive Optimizer 62 sensitivity analysis performing C API 125 performing in Interactive Optimizer 51 set Interactive Optimizer command 58 advance 50 available parameters 59 defaults 59 logfile 50 simplex 48 syntax 59 setOut method Java API 95 setRootAlgorithm method IloCplex class C API 83 setting parameters C API 85 parameters in Interactive Optimizer 58 parameters to default in Interactive Optimizer 59 setWarning method Java API 95 shadow price accessing in Intereact
61. allable Library files respectively Note The instructions below were current at the time of publication As compilers linkers and operating systems are released different instructions may apply Be sure to check the Release Notes that come with your ILOG CPLEX distribution for any changes Also check the ILOG CPLEX web page http www ilog com products cplex Building Callable Library Applications on UNIX Platforms To compile and execute an example 1pex1 do the following cd examples platform format make 1 1 to compile and execute the first CPLEX example In that command platform indicates the name of the subdirectory corresponding to your type of machine and format indicates your particular library format such as static multi threaded and so forth A list of all the examples that can be built this way is to be found in the makefile by looking for c EX C examples or you can view the files listed in examples src The makefile contains recommended compiler flags and other settings for your particular computer which you can find by searching in it for Compiler options and use in your applications that call ILOG CPLEX Building Callable Library Applications on Win32 Platforms Building an ILOG CPLEX application using Microsoft Visual C Integrated Development Environment or the Microsoft Visual C command line compiler are explained here Microsoft Visual C IDE To make an ILOG CPLEX Callable Library
62. an infeasible problem display display problem solution or parameter settings enter enter a new problem feasopt find relaxation to infeasible linear problem help provide information on CPLEX commands mipopt Solve a mixed integer program netopt Solve the problem using network method optimize Solve the problem primopt Solve using the primal method quit leave CPLEX read read problem or advanced start information from a file set set parameters tranopt Solve using the dual method write write problem or solution information to a file xecute execute a command from the operating system Enter enough characters to uniquely identify commands amp options Commands can be entered partially CPLEX will prompt you for further information or as a whole To find out more about a specific command type help followed by the name of that command For example to learn more about the primopt command type help primopt Typing the full name is unnecessary Alternatively you can try hp The following message appears to tell you more about the use and syntax of the primopt command The PRIMOPT command solves the current problem using a primal simplex method or crosses over to a basic solution if a barrier solution exists Syntax PRIMOPT A problem must exist in memory from using either the ENTER or READ command in order to use the PRIMOPT command Sensitivity information dual price and reduced cost information as well as other detailed
63. an vary without changing the optimal basis The current value of each RHS coefficient is also displayed for reference Righthand side sensitivity information is useful for determining how sensitive the optimal solution and resource values are to the availability of those resources ILOG CPLEX can also display lower bound sensitivity ranges with the command display sensitivity lb and upper bound sensitivity with the command ILOG CPLEX 10 1 GETTING STARTED display sensitivity ub Summary Display sensitivity analysis characteristics by entering a command with the syntax display sensitivity identifier Writing Problem and Solution Files The problem or its solution can be saved by using the write command This command writes the problem statement or a solution report to a file The tutorial example continues in the topics Selecting a Write File Format on page 53 Writing LP Files on page 54 Writing Basis Files on page 54 Using Path Names on page 55 Selecting a Write File Format When you type the write command in the Interactive Optimizer ILOG CPLEX displays a menu of options and prompts you for a file format like this File type options bas INSERT format basis file clp Conflict file dpe Binary format for dual perturbed problem dua MPS format of explicit dual of problem emb MPS format of embedded network lp LP format problem file min DIMACS min cost network flow format of embedded network mps MPS
64. ariable names in Interactive Optimizer 62 choosing optimizer C API 118 optimizer C API 82 optimizer in Interactive Optimizer 50 class library Java APT 88 classpath Java API 89 command line option 88 coefficient changing in Interactive Optimizer 64 column expressions C API 79 command executing from operating system in Interactive Optimizer 66 input formats in Interactive Optimizer 36 Interactive Optimizer list 37 compiler DNDEBUG option C API 77 error messages C API 72 Microsoft Visual C Command Line C API 114 using with CPLEX C API 71 compiling applications 24 applications C API 112 applications C API 71 Component Libraries defined 11 running examples 23 verifying installation 23 Concert Technology C classes 72 C objects 70 compiling and linking applications C API 71 CPLEX design in C API 70 error handling C APT 77 running examples C API 71 GETTING STARTED Concert Technology C API 69 to 86 Concert Technology Library description 11 example model 30 constraint adding C API 85 adding in Interactive Optimizer 60 changing names in Interactive Optimizer 62 changing sense in Interactive Optimizer 62 creating C API 79 default names in Interactive Optimizer 40 deleting in Interactive Optimizer 64 displaying in Interactive Optimizer 46 displaying names in Interactive Optimizer 44 displaying nonzero coefficients in Interactive Optimizer 43 displaying numbe
65. ary Do not change the problem by changing the original problem data arrays and then making a call to CPXcopylp Instead change the problem using the problem modification routines allowing ILOG CPLEX to make use of as much solution information as possible from the solution of the problem before the modifications took place For example suppose that a problem has been solved and that the user has changed the upper bound on a variable through an appropriate call to the ILOG CPLEX Callable Library A re optimization would then begin from the previous optimal basis and if that old basis were still optimal then that information would be returned without even the need to refactor the old basis Creating a Successful Callable Library Application 116 Callable Library applications are created to solve a wide variety of problems Each application shares certain common characteristics regardless of its apparent uniqueness The following steps can help you minimize development time and get maximum performance from your programs 1 Prototype the Model Identify the Routines to be Called Test Procedures in the Application Assemble the Data Choose an Optimizer Observe Good Programming Practices Debug Your Program Test Your Application p xL 9 A 9 M Use the Examples Prototype the Model Create a small model of the problem to be solved An algebraic modeling language is sometimes helpful during this step ILOG CPLEX 10
66. brary If you get a message like ilm CPLEX no license found for this product or ilm CPLEX invalid encrypted key MNJVUXTDJV82 in usr ilog ilm access ilm run ilmcheck then there is a problem with your license to use ILOG CPLEX Review the LOG License Manager User s Guide and Reference to see whether you can correct the problem If you have verified your system and license setup but continue to experience problems contact ILOG Technical Support and report the error messages ILOG CPLEX 10 1 GETTING STARTED 89 The Design of ILOG CPLEX in ILOG Concert Technology User Written Application Concert Technology modeling interfaces lloCplex CPLEX internals Figure 5 1 View of ILOG CPLEX in ILOG Concert Technology Figure 5 1 illustrates the design of ILOG Concert Technology and how a user application uses it ILOG Concert Technology defines a set of interfaces for modeling objects Such interfaces do not actually consume memory For this reason the box in the figure has a dotted outline When a user creates an ILOG Concert Technology modeling object using ILOG CPLEX an object is created in ILOG CPLEX to implement the interface defined by ILOG Concert Technology However a user application never accesses such objects directly but only communicates with them through the interfaces defined by ILOG Concert Technology For more detail about these ideas see ILOG CPLEX User s Ma
67. ception ILOG CPLEX 10 1 GETTING STARTED IloCplex provides the output streams out for general logging warning for warning messages and error for error messages They are preconfigured to cout cerr and cerr respectively Thus by default you will see logging output on the screen when invoking the method solve This can be turned off by calling cplex setOut env getNullStream that is by redirecting the out stream of the IloCplex object cplex to the null stream of the environment If a solution is found solution information is output through the channel env out which is initialized to cout by default The output operator is defined for type IloAlgorithm Status as returned by the call to cplex getStatus It is also defined for IloNumArray the ILOG Concert Technology class for an array of numerical values as returned by the calls to cplex getValues cplex getDuals cplex getSlacks and cplex getReducedCosts In general the output operator is defined for any ILOG Concert Technology array of elements if the output operator is defined for the elements The functions named populateby are purely about modeling and are completely decoupled from the algorithm IloCplex In fact they don t use the cplex object which is created only after executing one of these functions Modeling by Rows The function populatebyrow creates the variables and adds them to the array x Then the objective function and the constraints are creat
68. ct from it that defines the objective function to minimize the expression This new object is returned and assigned to the new handle obj After an objective extractable is created it must be added to the model As noted above this is done with the add method of 11oModel1 If this is all that the variable obj is needed for it can be written more compactly like this model add IloMinimize env x1 2 x2 3 x3 This way there is no need for the program variable obj and the program is shorter If in contrast the objective function is needed later for example to change it and reoptimize the model when doing scenario analysis the variable obj must be created in order to refer to the objective function From the standpoint of algorithmic efficiency the two approaches are comparable Creating constraints and adding them to the model can be done just as easily with the following statement model add x1 x2 x3 lt 20 The part xi x2 x3 lt 20creates an object of class IloRange that is immediately added to the model by passing it to the method IloMode1 add Again if a reference to the IloRange object is needed later an IloRange handle object must be stored for it Concert Technology provides flexible array classes for storing data such as these T1oRange objects As with variables Concert Technology provides a variety of constructors that help create range constraints While those examples use expressions with modeling
69. d For example control c indicates that you should press the control key and the c key simultaneously The symbol return indicates end of line or end of data entry On some keyboards the key is labeled enter or Enter Related Documentation In addition to this introductory manual the standard distribution of ILOG CPLEX comes with the ILOG CPLEX User s Manual and the ILOG CPLEX Reference Manual All ILOG documentation is available online in hypertext mark up language HTML It is delivered with the standard distribution of the product and accessible through conventional HTML browsers The ILOG CPLEX User s Manual explains the relationship between the Interactive Optimizer and the Component Libraries It enlarges on aspects of linear programming with ILOG CPLEX and shows you how to handle quadratic programming QP problems quadratically constrained programming QCP problems second order cone programming SOCP problems and mixed integer programming MIP problems It tells you how to control ILOG CPLEX parameters debug your applications and efficiently manage input and output It also explains how to use parallel CPLEX optimizers The ILOG CPLEX Callable Library Reference Manual documents the Callable Library routines and their arguments This manual also includes additional documentation about error codes solution quality and solution status It is available online as HTML and Microsoft compiled HTML help CHM The ILOG C
70. d intermediate prompts by specifying an LP problem type like this write example2 lp Another way of avoiding the prompt for a file format is by specifying the file type explicitly in the file name extension Try the following as an example write example lp Using a file extension to indicate the file type is the recommended naming convention This makes it easier to keep track of your problem and solution files When the file type is specified by the file name extension ILOG CPLEX ignores subsequent file type information issued within the write command For example ILOG CPLEX responds to the following command by writing an LP format problem file write example lp mps Writing Basis Files Another optional file format is BAS Unlike the LP and MPS formats this format is not used to store a description of the problem statement Rather it is used to store information about the solution to a problem information known as a basis Even after changes are made to the problem using a prior basis to start the optimization from an advanced basis can speed ILOG CPLEX 10 1 GETTING STARTED solution time considerably A basis can be written only after a problem has been solved Try this now with the following command write example bas In response ILOG CPLEX displays a confirmation message like this Basis written to file example bas Using Path Names A full path name may also be included to indicate on which drive and d
71. ding the problem in memory and then calling CPXcopylp avoids time consuming disk file reading Using the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist can lead to modular code that may be more easily maintained than if you assemble all model data in one step Another consideration is that if the Callable Library application reads an MPS or LP formatted file usually another application is required to generate that file Particularly in the case of MPS files the data structures used to generate the file could almost certainly be used ILOG CPLEX 10 1 GETTING STARTED 117 118 to build the problem defining arrays for CPXcopy1p directly The result would be less coding and a faster more efficient application These observations suggest that formatted files may be useful when prototyping your application while assembling the arrays in memory may be a useful enhancement for a production application Choose an Optimizer After a problem object has been instantiated and populated it can be solved using one of the optimizers provided by the ILOG CPLEX Callable Library The choice of optimizer depends on the problem type LP and QP problems can be solved by e the primal simplex optimizer e the dual simplex optimizer and e the barrier optimizer LP problems can also be solved by e the sifting optimizer and e the concurrent optimizer LP problems with a substantial network can also be solved by a sp
72. ds end terminates Xl 2x2 3x3 gt 50 end Problem addition successful When the problem is displayed again the new constraint appears like this display problem all Maximize obj x1 2 x2 3 x3 Subject To Cl SL o 2 x3 lt 20 C2 XL o 3 X26 x3 lt 30 C3 X14 2 x2 3 x3 gt 50 Bounds 0 lt lt 40 All other variables are gt 0 end ILOG CPLEX 10 1 GETTING STARTED Adding from a File Alternatively you may read in new constraints and bounds from a file If you enter a file name after the add command ILOG CPLEX will read a file matching that name The file contents must comply with standard ILOG CPLEX LP format ILOG CPLEX does not prompt for a file name if none is entered Without a file name interactive entry is assumed Summary The general syntax for the add command is add or add filename Changing a Problem The enter and add commands allow you to build a problem from the keyboard but they do not allow you to change what you have built You make changes with the change command The change command can be used for Changing Constraint or Variable Names Changing Sense Changing Bounds and Removing Bounds Changing Coefficients 99 Deleting entire constraints or variables Start out by changing the name of the constraint that you added with the add command In order to see a list of change options type change ILOG CPLEX 10 1 GETTING STARTED 61 6
73. e ILOG Concert Technology CPLEX application Constructing the Environment An environment that is an instance of IloEnv is typically the first object created in any Concert Technology application ILOG CPLEX 10 1 GETTING STARTED You construct an IloEnv object by declaring a variable of type IloEnv For example to create an environment named env you do this IloEnv env Note The environment object created in an ILOG Concert Technology application is different from the environment created in the ILOG CPLEX C library by calling the routine CPXopenCPLEX The environment object is of central importance and needs to be available to the constructor of all other ILOG Concert Technology classes because among other things it provides optimized memory management for objects of ILOG Concert Technology classes This provides a boost in performance compared to using the system memory management system As is the case for most ILOG Concert Technology classes IloEnv is a handle class This means that the variable env is a pointer to an implementation object which is created at the same time as env in the above declaration One advantage of using handles is that if you assign handle objects all that is assigned is a pointer So the statement IloEnv env2 env creates a second handle pointing to the implementation object that env already points to Hence there may be an arbitrary number of 11oEnv handle objects all pointin
74. e Optimizer 40 representing in model C API 74 sensitivity analysis C API 125 sensitivity analysis in Interactive Optimizer 52 operator C API 79 operator C API 79 optimal solution Java API 93 optimization model creating C APT 73 defining extractable objects C API 74 extracting C API 73 optimization problem interrupting in Interactive Optimizer 50 reading from file C API 82 representing C API 78 solving with I1oCplex C API 76 optimize Interactive Optimizer command 48 re solving 50 syntax 49 optimizer choosing by problem type C API 118 choosing by switch in application C API 83 choosing in Interactive Optimizer 50 options 12 parallel C 114 syntax for choosing C API 82 ordering variables in Interactive Optimizer 45 output method Java API 95 OutputStream Java API 95 GETTING STARTED P parallel choosing optimizers for 12 linking for optimizers C API 114 parameter Boolean C API 86 changing C 85 changing in Interactive Optimizer 58 displaying settings in Interactive Optimizer 59 integer C API 86 list of settable in Interactive Optimizer 59 numeric C API 86 resetting to defaults in Interactive Optimizer 59 string C API 86 parameter specification file in Interactive Optimizer 60 path names in Interactive Optimizer 55 populateByColumn method Java API 94 populateByNonzero method Java API 97 populateByNonzero method Java API 94 popu
75. e the output of step 2 to your local ILOG sales administration department They will send you a license key in return One way to communicate the results of step 2 to your local ILOG sales administration department is through the web page serving your region Europe and Africa https support ilog fr license index cfm Americas https support ilog com license index cfm Asia https support ilog com sg license index cfm 4 Create a file on your system to hold this license key and set the environment variable ILOG LICENSE FILE so that ILOG CPLEX will know where to find the license key The environment variable need not be used if you install the license key in a platform dependent default file location Using the Component Libraries After you have completed the installation and licensing steps you can verify that everything is working by running one or more of the examples that are provided with the standard distribution Verifying Installation on UNIX On a UNIX system go to the subdirectory examples machine libformat that matches your particular platform and in it you will find a file named Makefile Execute one of the examples for instance 1pex1 c by doing make lpex1 lpex1 r this example takes one argument either r or n If your interest is in running one of the C examples try make ilolpex1 ilolpex1 r this is the same as 1pex1 and takes the same arguments If your interest is in running one of the Java examp
76. ear coefficient of 1 0 to the expression in obj Column expressions can be built in loops using operator Column expressions objects of class IloNumColumn are handle objects like most other Concert Technology objects The method end must therefore be called to delete the associated implementation object when it is no longer needed However for implicit column expressions where no I1oNumColumn object is explicitly created such as the ones used in this example the method end should not be called The column expression is passed as a parameter to the constructor of class T1oNumVar For example the constructor IloNumVar obj 1 0 0 1 0 c 1 1 0 0 0 40 0 creates a new modeling variable with lower bound 0 0 upper bound 40 0 and by default type ILOFLOAT and adds it to the objective obj with a linear coefficient of 1 0 to the range c 0 with a linear coefficient of 1 0 and to c 1 with a linear coefficient of 1 0 Column expressions can be used directly to construct numerical variables with default bounds 0 IloInfinity and type ILOFLOAT as in the following statement x add obj 2 0 c 01 1 0 c 1 3 0 where IloNumVar does not need to be explicitly written Here the C compiler recognizes that an I1oNumVar object needs to be passed to the add method and therefore automatically calls the constructor IloNumVar IloNumColumn in order to create the variable from the column expression Modeling by Nonzero Ele
77. ecial network optimizer Ifthe problem includes integer variables branch amp cut must be used There are also many different possible parameter settings for each optimizer The default values will usually be the best for linear programs Integer programming problems are more sensitive to specific settings so additional experimentation will often be useful Choosing the best way to solve the problem can dramatically improve performance For more information refer to the sections about tuning LP performance and trouble shooting MIP performance in ILOG CPLEX User s Manual Observe Good Programming Practices Using good programming practices will save development time and make the program easier to understand and modify A list of good programming practices is provided in the ILOG CPLEX User s Manual in Developing CPLEX Applications on page 129 Debug Your Program Your program may not run properly the first time you build it Learn to use a symbolic debugger and other widely available tools that support the creation of error free code Use ILOG CPLEX 10 1 GETTING STARTED the list of debugging tips provided in the ILOG CPLEX User s Manual to find and correct problems in your Callable Library application Test Your Application After an application works correctly it still may have errors or features that inhibit execution speed To get the most out of your application be sure to test its performance as well as it
78. ed using expressions over the variables stored in x The range constraints are also added to the array of constraints c The objective and the constraints are added to the model Modeling by Columns Function populatebycolumn can be viewed as the transpose of populatebyrow While for simple examples like this one population by rows may seem the most straightforward and natural approach there are some models where modeling by column is a more natural or more efficient approach When modeling by columns range objects are created with their lower and upper bound only No expression is given which is impossible since the variables are not yet created Similarly the objective function is created with only its intended optimization sense and without any expression Next the variables are created and installed in the already existing ranges and objective The description of how the newly created variables are to be installed in the ranges and objective is by means of column expressions which are represented by the class IloNumColumn Column expressions consist of objects of class IloAddNumVar linked together with operator These IloAddNumVar objects are created using operator of the classes I1oObjective and IloRange They define how to install a new variable to the invoking objective or range objects For example obj 1 0 creates an IloAddNumVar ILOG CPLEX 10 1 GETTING STARTED 79 capable of adding a new modeling variable with a lin
79. en use the sample makefile located there to compile and link the examples that came in the standard distribution make all compiles and links examples for all of the APIs make all cpp compiles and links the examples of the C API 4 Execute one of the compiled examples make execute all executes all of the examples make execute cpp executes only the C examples Testing Your Installation on Windows To run the test on a Windows platform first consult the readme html file in the standard distribution That file will tell you where to find another text file that contains information about your particular platform That second file will have an abbreviated name that corresponds to a particular combination of machine architecture and compiler For example if you are working on a personal computer with Windows operating system and Microsoft Visual C compiler then the readme html1 file will direct you to the msvc html file where you will find detailed instructions about how to create a project to compile link and execute the examples in the standard distribution The examples have been tested repeatedly on all the platforms compatible with ILOG CPLEX so if you successfully compile link and execute them then you can be sure that your installation is correct ILOG CPLEX 10 1 GETTING STARTED 71 In Case of Problems If you encounter difficulty when you try this test then there is a problem in your installation and
80. eractive Optimizer 50 shadow prices in Interactive Optimizer 51 slack values in Interactive Optimizer 50 solution values C API 76 solution values in Interactive Optimizer 50 add Interactive Optimizer command 60 file name and 61 syntax 61 add obj method Java API 92 adding bounds in Interactive Optimizer 60 constraint to model C API 85 constraints in Interactive Optimizer 60 from a file in Interactive Optimizer 61 interactively in Interactive Optimizer 60 objective shortcut Java API 92 objective function to model C API 75 rows to a problem C API 123 addLe method Java API 95 ILOG CPLEX 10 1 Index addMinimize method Java API 92 95 advanced basis advanced start indicator in Interactive Optimizer 50 algorithm automatic Aut oA1g C API 82 creating object C API 76 role in application C APT 78 and method Java API 96 application and Callable Library 11 and Concert Technology 11 compiling and linking C API 71 compiling and linking Callable Library C APT 112 compiling and linking Component Libraries 24 development steps C API 116 error handling C APT 118 error handling C API 77 B baropt Interactive Optimizer command 50 barrier optimizer availability in Interactive Optimizer 50 selecting C API 82 BAS file format reading from Interactive Optimizer 57 writing from Interactive Optimizer 54 basis accessing information C API 83 basis information Java API 93 GETTING
81. es all default ILOG CPLEX output to appear on the screen If this parameter is not set then ILOG CPLEX will generate no viewable output on the screen or in a file At this point the routine CPXcreateprob is called to create an empty problem object Based on the problem building method selected by the command line argument the application then calls a routine to build the matrix by rows by columns or by nonzeros The routine populatebyrow first calls CPXnewcols to specify the column based problem data such as the objective bounds and variables names The routine CPXaddrows is then called to supply the constraints The routine populatebycolumn first calls CPXnewrows to specify the row based problem data such as the righthand side values and sense of constraints The routine CPXaddcols is then called to supply the columns of the matrix and the associated column bounds names and objective coefficients The routine populatebynonzero calls both CPXnewrows and CPXnewcols to supply all the problem data except the actual constraint matrix At this point the rows and columns are well defined but the constraint matrix remains empty The routine CPXchgcoeflist is then called to fill in the nonzero entries in the matrix After the problem has been specified the application optimizes it by calling the routine CPX1lpopt Its default behavior is to use the ILOG CPLEX Dual Simplex Optimizer If this routine returns a nonzero result then an error occurred I
82. escription of the problem you can use classes of ILOG Concert Technology for NET users with ILOG CPLEX to build a model Open the file Open the file yourCPLEXhome examples sre tutorials LPexllesson cs in your integrated development environment such as Microsoft Visual Studio Create the model object Go to the comment Step 3 in that file and add this statement to create the Cplex model for your application Cplex cplex new Cplex That statement creates an empty instance of the class Cplex In the next steps you will add methods that make it possible for your application populate the model with data either by rows by columns or by nonzeros Populate the model by rows Now go to the comment Step 4 in that file and add these lines to create a method to populate the empty model with data by rows internal static void PopulateByRow IMPModeler model INumVar var IRange rng double 1b double ub 0 0 0 0 0 0 40 0 System Double MaxValue System Double MaxValue INumVar x model NumVarArray 3 lb ub var 0 x double objvals 1 0 2 0 3 0 model AddMaximize model ScalProd x objvals rng 0 new IRange 2 rng 0 0 model AddLe model Sum model Prod 1 0 x 01 model Prod 1 0 1 model Prod 1 0 x 2 20 0 rng 0 1 model AddLe model Sum model Prod 1 0 x 01 model Prod 3 0 1 model Prod 1 0 x 2 30 0 ILOG CPLEX 10 1 GETTING STA
83. f no error occurred the application allocates arrays for solution values of the primal variables dual variables slack variables and reduced costs then it obtains the solution information by calling the routine CPXsolution This routine returns the status of the problem whether optimal infeasible or unbounded and whether a time limit or iteration limit was reached the objective value and the solution vectors The application then displays this information on the screen ILOG CPLEX 10 1 GETTING STARTED As a debugging aid the application writes the problem to a ILOG CPLEX LP file named 1 1 1 by calling the routine CPXwriteprob This file can be examined to determine whether any errors occurred in the routines creating the problem CPXwriteprob can be called at any time after CPXcreateprob has created the 1p pointer The label TERMINATE is used as a place for the program to exit if any type of failure occurs or if everything succeeds In either case the problem object represented by 1p is released by the call to CPX reeprob and any memory allocated for solution arrays is freed The application then calls CPXcloseCPLEX it tells ILOG CPLEX that all calls to the Callable Library are complete If an error occurs when this routine is called then a call to CPXgeterrorstring is needed to determine the error message since CPXcloseCPLEX causes no screen output Complete Program You can view the complete program online in the
84. following command read example bas The message of confirmation Basis example bas read indicates that the basis file was successfully read If the advanced basis indicator is on this basis will be used as a starting point for the next optimization and any new basis created during the session will be used for future optimizations If the basis changes during a session you can save it by using the write command Summary The general syntax for the read command is read filename file format or read filename file extension where file extension corresponds to one of the allowed file formats Setting ILOG CPLEX Parameters ILOG CPLEX users can vary parameters by means of the set command This command is used to set ILOG CPLEX parameters to values different from their default values The procedure for setting a parameter is similar to that of other commands Commands can be carried out incrementally or all in one line from the CPLEX gt prompt Whenever a parameter is set to a new value ILOG CPLEX inserts a comment in the log file that indicates the new value Setting a Parameter To see the parameters that can be changed type set 58 ILOG CPLEX 10 1 GETTING STARTED The parameters that can be changed are displayed with a prompt like this Available Parameters advance Set indicator for advanced starting information barrier Set parameters for barrier optimization clocktype Set type of clock used to measure time
85. for solving linear optimization problems commonly referred to as Linear Programming LP problems of the form Maximize or Minimize CjX CyX subject to b X T X T dX by AniX1 Am2X2 T AnnXy bm with these bounds hs lt x lt u lt X S Un where can be lt 2 and the upper bounds u and lower bounds may be positive infinity negative infinity or any real number The elements of data you provide as input for this LP are Objective function coefficients Cy Co Cy Constraint coefficients es Any Qni 2 Amn Righthand sides by b Om Upper and lower bounds Uj Up Uu and h b bp The optimal solution that ILOG CPLEX computes and returns is Variables X5 X ILOG CPLEX also can solve several extensions to LP Network Flow problems a special case of LP that CPLEX can solve much faster by exploiting the problem structure Quadratic Programming QP problems where the LP objective function is expanded to include quadratic terms Quadratically Constrained Programming QCP problems that include quadratic terms among the constraints In fact CPLEX can solve Second Order Cone Programming SOCP problems 10 ILOG CPLEX 10 1 GETTING STARTED Mixed Integer Programming MIP problems where any or all of the LP QP or QCP variables are further restricted to take integer values in the optima
86. fying an Optimization Problem Example ilolpex3 cpp This example demonstrates Setting ILOG CPLEX Parameters on page 85 Modifying an Optimization Problem on page 86 Starting from a Previous Basis on page 86 Here is the problem example ilolpex3 solves Minimize subject to Ax d b Ax I lt x lt u 84 ILOG CPLEX 10 1 GETTING STARTED where H 310101000 d 3 1 1 010000 1 01 1001 10 4 0 0 0 1 0 101 3 0000 10 1 1 5 A 2 1 2 1 2 1 2 3 b 4 1 32 3 1211 2 c 9142 8 2812 l 00000000 50 50 50 50 50 50 50 50 The constraints Hx d represent the flow conservation of a pure network flow The example solves this problem in two steps 1 The ILOG CPLEX Network Optimizer is used to solve Minimize C Tx subject to Hx d 1 lt lt 2 The constraints Ax b are added to the problem and the dual simplex optimizer is used to solve the full problem starting from the optimal basis of the network problem The dual simplex method is highly effective in such a case because this basis remains dual feasible after the slacks artificial variables of the added constraints are initialized as basic Notice that the 0 values in the data are omitted in the example program ILOG CPLEX makes extensive use of sparse matrix methods and although ILOG CPLEX correctly handles any explicit zero coefficients given to it most programs solving models of more than modest size benefit in terms of b
87. g to the same implementation object When terminating the ILOG Concert Technology application the implementation object must be destroyed as well This must be done explicitly by the user by calling env end for just ONE of the I1oEnv handles pointing to the implementation object to be destroyed The call to env end is generally the last ILOG Concert Technology operation in an application Creating a Model After creating the environment a Concert application is ready to create one or more optimization models Doing so consists of creating a set of modeling objects to define each optimization model Modeling objects like IloEnv objects are handles to implementation objects Though you will be dealing only with the handle objects it is the implementation objects that contain the data that specifies the optimization model If you need to remove an implementation object from memory you need to call the end method for one of its handle objects Modeling objects are also known as extractables because it is the individual modeling objects that are extracted one by one when you extract an optimization model to TloCplex So extractables are characterized by the possibility of being extracted to algorithms such as ILOG CPLEX 10 1 GETTING STARTED 73 74 IloCplex In fact they all are inherited from the class I1oExtractable In other words IloExtractable is the base class of all classes of extractables or modeling
88. getStatus method IloCplex class C API 76 79 getStatus method Java API 93 getValue method IloCplex class C API 76 getValues method IloCplex class C API 79 greater than equal to constraints adding to a model Java API 93 H handle class definition C API 73 empty handle C API 74 handling errors C API 118 errors C API 77 exceptions C API 77 help Interactive Optimizer command 36 syntax 37 histogram in Interactive Optimizer 47 IloAddNumVar class C API 79 TloAlgorithm Exception class C API 77 TloAlgorithm Status enumeration C API 79 IloColumn and method Java API 96 IloCplex class C API 70 exportModel method 80 getCplexStatus method 76 getDuals method 79 getObjValue method 77 getReducedCosts method 79 getSlacks method 79 getStatus method 76 79 getValue method 76 134 ILOG CPLEX 10 1 getValues method 79 importModel method 81 83 setParam method 82 setRootAlgorithm method 83 solve method 76 79 83 84 solving with 76 IloCplex class Java API 87 add modeling object 92 addLe method 95 addMinimize method 95 numVarArray method 95 prod method 95 scalProd method 95 sum method 95 IloCplex Algorithm enumeration C API 82 IloCplex BoolParam enumeration C API 86 IloCplex Exception class C API 77 TloCplex Int Param enumeration C API 86 TloCplex NumParam enumeration C API 86 IloCplex StringParam enumeration C API 8
89. gs that differ from the default values can be displayed with the command ILOG CPLEX 10 1 GETTING STARTED 59 display settings changed For a description of all parameters and their default values see the reference manual ILOG CPLEX Parameters ILOG CPLEX also accepts customized system parameter settings via a parameter specification file See the reference manual ILOG CPLEX File Formats for a description of the parameter specification file and its use Adding Constraints and Bounds 60 If you wish to add either new constraints or bounds to your problem use the add command This command is similar to the enter command in the way it is used but it has one important difference the enter command is used to start a brand new problem whereas the add command only adds new information to the current problem Suppose that in the example you need to add a third constraint XI 2 2 3x3 gt 50 You may do either interactively or from a file Adding Interactively Type the add command then enter the new constraint on the blank line After validating the constraint the cursor moves to the next line You are in an environment identical to that of the enter command after having issued subject to At this point you may continue to add constraints or you may type bounds and enter new bounds for the problem For the present example type end to exit the add command Your session should look like this add Enter new constraints and boun
90. he CPLEX gt prompt will reappear without causing any action The same can be done at any CPLEX gt prompt If you do not want to complete the command simply press the lt return gt key For now type in the name example at the prompt Enter name for problem example ILOG CPLEX 10 1 GETTING STARTED The following message appears Enter new problem end on a separate line terminates and the cursor is positioned on a blank line below it where you can enter the new problem You can also type the problem name directly after the enter command and avoid the intermediate prompt Summary The syntax for entering a problem is enter problem name Using the LP Format Entering a new problem is basically like typing it on a page but there are a few rules to remember These rules conform to the ILOG CPLEX LP file format and are documented in the reference manual ILOG CPLEX File Formats LP format appears throughout this tutorial The problem should be entered in the following order 1 Objective Function 2 Constraints 3 Bounds Objective Function Before entering the objective function you must state whether the problem is a minimization or maximization For this example you type maximize 1 2x2 3x3 You may type minimize or maximize on the same line as the objective function but you must separate them by at least one space Variable Names In the example the variables are named simply x1 x2 x3 but you can gi
91. he addition of constraints Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src ilolpex3 cpp ILOG CPLEX 10 1 GETTING STARTED Concert Technology Tutorial for Java Users This chapter is an introduction to using ILOG CPLEX through ILOG Concert Technology in the Java programming language It gives you an overview of a typical application program and highlights procedures for Creating a model Solving that model Querying results after solving Handling error conditions ILOG Concert Technology allows your application to call ILOG CPLEX directly through the Java Native Interface JNI This Java interface supplies a rich means for you to use Java objects to build your optimization model The class 11oCplex implements the ILOG Concert Technology interface for creating variables and constraints It also provides functionality for solving Mathematical Programing MP problems and accessing solution information ILOG CPLEX 10 1 GETTING STARTED 87 Compiling ILOG CPLEX Applications in ILOG Concert Technology 88 When compiling a Java application that uses ILOG Concert Technology you need to inform the Java compiler where to find the file cplex jar containing the ILOG CPLEX Concert Technology class library do this you add the cplex jar file to your classpath This is most easily done by passing the command line opt
92. he same line separated by at least one space The constraint name is new3 and the variable is number 3 so in response to the following prompt type new3 and 3 like this to identify the one to change Change which coefficient constraint variable new3 3 Present coefficient of constraint new3 variable 3 is 3 000000 The final step is to enter the new value for the coefficient of x3 Change coefficient of constraint new3 variable 3 to what 30 Coefficient of constraint new3 variable 3 changed to 30 000000 Objective amp RHS Coefficients To change a coefficient in the objective function or in the righthand side use the corresponding change command option objective or rhs For example to specify the righthand side of constraint 1 to be 25 0 a user could enter the following but for this tutorial do not enter this now change rhs 1 25 0 Deleting Another option to the change command is delete This option is used to remove an entire constraint or a variable from a problem Return the problem to its original form by removing the constraint you added earlier Type change delete ILOG CPLEX 10 1 GETTING STARTED ILOG CPLEX displays a list of delete options Delete options constraints delete range of constraints qconstraints delete range of quadratic constraints indconstraints delete range of indicator constraints soss delete range of special ordered sets variables delete range of
93. ice of several means and obtain the solution lpex3 c demonstrates how to add rows to a problem object and reoptimize Itis a good idea to compile link and run all of the examples provided in the standard distribution Building and Solving a Small LP Model in C The example 1pex1 c shows you how to use problem modification routines from the ILOG CPLEX Callable Library in three different ways to build a model The application in the example takes a single command line argument that indicates whether to build the ILOG CPLEX 10 1 GETTING STARTED 119 120 constraint matrix by rows columns or nonzeros After building the problem the application optimizes it and displays the solution Here is the problem that the example optimizes Maximize 2X2 3X3 subject to X Xp amp 20 3X2 lt 30 with these bounds 0 lt lt 40 OS lt OS lt Before any ILOG CPLEX Callable Library routine can be called your application must call the routine CPXopenCPLEX to get a pointer called env to the ILOG CPLEX environment Your application will then pass this pointer to every Callable Library routine If this routine fails it returns an error code This error code can be translated to a string by the routine CPXgeterrorstring After the ILOG CPLEX environment is initialized the ILOG CPLEX screen indicator parameter CPX PARAM SCRIND is turned on by the routine CPXsetintparam This caus
94. in the file name ILOG CPLEX will recognize the file as being in MPS format If you omit the extension ILOG CPLEX will attempt to determine whether the file is of a type that it recognizes read afiro mps After the file has been read the following message appears Selected objective sense MINIMIZE Selected objective name obj Selected RHS name rhs Problem afiro read Read time 0 01 sec ILOG CPLEX reports additional information when it reads MPS formatted files Since these files can contain multiple objective function righthand side bound and other information ILOG CPLEX displays which of these is being used for the current problem See the ILOG CPLEX User s Manual to learn more about special considerations for using MPS formatted files Reading Basis Files In addition to other file formats the xead command is also used to read basis files These files contain information for ILOG CPLEX that tells the simplex method where to begin the next optimization Basis files usually correspond to the result of some previous optimization ILOG CPLEX 10 1 GETTING STARTED 57 and help to speed re optimization They are particularly helpful when you are dealing with very large problems if small changes are made to the problem data Writing Basis Files on page 54 showed you how to save a basis file for the example after it was optimized For this tutorial first read the example 1p file Then read this basis file by typing the
95. information about the solution can be viewed using the DISPLAY command after a solution is generated Summary The syntax for the help command is ILOG CPLEX 10 1 GETTING STARTED 37 help command name Entering a Problem 38 Most users with larger problems enter problems by reading data from formatted files That practice is explained in Reading Problem Files on page 55 For now you will enter a smaller problem from the keyboard by using the enter command The process is outlined step by step in these topics Entering the Example Problem on page 38 Using the LP Format on page 39 Entering Data on page 41 Entering the Example Problem As an example this manual uses the following problem Maximize X 2X2 3X3 subject to X X2 lt 20 with these bounds 0 lt lt 40 0 lt 2 lt 0 lt amp This problem has three variables x and x5 and two less than or equal to constraints The enter command is used to enter a new problem from the keyboard The procedure is almost as simple as typing the problem on a page At the CPLEX prompt type enter A prompt appears on the screen asking you to give a name to the problem that you are about to enter Naming a Problem The problem name may be anything that is allowed as a file name in your operating system If you decide that you do not want to enter a new problem just press the return key without typing anything T
96. ion classpath path to cplex jar gt to the Java compiler javac If you need to include other Java class libraries you should add the corresponding jar files to the classpath as well Ordinarily you should also include the current directory to be part of the Java classpath At execution time the same classpath setting is needed Additionally since ILOG CPLEX is implemented via JNI you need to instruct the Java Virtual Machine JVM where to find the shared library or dynamic link library containing the native code to be called from Java You indicate this location with the command line option Djava library path path to shared 1 gt to the java command Note that unlike the cplex jar file the shared library is system dependent thus the exact pathname of the location for the library to be used may differ depending on the platform you are using Pre configured compilation and runtime commands are provided in the standard distribution through the UNIX makefiles and Windows javamake file for Nmake However these scripts presume a certain relative location for the files already mentioned for application development most users will have their source files in some other location Here are suggestions for establishing build procedures for your application 1 First check the readme html file in the standard distribution under the Supported Platforms heading to locate the machine and 1ibformat entry for your U
97. ion and highlights procedures for Creating a model Populating the model with data either by rows by columns or by nonzeros Solving that model Displaying results after solving This chapter concentrates on an example using C NET There are also examples of VB NET Visual Basic in the NET framework delivered with ILOG CPLEX in yourCPLEXhome examples src vb Because of their NET framework those VB NET examples differ from the traditional Visual Basic examples that may already be familiar to some ILOG CPLEX users ILOG CPLEX 10 1 GETTING STARTED 99 Note This chapter consists of a tutorial based on a procedure based learning strategy The tutorial is built around a sample problem available in a file that can be opened in an integrated development environment such as Microsoft Visual Studio As you follow the steps in the tutorial you can examine the code and apply concepts explained in the tutorials Then you compile and execute the code to analyze the results Ideally as you work through the tutorial you are sitting in front of your computer with ILOG Concert Technology for NET users and ILOG CPLEX already installed and available in your integrated development environment What You Need to Know Prerequisites 100 This tutorial requires a working knowledge of C NET If you are experienced in mathematical programming or operations research you are probably already familiar with many concepts used in this tu
98. ion about the version of ILOG CPLEX you have installed 20 ILOG CPLEX 10 1 GETTING STARTED cplex L bin e Ln EXECUTABLE FILES Interactive Optimizer dll and so files examples data tutorials available only for NET L src platform L lib format L Makefile or MSVC project files include L ilcplex L lib platform Lo lib format CPLEX LIBRARY Java LIBRARY cplex jar Figure 1 1 Structure of the ILOG CPLEX installation directory ILOG CPLEX 10 1 GETTING STARTED 21 concert include L ilconcert L lib platform es lib format L CONCERT LIBRARY examples data src platform lib format Makefile or MSVC project files Figure 1 2 Structure of the Concert Technology Installation Directory Setting Up Licensing 22 ILOG CPLEX 10 1 runs under the control of the ILOG License Manager ILM Before you can run ILOG CPLEX or any application that calls it you must have established a valid license that ILM can read Licensing instructions are provided in the ILOG License Manager User s Guide amp Reference which is included with the standard ILOG CPLEX product distribution The basic steps are 1 Install ILM Normally you obtain ILM distribution media from the same place that you obtain ILOG CPLEX 2 Run the ihostid program which is found in the directory where you install ILM ILOG CPLEX 10 1 GETTING STARTED 3 Communicat
99. ion constraints of a pure network flow problem The example solves this problem in two steps ILOG CPLEX 10 1 GETTING STARTED 123 124 1 The ILOG CPLEX Network Optimizer is used to solve Minimize subject to Hx I lt xs lt u 2 The constraints Ax b are added to the problem and the dual simplex optimizer is used to solve the new problem starting at the optimal basis of the simpler network problem The data for this problem consists of the network portion using variable names beginning with the letter H and the complicating constraints using variable names beginning with the letter A The example first calls CPXopenCPLEX to create the environment and then turns on the ILOG CPLEX screen indicator CPX PARAM SCRIND Next it sets the simplex display level PARAM SIMDISPLAY to 2 to indicate iteration by iteration output so that the progress of each iteration of the optimizer can be observed Setting this parameter to 2 is not generally recommended the example does so only for illustrative purposes The example creates a problem object by a call to CPXcreateprob Then the network data is copied via a call to CPXcopylp After the network data is copied the parameter CPX PARAM LPMETHOD is set to CPX ALG NET and the routine CPX1popt is called to solve the network part of the optimization problem using the network optimizer The objective value of this problem is retrieved by CPXgetobjval Then the extra rows are
100. irectory any file should be saved The following might be a valid write command if the disk drive on your system contains a root directory named problems write problems example lp Summary The general syntax for the write command is write filename file format or write filename file extension where file extension indicates the format in which the file is to be saved Reading Problem Files When you are using ILOG CPLEX to solve linear optimization problems you may frequently enter problems by reading them from files instead of entering them from the keyboard Continuing the tutorial from Writing Problem and Solution Files on page 53 the topics are Selecting a Read File Format on page 56 Reading LP Files on page 56 Using File Extensions on page 57 Reading MPS Files on page 57 0 Reading Basis Files on page 57 ILOG CPLEX 10 1 GETTING STARTED 55 56 Selecting a Read File Format When you type the read command in the Interactive Optimizer with the name of a file bearing an extension that it does not recognize ILOG CPLEX displays the following prompt about file formats on the screen File type options bas INSERT format basis file lp LP format problem file min DIMACS min cost network flow format file mps MPS format problem file mst MIP start file net CPLEX network flow format file ord Integer priority order file prm Non default parameter file sav Binary matrix and basis file sol Soluti
101. is manual the phrase CPLEX Component Libraries is used to refer equally to any of these libraries While all of the libraries are callable the term CPLEX Callable Library as used here refers specifically to the C library Compatible Platforms ILOG CPLEX is available on Windows UNIX and other platforms The programming interface works the same way and provides the same facilities on all platforms ILOG CPLEX 10 1 GETTING STARTED 11 12 Installation Requirements If you have not yet installed ILOG CPLEX on your platform please consult Chapter 1 Setting Up ILOG CPLEX It contains instructions for installing ILOG CPLEX Optimizer Options This manual explains how to use the LP algorithms that are part of ILOG CPLEX The QP QCP and MIP problem types are based on the LP concepts discussed here and the extensions to build and solve such problems are explained in the ILOG CPLEX User s Manual Default settings will result in a call to an optimizer that is appropriate to the class of problem you are solving However you may wish to choose a different optimizer for special purposes An LP or QP problem can be solved using any of the following CPLEX optimizers Dual Simplex Primal Simplex Barrier and perhaps also the Network Optimizer if the problem contains an extractable network substructure Pure network models are all solved by the Network Optimizer QCP models including the special case of SOCP models are all solved by the
102. iteration log in Interactive Optimizer 48 49 J Java Native Interface JNI 87 Java Virtual Machine JVM 88 javamake for Windows 88 L libformat Java API 88 licensing ILOG CPLEX 10 1 CPLEX 22 linear optimization 10 linker error messages C API 72 using with CPLEX C API 71 linking applications 24 applications C API 71 Callable Library C API applications 112 Concert Technology library files 24 CPLEX library files 24 log file adding to in Interactive Optimizer 58 cplex log in Interactive Optimizer 49 creating in Interactive Optimizer 49 iteration log in Interactive Optimizer 48 49 LP creating a model 27 node C API 82 problem format 10 root C API 82 solving a model 27 solving pure C API 82 LP file format in Interactive Optimizer 39 reading in Interactive Optimizer 56 writing in Interactive Optimizer 54 lpexl c example C API 119 sensitivity and C API 125 LPex1 java example 94 LPMETHOD parameter in Interactive Optimizer 48 makefile Java API 88 maximization in LP problem in Interactive Optimizer 39 memory management by environment object C API 73 minimization in LP problem in Interactive Optimizer 39 MIP description 11 optimizer in Interactive Optimizer 50 solving C API 81 mipopt Interactive Optimizer command 50 GETTING STARTED 135 model adding constraints C API 85 creating C API 73 creating 1 1 C APT 73 creating objects in
103. ive Optimizer and the application programming interfaces APIs to CPLEX Full details of writing a practical program are in the chapters containing the tutorials Problem Statement on page 28 Using the Interactive Optimizer on page 29 Using Concert Technology in C on page 30 Using Concert Technology in Java on page 31 Using Concert Technology in NET on page 32 9 9 9 Using the Callable Library on page 33 ILOG CPLEX 10 1 GETTING STARTED 27 Problem Statement The problem to be solved is Maximize 2X2 3X3 subject to X Xp S 20 3X2 lt 30 with these bounds 0 lt lt 40 OS x5 OS xg 28 ILOG CPLEX 10 1 GETTING STARTED Using the Interactive Optimizer The following sample is screen output from a CPLEX Interactive Optimizer session where the model of an example is entered and solved CPLEX gt indicates the CPLEX prompt and text following this prompt is user input Welcome to CPLEX Interactive Optimizer 10 0 0 with Simplex Mixed Integer amp Barrier Optimizers Copyright c ILOG 1997 2006 CPLEX is a registered trademark of ILOG Type help for a list of available commands Type help followed by a command name for more information on commands CPLEX enter example Enter new problem end on a separate line terminates maximize xl 2 x2 3 x3 subject to x1l 2 x3 lt 20 xl 3 x2 x3 lt 30 bounds 0 lt x1 l
104. ive Optimizer 51 sifting algorithm C API 82 slack accessing Java API 93 accessing in Interactive Optimizer 50 accessing values in Interactive Optimizer 51 SOCP 138 ILOG CPLEX 10 1 description 10 optimizer for 12 solution accessing basic rows and columns in Interactive Optimizer 51 accessing values C API 76 accessing values in Interactive Optimizer 50 51 displaying basic rows and columns in Interactive Optimizer 51 displaying in Interactive Optimizer 50 outputting C API 79 process in Interactive Optimizer 48 querying results C API 76 reporting optimal in Interactive Optimizer 48 restarting in Interactive Optimizer 50 sensitivity analysis C API 125 sensitivity analysis in Interactive Optimizer 51 solution file writing in Interactive Optimizer 53 solve method IloCplex class C API 76 79 83 84 solve method Java API 93 95 solving model C API 76 83 node LP C API 82 problem C API 120 problem in Interactive Optimizer 48 root LP C API 82 with network optimizer C API 85 SOS creating C API 81 sparse matrix C API 85 starting CPLEX in Interactive Optimizer 36 from previous basis C API 86 Interactive Optimizer 36 new problem in Interactive Optimizer 38 string parameter C API 86 structure of a CPLEX application Java API 91 Supported Platforms Java API 88 System out method Java API 95 T tranopt Interactive Optimizer command 50 GETTING STARTED U
105. ject provides the functionality to create an optimization model that can be solved with IloCplex The class IloCplex implements the ILOG Concert Technology interface I1oModeler and its extensions IloMPModeler and IloCplexModeler These interfaces define the constructors for modeling objects of the following types which can be used with IloCplex IloNumVar modeling variables IloRange ranged constraints of the type lb lt expr lt ub IloObjective optimization objective IloNumExpr expression using variables Modeling variables are represented by objects implementing IloNumVar interface defined by ILOG Concert Technology Here is how to create three continuous variables all with bounds 0 and 100 IloNumVar x cplex numVarArray 3 0 0 100 0 ILOG CPLEX 10 1 GETTING STARTED 91 92 There is a wealth of other methods for creating arrays or individual modeling variables The documentation for IloModeler IloCplexModeler and IloMPModeler will give you the complete list Modeling variables build expressions of type IloNumExpr for use in constraints or the objective function of an optimization model For example the expression x 0 2 x 1 3 x 2 can be created like this IloNumExpr expr cplex sum x 0 cplex prod 2 0 x 11 cplex prod 3 0 x 21 Another way of creating an object representing the same expression is to use an expression of IloLinearNumExpr Here is how IloLinearNumExpr expr cplex linearNumExp
106. l solution and where MIP itself is extended to include constructs like Special Ordered Sets SOS and semi continuous variables ILOG CPLEX Components CPLEX comes in three forms to meet a wide range of users needs The CPLEX Interactive Optimizer is an executable program that can read a problem interactively or from files in certain standard formats solve the problem and deliver the solution interactively or into text files The program consists of the file cplex exe on Windows platforms or cplex on UNIX platforms Concert Technology is a set of C Java and NET class libraries offering an API that includes modeling facilities to allow the programmer to embed CPLEX optimizers in C Java or NET applications Table 1 lists the files that contain the libraries Table 1 Concert Technology Libraries Microsoft Windows UNIX ilocplex lib libilocplex a concert lib libconcert a Java cplex jar cplex jar NET ILOG CPLEX dl11l ILOG Concert d1l The ILOG Concert Technology libraries make use of the Callable Library described next The CPLEX Callable Library is a C library that allows the programmer to embed ILOG CPLEX optimizers in applications written in C Visual Basic FORTRAN or any other language that can call C functions The library is provided in files cplex101 1lib and cplex101 d11 on Windows platforms and in libcplex a libcplex so and libcplex s1 on UNIX platforms In th
107. lateByRow Java API 94 primal simplex optimizer availability in Interactive Optimizer 50 selecting C API 82 primopt Interactive Optimizer command 50 problem change options in Interactive Optimizer 62 changing in Interactive Optimizer 61 creating binary representation C API 119 data entry options 13 displaying a part in Interactive Optimizer 44 displaying in Interactive Optimizer 42 displaying options in Interactive Optimizer 42 displaying statistics in Interactive Optimizer 43 entering from the keyboard in Interactive Optimizer 38 entering in LP format in Interactive Optimizer 39 naming in Interactive Optimizer 38 reading files C API 121 solving C API 120 solving in Interactive Optimizer 48 verifying entry in Interactive Optimizer 42 62 problem file reading in Interactive Optimizer 55 writing in Interactive Optimizer 53 problem formulation ILOG CPLEX 10 1 1 1 1 C API 78 Interactive Optimizer and 38 1 1 API 120 lpexi cs 103 LPex1 java Java API 94 standard notation for 10 problem object creating C API 115 modifying C API 116 problem types solved by CPLEX 10 Q QCP description 10 optimizer for 12 QP applicable algorithms C API 82 description 10 solving pure C API 82 quit Interactive Optimizer command 66 quitting ILOG CPLEX in Interactive Optimizer 66 Interactive Optimizer 66 R range constraint adding to a model Java API 93 range constraint C API 79 re
108. lay variable names like this Display which variable name s In the example there are three variables with default names ILOG CPLEX displays these three names xl x2 x3 If you want to see only the second and third names you could either enter the range as 2 3 or specify everything following the second variable with 2 Try this technique display problem names variables Display which variable name s 2 x2 x3 If you enter a number without a hyphen you will see a single variable name display problem names variables Display which variable name s 2 x2 Summary You can use a wildcard in the display command to specify a range of items You can display variable names by entering the command display problem names variables You can display constraint names by entering the command display problem names constraints Ordering Variables In the example problem there is a direct correlation between the variable names and their numbers x1 is variable 1 x2 is variable 2 etc that is not always the case The internal ILOG CPLEX 10 1 GETTING STARTED 45 46 ordering of the variables is based on their order of occurrence when the problem is entered For example if x2 had not appeared in the objective function then the order of the variables would be x1 x3 x2 You can see the internal ordering by using the hyphen when you specify the range for the variables option The variables are displayed in the
109. laying Post Solution 50 Performing Sensitivity Analysis 51 Writing Problem and Solution 53 Selecting a Write File Format 0 0 0 0 cece RR 53 Writing EP RIS reU Puer 54 ILOG CPLEX 10 1 GETTING STARTED Chapter 4 Writing Basis Elles 223 Bidet ee VE NORIS tat Ao s 54 Using Patti Names iu eed de ee hd bee RUE enis 55 Reading Problem Files 00 0 cece eee eee eee eee Rh hh hn 55 Selecting a Read File Format 1 0 0 0 cece eens 56 Reading LP Files ere reel ead igh oor Ged gi gabe ee ba es Re 56 Using File Extensions o iit ice ee s re eoe ele ee eS 57 Reading MPS Files Rete Uude 57 Reading Basis Files i 5 arin Dx ERU REESE RAUS 57 Setting ILOG CPLEX lt 58 Adding Constraints and Bounds 60 Changing a Problem 5 2 2 0000 te eee eee eb eee 61 Changing Constraint or Variable 62 Changing Sernse s doa sea ge RR te ER Sane da ede E eicere ORT x 62 Ghanging Bounds GU eM oy ibe
110. lding and Solving a Small LP Model in C on page 119 e Building and Solving a Small LP Model in C on page 78 e Building and Solving a Small LP Model in Java on page 94 Describe The first step is for you to describe the problem in natural language and answer basic questions about the problem What is the known information in this problem That is what data is available What is the unknown information in this problem That is what are the decision variables What are the limitations in the problem That is what are the constraints on the decision variables What is the purpose of solving this problem That is what is the objective function ILOG CPLEX 10 1 GETTING STARTED 101 Describe 102 Note Though the Describe step of the process may seem trivial in a simple problem like this one you will find that taking the time to fully describe a more complex problem is vital for creating a successful application You will be able to code your application more quickly and effectively if you take the time to describe the model isolating the decision variables constraints and objective Model The second stage is for you to use the classes of ILOG Concert Technology for NET users to build a model of the problem The model is composed of decision variables and constraints on those variables The model of this problem also contains an objective Solve The third stage is for you to use an instance of the clas
111. le format for Interactive Optimizer 53 LP files in Interactive Optimizer 54 model to file C API 81 problem files in Interactive Optimizer 53 solution files in Interactive Optimizer 53 X xecute Interactive Optimizer command 66 syntax 66 GETTING STARTED 139 140 ILOG CPLEX 10 1 GETTING STARTED
112. les try make LPexl class java Djava library path bin platform classpath lib cplex jar LPexl r Any of these examples should return an optimal objective function value of 202 5 ILOG CPLEX 10 1 GETTING STARTED 23 Verifying Installation on Windows On a Windows machine you can follow a similar process using the facilities of your compiler interface to compile and then run any of the examples A project file for each example is provided in a format for Microsoft Visual Studio 6 and Visual Studio NET In Case of Errors If an error occurs during the make or compile step then check that you are able to access the compiler and the necessary linker loader files and system libraries If an error occurs on the next step when executing the program created by make then the nature of the error message will guide your actions If the problem is in licensing consult the ILOG License Manager User s Guide and Reference for further guidance For Windows users if the program has trouble locating cplex101 d11 or ILOG CPLEX d11 make sure the DLL is stored either in the current directory or in a directory listed in your PATH environment variable The UNIX Makefile or Windows project file contains useful information regarding recommended compiler flags and other settings for compilation and linking Compiling and Linking Your Own Applications The source files for the examples and the makefiles provide guidance for ho
113. lex getObjValue respectively The program then concludes by printing the values that have been obtained in the previous steps and terminates after calling cplex end to free the memory used by the model object the catch method of IloException provides screen output in case of any error conditions along the way The remainder of the example source code is devoted to the details of populating the model object and the following three sections provide details on how the methods work Modeling by Rows The method populateByRow creates the model by adding the finished constraints and objective function to the active model one by one It does so by first creating the variables with the method cplex numVarArray Then the minimization objective function is created and added to the active model with the method IloCplex addMinimize The expression that defines the objective function is created by a method 11oCplex scalProd that forms a scalar product using an array of objective coefficients times the array of variables Finally each of the two constraints of the model are created and added to the active model with the method 11oCplex addLe For building the constraint expression the methods IloCplex sum and IloCplex prod are used as a contrast to the approach used in constructing the objective function Modeling by Columns While for many examples population by rows may seem most straightforward and natural there are some models where population
114. lumn objects An instance of IloColumn created with the method 11oCplex column contains information about how to use this column to introduce a new variable into an existing modeling object For example if obj is an instance of a class that implements the interface IloObjective then cplex column obj 2 0 creates an instance of IloColumn containing the information to install a new variable in the expression of the IloObjective object obj with a linear coefficient of 2 0 Similarly for rng a constraint that is an instance of a class that implements the interface IloRange the invocation of the method cplex column rng 1 0 creates an IloColumn object containing the information to install a new variable into the expression of rng as a linear term with coefficient 1 0 When you use the approach of modeling by column new columns are created and installed as variables in all existing modeling objects where they are needed To do this with ILOG Concert Technology you create an IloColumn object for every modeling object in which you want to install a new variable and link them together with the method IloColumn and For example the first variable in populateByColumn is created like this var 0 0 model numVar model column obj 1 0 and model column rO0 1 0 and model column r1 1 0 0 0 40 0 The three methods model column create 110Column objects for installing a new variable in the objective obj and in the constraints ro a
115. lution Nn dWNn solstat n objval f NN x 0 x 1 x 21 amp lp eeprob failed error code d n status nv fprintf stderr Could not close CPLEX environment Wn CPXgeterrorstring env fprintf stderr s return status END main ILOG CPLEX 10 1 status errmsg errmsg GETTING STARTED This step by step tutorial introduces the major features of the ILOG CPLEX Interactive Interactive Optimizer Tutorial Optimizer In this chapter you will learn about 9 9 9 9 9 9 9 OH OH o Starting ILOG CPLEX on page 36 Using Help on page 36 Entering a Problem on page 38 Displaying a Problem on page 42 Solving a Problem on page 48 Performing Sensitivity Analysis on page 51 Writing Problem and Solution Files on page 53 Reading Problem Files on page 55 Setting ILOG CPLEX Parameters on page 58 Adding Constraints and Bounds on page 60 Changing a Problem on page 61 Executing Operating System Commands on page 66 Quitting ILOG CPLEX on page 66 ILOG CPLEX 10 1 GETTING STARTED 35 Starting ILOG CPLEX Using Help 36 To start the ILOG CPLEX Interactive Optimizer at your operating system prompt type the command cplex A message similar to the following one appears on the screen Welcome to CPLEX Interactive Optimizer 10 0 0 with Simplex Mixed Integer amp Barrier Optimizers Copyright c ILOG 1997 2006 CPLEX is a regi
116. ments The last of the three functions that can be used to build the model is populatebynonzero It creates objects for the objective and the ranges without expressions and variables without columns The methods I1oObjective setLinearCoef setLinearCoefs and IloRange setLinearCoef setLinearCoefs are used to set individual nonzero values in the expression of the objective and the range constraints As usual the objective and ranges must be added to the model Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src ilolpexl cpp Writing and Reading Models and Files In example ilolpex1 cpp one line is still unexplained cplex exportModel lpex1 1p 80 ILOG CPLEX 10 1 GETTING STARTED This statement causes cplex to write the model it has currently extracted to the file called lpex1 1p In this case the file will be written in LP format Use of that format 15 documented in the reference manual JLOG CPLEX File Formats Other formats supported for writing problems to a file are MPS and SAV also documented in the reference manual ILOG CPLEX File Formats 11oCplex decides which file format to write based on the extension of the file name IloCplex also supports reading of files through one of its importModel methods A call to cplex importModel model file lp causes ILOG CPLEX to read a problem from the file ile 1p and add all the data i
117. mizers in the ILOG CPLEX User s Manual for information on using CPLEX on a parallel computer Data Entry Options CPLEX provides several options for entering your problem data When using the Interactive Optimizer most users will enter problem data from formatted files CPLEX supports the industry standard MPS Mathematical Programming System file format as well as CPLEX LP format a row oriented format many users may find more natural Interactive entry using CPLEX LP format is also a possibility for small problems Data entry options are described briefly in this manual File formats are documented in the reference manual CPLEX File Formats Concert Technology and Callable Library users may read problem data from the same kinds of files as in the Interactive Optimizer or they may want to pass data directly into CPLEX to gain efficiency These options are discussed in a series of examples that begin with Building and Solving a Small LP Model in C Building and Solving a Small LP Model in Java and Building and Solving a Small LP Model in C for the CPLEX Callable Library users What You Need to Know In order to use ILOG CPLEX effectively you need to be familiar with your operating system whether UNIX or Windows This manual assumes you already know how to create and manage files In addition if you are building an application that uses the Component Libraries this manual assumes that you know how to compile link and exec
118. n it to model as new objects Again MPS and SAV format files are also supported In particular ILOG CPLEX creates an instance of IloObjective for the objective function found in file 1p IloNumVar for each variable found in ile lp except IloSemiContVar for each semi continuous or semi integer variable found in 1 1 IloRange for each row found in file 1p IloSOS1 for each SOS of type 1 found in file 1p and 1105082 for each SOS of type 2 found in ile lp If you also need access to the modeling objects created by importModel two additional signatures are provided void IloCplex importModel IloModel amp m const char filename IloObjective amp obj IloNumVarArray vars IloRangeArray rngs const and void IloCplex importModel IloModel m const char filename IloObjective amp obj IloNumVarArray vars IloRangeArray rngs IloSOS1Array sos1 IloSOS2Array sos2 const They provide additional parameters so that the newly created modeling objects will be returned to the caller Example program ilolpex2 cpp gives an example of how to use method importModel Selecting an Optimizer IloCplex treats all problems it solves as Mixed Integer Programming MIP problems The algorithm used by 11oCplex for solving MIP is known as branch amp cut referred to in ILOG CPLEX 10 1 GETTING STARTED 81 some contexts as branch amp bound and is documented in more detail in the ILOG CPLEX User s Manual For
119. n to install a new variable in the expression of the IObjective object obj with a linear coefficient of 2 0 Similarly for an IRange constraint rng the method call cplex Column rng 1 0 creates an IColumn object containing the information to install a new variable into the expression of rng as a linear term with coefficient 1 0 In short when you use a modeling by column approach new columns are created and installed as variables in all existing modeling objects where they are needed To do this with ILOG Concert Technology you create an IColumn object for every modeling object in which you want to install a new variable and link them together with the method IColumn And Populate the model by nonzeros Go to the comment Step 6 in the file and add these lines to create a method to populate the empty model with data by nonzeros internal static void PopulateByNonzero IMPModeler model INumVar var IRange rng double lb 0 0 0 0 0 0 double ub 40 0 System Double MaxValue System Double MaxValue INumVar x model NumVarArray 3 lb ub var 0 x double objvals 1 0 2 0 3 0 model Add model Maximize model ScalProd x objvals rng 0 new IRange 2 rng 0 0 model AddRange System Double MaxValue 20 0 rng 0 1 model AddRange System Double MaxValue 30 0 rng 0 0 Expr model Sum model Prod 1 0 0 model Prod 1 0 x 11 model Prod 1 0 x 21 rng 0
120. nd execute Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src LPexl cs ILOG CPLEX 10 1 GETTING STARTED 109 110 ILOG CPLEX 10 1 GETTING STARTED Callable Library Tutorial This tutorial shows how to write programs that use the ILOG CPLEX Callable Library In this chapter you will learn about The Design of the ILOG CPLEX Callable Library on page 111 Compiling and Linking Callable Library Applications on page 112 How ILOG CPLEX Works on page 114 Creating a Successful Callable Library Application on page 116 Building and Solving a Small LP Model in C on page 119 Reading a Problem from a File Example lpex2 c on page 121 Adding Rows to a Problem Example lpex3 c on page 123 9 99 Performing Sensitivity Analysis on page 125 The Design of the ILOG CPLEX Callable Library Figure 7 1 shows a picture of the ILOG CPLEX world The ILOG CPLEX Callable Library together with the ILOG CPLEX internals make up the ILOG CPLEX core The core becomes associated with your application through Callable Library routines The ILOG CPLEX 10 1 GETTING STARTED 111 ILOG CPLEX environment and all problem defining data are established inside the ILOG CPLEX core User Written Application ILOG CPLEX Callable Library ILOG CPLEX internals Figure 7 1 View of the ILOG CPLEX Callable Lib
121. nd r1 with linear coefficients 1 0 1 0 and 1 0 respectively They are all linked to an aggregate column object by the method and This aggregate column object is passed as the first argument to the method numvar along with the bounds 0 0 and 40 0 as the other two arguments The method numVar now creates a new variable and immediately installs it in the modeling objects obj ro and r1 as defined by the aggregate column object After it has been installed the new variable is returned and stored in var 0 0 ILOG CPLEX 10 1 GETTING STARTED Modeling by Nonzeros The last of the three functions for building the model is populateByNonzero This function creates the variables with only their bounds and the empty constraints that is ranged constraints with only lower and upper bound but with no expression Only after that are the expressions constructed over these existing variables in a manner similar to the ones already described they are installed in the existing constraints with the method IloRange setExpr Complete Program You can view the complete program online in the standard distribution of the product at yourCPLEXinstallation examples src LPexl java ILOG CPLEX 10 1 GETTING STARTED 97 98 ILOG CPLEX 10 1 GETTING STARTED Concert Technology Tutorial for NET Users This chapter introduces ILOG CPLEX through ILOG Concert Technology in the NET framework It gives you an overview of a typical applicat
122. nd you would like to change For the example change the upper bound of variable x2 from to 50 Change bounds on which variable x2 Present bounds on variable x2 The indicated variable is O0 Change lower or upper bound or both l u or b u Change upper bound to what inf for no upper bound 50 New bounds on variable x2 0 lt x2 lt 50 Removing Bounds To remove a bound set it to or ee Interactively use the identifiers inf and inf instead of the symbols To change the upper bound of x2 back to use the one line command change bounds x2 u inf You receive the message New bounds on variable x2 The indicated variable is O0 The bound is now the same as it was when the problem was originally entered ILOG CPLEX 10 1 GETTING STARTED 63 Changing Coefficients Up to this point all of the changes that have been made could be referenced by specifying a single constraint or variable In changing a coefficient however a constraint and a variable must be specified in order to identify the correct coefficient As an example change the coefficient of x3 in the new3 constraint from 3 to 30 As usual you must first specify which change command option to use change coefficient You must now specify both the constraint row and the variable column identifying the coefficient you wish to change Enter both the constraint name or number and variable name or number on t
123. nology modeling objects CPLEX internals Figure 4 1 View of ILOG CPLEX with ILOG Concert Technology The ILOG CPLEX internals include the computing environment its communication channels and your problem objects This chapter gives a brief tutorial illustrating the modeling and solution classes provided by ILOG Concert Technology and ILOG CPLEX More information about the algorithm class IloCplex and its nested classes can be found in the ILOG CPLEX User s Manual and ILOG CPLEX Reference Manual ILOG CPLEX 10 1 GETTING STARTED Compiling and Linking ILOG CPLEX in Concert Technology Applications When compiling a C application with a C library like ILOG CPLEX in ILOG Concert Technology you need to tell your compiler where to find the ILOG CPLEX and Concert include files that is the header files and you also need to tell the inker where to find the ILOG CPLEX and Concert libraries The sample projects and makefiles illustrate how to carry out these crucial steps for the examples in the standard distribution They use relative path names to indicate to the compiler where the header files are and to the linker where the libraries are Testing Your Installation on UNIX To run the test follow these steps 1 First check the readme html file in the standard distribution to locate the right subdirectory containing a makefile appropriate for your platform 2 Go to that subdirectory 3 Th
124. nter to a problem object Populating the Problem Object The problem object instantiated by CPXcreateprob represents an empty problem that contains no data it has zero constraints zero variables and an empty constraint matrix This empty problem object must be populated with data This step can be carried out in several ways The problem object can be populated by assembling arrays of data and then calling CPXcopylp to copy the data into the problem object For example see Building and Solving a Small LP Model in C on page 119 Alternatively you can populate the problem object by sequences of calls to the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist these routines may be called in any order that is convenient For example see Adding Rows to a Problem Example lpex3 c on page 123 Ifthe data already exist in a file using MPS format or LP format you can use CPXreadcopyprob to read the file and copy the data into the problem object For example see Reading a Problem from a File Example 2 on page 121 ILOG CPLEX 10 1 GETTING STARTED 115 Changing the Problem Object A major consideration in the design of ILOG CPLEX is the need to efficiently re optimize modified linear programs In order to accomplish that ILOG CPLEX must be aware of changes that have been made to a linear program since it was last optimized Problem modification routines are available in the Callable Libr
125. nual especially ILOG Concert Technology for Java Users on page 67 The Anatomy of an ILOG Concert Technology Application To use the ILOG CPLEX Java interfaces you need to import the appropriate packages into your application This is done with the lines 90 ILOG CPLEX 10 1 GETTING STARTED import ilog concert import ilog cplex As for every Java application an ILOG CPLEX application is implemented as a method of a class In this discussion the method will be the static main method The first task is to create an IloCplex object It is used to create all the modeling objects needed to represent the model For example an integer variable with bounds 0 and 10 is created by calling cplex intVar 0 10 where cplex is the IloCplex object Since Java error handling in ILOG CPLEX uses exceptions you should include the ILOG Concert Technology part of an application in a t ry catch statement All the exceptions thrown by any ILOG Concert Technology method are derived from IloException Thus IloException should be caught in the catch statement In summary here is the structure of a Java application that calls ILOG CPLEX import ilog concert import ilog cplex static public class Application static public main String args try IloCplex cplex new IloCplex create model and solve it catch IloException e System err println Concert exception caught e Create the Model The r1oCplex ob
126. o ways of specifying this constraint if you know the name for example new3 you can enter the name if you do not know the name you can specify the index of the constraint In this example the index is 3 for the new3 constraint Try the first method and type Change sense of which constraint new3 Sense of constraint new3 is ILOG CPLEX 10 1 GETTING STARTED ILOG CPLEX tells you the current sense of the selected constraint All that is left now is to enter the new sense which can be entered as lt gt or You can also type simply lt interpreted as X or gt interpreted as 2 The letters 1 g and e are also interpreted as lt gt and respectively New sense or s or lt Sense of constraint new3 changed to The sense of the constraint has been changed The sense of the objective function may be changed by specifying the objective function name its default is obj or the number 0 when ILOG CPLEX prompts you for the constraint You are then prompted for a new sense The sense of an objective function can take the value maximum or minimum or the abbreviation max or min Changing Bounds When the example was entered bounds were set specifically only for the variable x1 The bounds can be changed on this or other variables with the bounds option Again start by selecting the command and option change bounds Select the variable by name or number and then select which bou
127. objects The most fundamental extractable class is 110Model1 Objects of this class are used to define a complete optimization model that can later be extracted to an IloCplex object You create a model by constructing an object of type 11oModel For example to construct a modeling object named mode1 within an existing environment named env you would do the following IloModel model env At this point it is important to note that the environment is passed as a parameter to the constructor There is also a constructor that does not use the environment parameter but this constructor creates an empty handle the handle corresponding to a NULL pointer Empty handles cannot be used for anything but for assigning other handles to them Unfortunately itis a common mistake to try to use empty handles for other things After an I1oModel object has been constructed it is populated with the extractables that define the optimization model The most important classes here are IloNumVar representing modeling variables IloRange defining constraints of the form lt expr lt where expr is a linear expression and IloObjective representing an objective function You create objects of these classes for each variable constraint and objective function of your optimization problem Then you add the objects to the model by calling model add object for each extractable object There is no need to explicitly add the variable objects to a m
128. odel as they are implicitly added when they are used in the range constraints instances of IloRange or the objective At most one objective can be used a model with 11oCplex Modeling variables are constructed as objects of class IloNumVar by defining variables of type IloNumVar Concert Technology provides several constructors for doing this the most flexible form is IloNumVar 1 0 0 40 0 ILOFLOAT This definition creates the modeling variable x1 with lower bound 0 0 upper bound 40 0 and type ILOFLOAT which indicates the variable is continuous Other possible variable types include ILOINT for integer variables and ILOBOOL for Boolean variables For each variable in the optimization model a corresponding object of class TloNumvar must be created Concert Technology provides a wealth of ways to help you construct all the IloNumVar objects ILOG CPLEX 10 1 GETTING STARTED After all the modeling variables have been constructed they can be used to build expressions which in turn are used to define objects of class 1100bjective and IloRange For example IloObjective obj IloMinimize env 1 2 x2 3 x3 This creates the extractable obj of type I1o0bjective which represents the objective function of the example presented in Introducing ILOG CPLEX Consider in more detail what this line does The function IloMinimize takes the environment and an expression as arguments and constructs a new IloObjective obje
129. on file File type Reminder All these file formats are documented in more detail in the reference manual ILOG CPLEX File Formats Reading LP Files At the CPLEX gt prompt type read The following message appears requesting a file name Name of file to read Four files have been saved at this point in this tutorial example example2 example lp example bas Specify the file named example that you saved while practicing the write command You recall that the example problem was saved in LP format so in response to the file type prompt enter lp ILOG CPLEX displays a confirmation message like this ILOG CPLEX 10 1 GETTING STARTED Problem example read Read Time 0 03 sec The example problem is now in memory and you can manipulate it with ILOG CPLEX commands Tip The intermediate prompts for the xead command can be avoided by entering the entire command on one line like this read example lp Using File Extensions If the file name has an extension that corresponds to one of the supported file formats ILOG CPLEX automatically reads it without your having to specify the format Thus the following command automatically reads the problem file example 1p in LP format read example lp Reading MPS Files ILOG CPLEX can also read industry standard MPS formatted files The problem called afiro mps provided in the ILOG CPLEX distribution serves as an example If you include the mps extension
130. onstraint in Interactive Optimizer 43 variable names in Interactive Optimizer 44 variables in Interactive Optimizer 43 dual simplex optimizer as default in Interactive Optimizer 48 availability in Interactive Optimizer 50 finding a solution C API 120 GETTING STARTED selecting C API 82 dual values accessing Java API 93 accessing in Interactive Optimizer 51 E enter Interactive Optimizer command 38 bounds 40 maximize 39 minimize 39 subject to 40 60 syntax 39 entering bounds in Interactive Optimizer 40 constraint names in Interactive Optimizer 40 constraints in Interactive Optimizer 40 example problem in Interactive Optimizer 38 item ranges in Interactive Optimizer 44 keyboard data in Interactive Optimizer 41 objective function in Interactive Optimizer 39 40 objective function names in Interactive Optimizer 40 problem in Interactive Optimizer 38 39 problem name in Interactive Optimizer 38 variable bounds in Interactive Optimizer 40 variable names in Interactive Optimizer 39 environment object creating C API 72 78 destroying C API 73 memory management and C API 73 equality constraints adding to a model Java API 93 error invalid encrypted key Java API 89 no license found Java API 89 NoClassDefFoundError Java API 89 UnsatisfiedLinkError Java API 89 error handling compiler C API 72 license manager C API 72 linker C API 72 programming errors C API 77 runtime errors C API
131. or as complex as starting a text editor to modify a file Anything that can be entered on one line after the operating system prompt can also be executed from within ILOG CPLEX However this command differs from other ILOG CPLEX commands in that it must be entered on a single line No prompt will be issued In addition the operating system may fail to carry out the command if insufficient memory is available In that case no message is issued by the operating system and the result is a return to the CPLEX gt prompt Summary The general syntax for the xecute command is xecute command line Quitting ILOG CPLEX When you are finished using ILOG CPLEX and want to leave it type quit 66 ILOG CPLEX 10 1 GETTING STARTED If a problem has been modified be sure to save the file before issuing a quit command ILOG CPLEX will not prompt you to save your problem ILOG CPLEX 10 1 GETTING STARTED 67 68 ILOG CPLEX 10 1 GETTING STARTED Concert Technology Tutorial for C Users This tutorial shows you how to write C applications using ILOG CPLEX with Concert Technology In this chapter you will learn about The Design of CPLEX in Concert Technology on page 70 Compiling and Linking ILOG CPLEX in Concert Technology Applications on page 71 The Anatomy of an ILOG Concert Technology Application on page 72 Building and Solving a Small LP Model in C on page 78 Writing and Reading Models and Files on page 80 Selecting
132. ot a requirement the static link implementations mentioned above are easier to use Building Applications that Use the ILOG CPLEX Parallel Optimizers When you are compiling and linking programs that use the ILOG CPLEX Parallel Optimizers it is especially important to review the relevant flags for the compiler and linker These are found in the makefile provided with UNIX distributions or in the sample project files provided with Windows distributions It is also a good idea to review the section on Using Parallel Optimizers in the ILOG CPLEX User s Manual for important details pertaining to each specific parallel optimizer How ILOG CPLEX Works 114 When your application uses routines of the ILOG CPLEX Callable Library it must first open the ILOG CPLEX environment then create and populate a problem object before it solves a problem Before it exits the application must also free the problem object and release the ILOG CPLEX environment The following sections explain those steps Opening the ILOG CPLEX Environment ILOG CPLEX requires a number of internal data structures in order to execute properly These data structures must be initialized before any call to the ILOG CPLEX Callable Library The first call to the ILOG CPLEX Callable Library is always to the function CPXopenCPLEX This routine checks for a valid ILOG CPLEX license and returns a pointer to the ILOG CPLEX environment This pointer is then passed to every ILOG CPLEX
133. oth storage space and speed if the natural sparsity of the model is exploited from the very start Before the model is solved the network optimizer is selected by setting the RootAlg parameter to the value IloCplex Network as shown in example ilolpex2 cpp The simplex display parameter I1oCplex SimDisplay is set so that the simplex algorithm issues logging information as it executes Setting ILOG CPLEX Parameters IloCplex provides a variety of parameters that allow you to control the solution process They can be categorized as Boolean integer numerical and string parameters and are ILOG CPLEX 10 1 GETTING STARTED 85 86 represented by the enumeration types IloCplex BoolParam IloCplex IntParam IloCplex NumParam and IloCplex StringParam respectively Modifying an Optimization Problem After the simple model is solved and the resulting objective value is passed to the output channel cplex out the remaining constraints are created and added to the model At this time the model has already been extracted to cplex As a consequence whenever the model is modified by adding a constraint this addition is immediately reflected in the cplex object via notification Starting from a Previous Basis Before solving the modified problem example ilolpex3 cpp sets the optimizer option to IloCplex Dual as this is the algorithm that can generally take best advantage of the optimal basis from the previous solve after t
134. ow prices basic rows and columns For information on the write commands see Writing Problem and Solution Files on page 53 Sensitivity analysis can also be performed in analyzing results as explained in Performing Sensitivity Analysis on page 51 For example to view the optimal value of each variable enter the command display solution variables In response the list of variable names with the solution value for each variable is displayed like this Variable Name Solution Value x1 40 000000 x2 17 500000 x3 42 500000 To view the slack values of each constraint enter the command display solution slacks The resulting message indicates that for this problem the slack variables are all zero All slacks in the range 1 2 are O0 To view the dual values sometimes called shadow prices for each constraint enter the command display solution dual The list of constraint names with the solution value for each constraint appears like this Constraint Name Dual Price cl 2 750000 c2 0 250000 Summary Display solution characteristics by entering a command with the syntax display solution identifier Performing Sensitivity Analysis Sensitivity analysis of the objective function and righthand side provides meaningful insight about ways in which the optimal solution of a problem changes in response to small changes in these parts of the problem data Sensitivity analysis can be performed on the following ILOG
135. r expr addTerm 1 0 x 01 expr addTerm 2 0 x 11 expr addTerm 3 0 2 The advantage of using IloLinearNumExpr over the first way is that you can more easily build up your linear expression in a loop which is what is typically needed in more complex applications Interface IloLinearNumExpr is an extension of IloNumExpr and thus can be used anywhere an expression can be used As mentioned before expressions can be used to create constraints or an objective function for a model Here is how to create a minimization objective for that expression IloObjective obj cplex minimize expr In addition to your creating an objective you must also instruct IloCplex to use that objective in the model it solves do so add the objective to 11oCplex like this cplex add obj Every modeling object that is to be used in model must be added to the IloCplex object The variables need not be explicitly added as they are treated implicitly when used in the expression of the objective More generally every modeling object that is referenced by another modeling object which itself has been added to 11oCplex is implicitly added to IloCplex as well There is a shortcut notation for creating and adding the objective to IloCplex cplex addMinimize expr Since the objective is not otherwise accessed it does not need to be stored in the variable obj Adding constraints to the model is just as easy For example the constraint ILOG
136. r in Interactive Optimizer 43 displaying type in Interactive Optimizer 43 entering in LP format in Interactive Optimizer 40 name limitations in Interactive Optimizer 40 naming in Interactive Optimizer 40 range C API 79 representing in model C API 74 constraints adding to a model Java API 92 continuous variable representing C API 74 CPLEX compatible platforms 11 Component Libraries 11 description 10 directory structure 20 installing 20 licensing 22 problem types 10 quitting in Interactive Optimizer 66 setting up 19 starting in Interactive Optimizer 36 technologies 11 cplex command in Interactive Optimizer 36 cplex jar location 88 cplex log file in Interactive Optimizer 49 CPXaddcols routine example in C API 120 modular data in C API 117 ILOG CPLEX 10 1 populating problem C API 115 CPXaddrows routine LP example in C API 120 modular data in C API 117 network example in C API 124 populating model in C API 115 CPXboundsa routine 126 CPXchgcoeflist routine example in C API 120 modular data in C API 117 populating model in C API 115 CPXcloseCPLEX routine LP example in C API 121 MPS example in C API 123 network example in C API 124 purpose in C API 115 CPXcopylp routine building model in memory for C API 117 efficient arrays in C API 118 example in C API 124 not for changing model in C API 116 populating model in C API 115 CPXcreateprob routine LP example in C API 122 network example in
137. rary The ILOG CPLEX Callable Library includes several categories of routines optimization and result routines for defining a problem optimizing it and getting the results utility routines for addressing application programming matters problem modification routines to change a problem after it has been created within the ILOG CPLEX internals problem query routines to access information about a problem after it has been created file reading and writing routines to move information from the file system into your application or out of your application to the file system parameter setting and query routines to access and modify the values of control parameters maintained by ILOG CPLEX Compiling and Linking Callable Library Applications 112 Each Callable Library is distributed as a single library file Libcplex a or cplex101 1ib Use of the library file is similar to that with o or obj files Simply substitute the library file in the link procedure This procedure simplifies linking and ensures that the smallest possible executable is generated ILOG CPLEX 10 1 GETTING STARTED The following compilation and linking instructions assume that the example source programs and ILOG CPLEX Callable Library files are in the directories associated with a default installation of the software If this is not true additional compile and link flags would be required to point to the locations of the include file cplex h and C
138. rithm Exception or IloCplex Exception To handle exceptions gracefully in a Concert Technology application include all of the code in a try catch clause like this IloEnv env try catch IloException amp e cerr Concert Exception e endl catch cerr Other Exception endl env end Note The construction of the environment comes before the try catch clause In case of an exception env end must still be called To protect against failure during the construction of the environment another try catch clause may be added If code other than Concert Technology code is used in the part of that sample denoted by all other exceptions will be caught with the statement catch Doing so is good practice as it assures that no exception is unhandled ILOG CPLEX 10 1 GETTING STARTED 77 Building and Solving a Small LP Model in C 78 A complete example of building and solving a small LP model can now be presented This example demonstrates General Structure of an ILOG CPLEX Concert Technology Application on page 78 Modeling by Rows on page 79 Modeling by Columns on page 79 Modeling by Nonzero Elements on page 80 Example ilolpex1 cpp which is one of the example programs in the standard ILOG CPLEX distribution is an extension of the example presented in Introducing ILOG CPLEX It shows three different ways of creating an ILOG Concer
139. rows of the constraint matrix This kind of display is known as a histogram There are two commands for displaying histograms one for columns one for rows display problem histogram c display problem histogram r For the small example in this tutorial the column histogram looks like this Column counts excluding fixed variables Nonzero Count 2 Number of Columns 3 It tells you that there are three columns each having two nonzeroes and no other columns Similarly the row histogram of the same small problem looks like this Row counts excluding fixed variables Nonzero Count 3 Number of Rows 2 It tells you that there are two rows with three nonzeroes in each of them Of course in a more complex model there would usually be a wider variety of nonzero counts than those histograms show Here is an example in which there are sixteen columns where only one row is non zero 756 columns where two rows are non zero and so forth Column counts excluding fixed variables Nonzero Count 1 2 3 4 5 6 15 16 Number of Columns 16 756 1054 547 267 113 2 1 If there has been an error during entry of the problem perhaps a constraint coefficient having been omitted by mistake for example summaries like these of a model where the structure of the constraint matrix is known may help you find the source of the error ILOG CPLEX 10 1 GETTING STARTED 47 Solving a Problem 48 The problem is now correctly entered and ILOG C
140. s correctness Again the ILOG CPLEX Interactive Optimizer can help Since the Interactive Optimizer uses the same routines as the Callable Library it should take the same amount of time to solve a problem as a Callable Library application Use the CPXwriteprob routine with the SAV format to create a binary representation of the problem object then read it in and solve it with the Interactive Optimizer If the application sets optimization parameters use the same settings with the Interactive Optimizer If your application takes significantly longer than the Interactive Optimizer performance within your application can probably be improved In such a case possible performance inhibitors include fragmentation of memory unnecessary compiler and linker options and coding approaches that slow the program without causing it to give incorrect results Use the Examples The ILOG CPLEX Callable Library is distributed with a variety of examples that illustrate the flexibility of the Callable Library The C source of all examples is provided in the standard distribution For explanations about the examples of quadratic programming problems QPs mixed integer programming problems MIPs and network flows see the ILOG CPLEX User s Manual Explanations of the following examples of LPs appear in this manual lpexl c illustrates various ways of generating a problem object lpex2 c demonstrates how to read a problem from a file optimize it via a cho
141. s Cplex to search for a solution and to solve the problem Solving the problem consists of finding a value for each variable while simultaneously satisfying the constraints and minimizing the objective The aim in this tutorial is to see three different ways to build a model by rows by columns or by nonzeros After building the model of the problem in one of those ways the application optimizes the problem and displays the solution Describe the Problem Write a natural language description of the problem and answer these questions What is known about the problem What are the unknown pieces of information the decision variables in this problem What are the limitations the constraints on the decision variables What is the purpose the objective of solving this problem ILOG CPLEX 10 1 GETTING STARTED Building a Small LP Problem in C Here is a conventional formulation of the problem that the example optimizes Maximize 2X2 3X3 subject to X X2 lt 20 3X2 lt 30 with these bounds 0 lt lt 40 OS x5 OS x3 What are the decision variables in this problem X5 X3 What are the constraints X X X 20 Xj 3X2 lt 30 0 lt x lt 40 O lt X3 lt 00 0 What is the objective Maximize x 2 3x3 ILOG CPLEX 10 1 GETTING STARTED 103 Model 104 After you have written a d
142. s using NET facilities Chapter 7 Callable Library Tutorial describes the same activities using the routines in the ILOG CPLEX Callable Library All tutorials use examples that are delivered with the standard distribution Notation in this Manual 14 This manual observes the following conventions in notation and names Important ideas are emphasized the first time they appear Text that is entered at the keyboard or displayed on the screen as well as commands and their options available through the Interactive Optimizer appear in this typeface for example set preprocessing aggregator n Entries that you must fill in appear in this typeface for example write filename The names of C routines and parameters in the ILOG CPLEX Callable Library begin with CPX and appearin this typeface for example CPXcopyobjnames The names of C classes in the CPLEX Concert Technology Library begin with Ilo and appear in this typeface for example IloCplex The names of Java classes begin with Ilo and appear in this typeface for example IloCplex The name of a class or method in NET is written as concatenated words with the first letter of each word in upper case for example IntVar or IntVar VisitChildren Generally accessors begin with the key word Get Accessors for Boolean members begin with Is Modifiers begin with Set ILOG CPLEX 10 1 GETTING STARTED Combinations of keys from the keyboard are hyphenate
143. so in ILOG CPLEX by typing a constraint name and a colon before the actual constraint If you do not give the constraints explicit names ILOG CPLEX will give them the default names c1 c2 cn Inthe example if you want to call the constraints time and labor for example enter the constraints like this st time 1 x2 x3 lt 20 labor 3x2 x3 lt 30 Constraint names are subject to the same guidelines as variable names They must have no more than 255 characters consist of only allowed characters and not begin with a number a period or the letter e followed by a positive or negative number or another e Objective Function Names The objective function can be named in the same manner as constraints The default name for the objective function is obj ILOG CPLEX assigns this name if no other is entered Bounds Finally you must enter the lower and upper bounds on the variables If no bounds are specified ILOG CPLEX will automatically set the lower bound to 0 and the upper bound to You must explicitly enter bounds only when the bounds differ from the default values In our example the lower bound on x1 is 0 which is the same as the default The upper bound 40 however is not the default so you must enter it explicitly You must type bounds on a separate line before you enter the bound information ILOG CPLEX 10 1 GETTING STARTED bounds xl lt 40 Since the bounds on x2 and x3 are the same as
144. stered trademark of ILOG Type help for a list of available commands Type help followed by a command name for more information on commands CPLEX gt The last line CPLEX gt is the prompt indicating that the product is running and is ready to accept one of the available ILOG CPLEX commands Use the help command to see a list of these commands ILOG CPLEX accepts commands in several different formats You can type either the full command name or any shortened form that uniquely identifies that name For example enter help after the CPLEX gt prompt as shown CPLEX gt help You will see a list of the ILOG CPLEX commands on the screen Since all commands start with a unique letter you could also enter just the single letter h CPLEX gt h ILOG CPLEX does not distinguish between upper and lower case letters so you could enter h H help or HELP All of these variations invoke the help command The same rules apply to all ILOG CPLEX commands You need only type enough letters of the command to distinguish it from all other commands and it does not matter whether you type upper or lower case letters This manual uses lower case letters ILOG CPLEX 10 1 GETTING STARTED After you type the help command a list of available commands with their descriptions appears on the screen like this add add constraints to the problem baropt Solve using barrier algorithm change change the problem conflict refine a conflict for
145. t 40 0 lt x2 0 lt x3 end CPLEX optimize Tried aggregator 1 time No LP presolve or aggregator reductions Presolve time 0 00 sec Iteration log Iteration L Dual infeasibility 0 000000 Iteration 2 Dual objective 202 500000 Dual simplex Optimal Objective 2 0250000000e 002 Solution time 0 01 sec Iterations 2 1 CPLEX gt display solution variables x1 x3 Variable Name Solution Value 1 40 000000 2 17 500000 x3 42 500000 CPLEX quit ILOG CPLEX 10 1 GETTING STARTED 29 Using Concert Technology in C 30 Here is a C application using ILOG CPLEX in Concert Technology to solve the example An expanded form of this example is discussed in detail in Concert Technology Tutorial for C Users on page 69 include lt ilcplex ilocplex h gt ILOSTLBEGIN int main int argc char argv IloEnv env try IloModel model env IloNumVarArray vars env vars add IloNumVar env 0 0 40 0 vars add IloNumVar env vars add IloNumVar env model add IloMaximize env vars 0 2 vars 1 3 vars 2 model add vars 0 vars 1 vars 2 lt 20 model add vars 0 3 vars 1 vars 2 lt 30 IloCplex cplex model if cplex solve env error Failed to optimize LP endl throw 1 IloNumArray vals env env out Solution status cplex getStatus endl env out Solution value cplex getObjValue
146. t Technology LP model how to solve it using I1o0Cplex and how to access the solution Here is the problem that the example optimizes Maximize X4 2X2 3X3 subject to Xp lt 20 3X2 lt 30 with these bounds 0 lt x1 40 OS x5 amp OS x3 General Structure of an ILOG CPLEX Concert Technology Application The first operation is to create the environment object env and the last operation is to destroy it by calling env end The rest of the code is enclosed in a try catch clause to gracefully handle any errors that may occur First the example creates the model object and after checking the correctness of command line parameters it creates empty arrays for storing the variables and range constraints of the optimization model Then depending on the command line parameter the example calls one of the functions populatebyrow populatebycolumn or populatebynonzero to fill the model object with a representation of the optimization problem These functions place the variable and range objects in the arrays var and con which are passed to them as parameters After the model has been populated the IloCplex algorithm object cplex is created and the model is extracted to it The following call of the method solve invokes the optimizer If it fails to generate a solution an error message is issued to the error stream of the environment cplex error and the integer 1 is thrown as an ex
147. t works because the modeling object model contains within it the reference to the environment named env After this line object cplex is ready to solve the optimization problem defined by model Solving the model is done by calling cplex solve This method returns 10 1 value where IloTrue indicates that cplex successfully found a feasible yet not necessarily optimal solution and I1oFalse indicates that no solution was found More precise information about the outcome of the last call to the method solve can be obtained by calling cplex getStatus The returned value tells you what ILOG CPLEX found out about the model whether it found the optimal solution or only a feasible solution whether it proved the model to be unbounded or infeasible or whether nothing at all has been determined at this point Even more detailed information about the termination of the solve call is available through method IloCplex getCplexStatus Querying Results After successfully solving the optimization problem you probably are interested in accessing the solution The following methods can be used to query the solution value for a variable or a set of variables IloNum IloCplex getValue IloNumVar var const void IloCplex getValues IloNumArray val const IloNumVarArray var const For example IloNum vall cplex getValue x1 ILOG CPLEX 10 1 GETTING STARTED stores the solution value for the modeling variable x1
148. t you want these variables can be explicitly removed using the delete option Summary The general syntax for the change command is ILOG CPLEX 10 1 GETTING STARTED 65 change option identifier identifier2 new value Executing Operating System Commands The execute command xecute is simple but useful It executes operating system commands outside of the ILOG CPLEX environment By using xecute you avoid having to save a problem and quit ILOG CPLEX in order to carry out a system function such as viewing a directory for example As an example if you wanted to check whether all of the files saved in the last session are really in the current working directory the following ILOG CPLEX command shows the contents of the current directory in a UNIX operating system using the UNIX command 1s xecute ls 1 total 7448 r r r 1 3258 Jul 14 10 34 afiro mps rwxr Xr x 1 3783416 Apr 22 10 32 cplex rw r r 1 3225 Jul 14 14 21 cplex log rw r r 1 145 Jul 14 11 32 example rw r r 1 112 Jul 14 11 32 example bas rw r r 1 148 Jul 14 11 32 example lp rw r r 1 146 Jul 14 11 32 example2 After the command is executed the CPLEX gt prompt returns indicating that you are still in ILOG CPLEX Most commands that can normally be entered from the prompt for your operating system can also be entered with the xecute command The command may be as simple as listing the contents of a directory or printing the contents of a file
149. than an optimizer Calling importModel does not extract the model to the invoking cplex object This must be done later by a call to cplex extract model The objects obj var and rng are passed to importModel so that later on when results are queried the variables will be accessible Selecting the Optimizer The selection of the optimizer option is done in the switch statement controlled by the second command line parameter A call to setParam IloCplex RootAlg alg selects the desired I1oCplex Algorithm option Accessing Basis Information After solving the model by calling the method solve the results are accessed in the same way as in ilolpex1 cpp with the exception of basis information for the variables It is important to understand that not all optimizer options compute basis information and thus it cannot be queried in all cases In particular basis information is not available when the model is solved using the barrier optimizer IloCplex Barrier without crossover parameter IloCplex BarCrossAlg set to IloCplex NoAl19g Querying Quality Measures Finally the program prints the maximum primal infeasibility or bound violation of the solution To cope with the finite precision of the numerical computations done on the computer IloCplex allows some tolerances by which for instance optimality conditions may be violated A long list of other quality measures is available ILOG CPLEX 10 1 GETTING STARTED 83
150. to CPXcreateprob The user need not be concerned with the memory management of the data Memory management is handled transparently by CPXreadcopyprob After calling CPXopenCPLEX and turning on the screen indicator by setting the CPX PARAM SCRIND parameter to CPX ON the example creates an empty problem object with a call to CPXcreateprob This call returns a pointer 1p to the new problem object Then the data is read in by the routine CPXreadcopyprob After the data is copied the appropriate optimization routine is called based on the command line argument After optimization the status of the solution is determined by a call to CPXgetstat The cases of infeasibility or unboundedness in the model are handled in a simple fashion here a more complex application program might treat these cases in more detail With these two cases out of the way the program then calls CPXsolninfo to determine the nature of the solution After it has been determined that a solution in fact exists then a call to CPXgetobjval is made to obtain the objective function value for this solution and report it Next preparations are made to print the solution value and basis status of each individual variable by allocating arrays of appropriate size these sizes are determined by calls to the routines CPXgetnumcols and CPXgetnumrows Note that a basis is not guaranteed to exist depending on which optimizer was selected at run time so some of these steps including the
151. to perform sensitivity analysis in the Interactive Optimizer As with most interactive features of ILOG CPLEX there is a direct approach to this task from the Callable Library This section modifies the example 1pex1 c in Building and Solving a Small LP Model in C on page 119 to show how to perform sensitivity analysis with routines from the Callable Library To begin make copy of 1pex1 c and edit this new source file Among the declarations for example immediately after the declaration for dj insert these additional declarations double lowerc NULL upperc NULL double lowerr NULL upperr NULL At some point after the call to CPX1popt for example just before the call to CPXwriteprob perform sensitivity analysis on the objective function and on the righthand side coefficients by inserting this fragment of code upperc double malloc cur numcols sizeof double lowerc double malloc cur numcols sizeof double Status CPXobjsa env lp 0 cur numcols 1 lowerc upperc if status fprintf stderr Failed to obtain objective sensitivity WNn goto TERMINATE printf nObjective coefficient sensitivity Mn for j 0 j lt cur numcols j printf Column d Lower 10g Upper 10gWn j lowerc j 51 upperr double malloc cur numrows sizeof double lowerr double malloc cur_numrows sizeof double status
152. torial However little or no experience in mathematical programming or operations research is required to follow this tutorial You should have ILOG CPLEX and ILOG Concert Technology for NET users installed in your development environment before starting this tutorial In your integrated development environment you should be able to compile link and execute a sample application provided with ILOG CPLEX and ILOG Concert Technology for NET users before starting the tutorial To check your installation before starting the tutorial open yourCPLEXhomeNexamplesNplatformMformatNexamples net sln in your integrated development environment where yourCPLEXhome indicates the place you installed ILOG CPLEX on your platform and format indicates one of these possibilities stat mda stat mta or stat_sta An integrated development environment such as Microsoft Visual Studio will then check for the DLLs of ILOG CPLEX and ILOG Concert Technology for NET users and warn you if they are not available to it Another way to check your installation is to load the project for one of the samples delivered with your product For example you might load the following project into Microsoft Visual Studio to check a C example of the diet problem yourCPLEXhome examples platform format Diet csproj ILOG CPLEX 10 1 GETTING STARTED What You Will Be Doing ILOG CPLEX can work together with ILOG Concert Technology for NET users a NET library that allo
153. ute programs written in a high level language The Callable Library is written in the C programming language while Concert Technology is available for users of C Java and the NET framework This manual also assumes that you already know how to program in the appropriate language and that you will consult a programming guide when you have questions in that area Whats in This Manual Chapter 1 Setting Up ILOG CPLEX tells how to install CPLEX Chapter 2 Solving an LP with ILOG CPLEX shows you at a glance how to use the Interactive Optimizer and each of the application programming interfaces APIs C ILOG CPLEX 10 1 GETTING STARTED 13 Java NET and C This overview is followed by more detailed tutorials about each interface Chapter 3 Interactive Optimizer Tutorial explains step by step how to use the Interactive Optimizer how to start it how to enter problems and data how to read and save files how to modify objective functions and constraints and how to display solutions and analytical information Chapter 4 Concert Technology Tutorial for C Users describes the same activities using the classes in the C implementation of the CPLEX Concert Technology Library Chapter 5 Concert Technology Tutorial for Java Users describes the same activities using the classes in the Java implementation of the CPLEX Concert Technology Library Chapter 6 Concert Technology Tutorial for NET Users describes the same activitie
154. ve your variables more meaningful names such as cars or gallons The only limitations on variable names in LP format are that the names must be no more than 255 characters long and use only the alphanumeric characters a z A Z 0 9 and certain symbols 96 amp 9 Any line with more than 510 characters is truncated A variable name cannot begin with a number or a period and there is one character combination that cannot be used the letter e or E alone or followed by a number or another e since this notation is reserved for exponents Thus a variable cannot be named e24 nor ILOG CPLEX 10 1 GETTING STARTED 39 40 e9cats nor eels nor any other name with this pattern This restriction applies only to problems entered in LP format Constraints After you have entered the objective function you can move on to the constraints However before you start entering the constraints you must indicate that the subsequent lines are constraints by typing subject to or st These terms can be placed alone on a line or on the same line as the first constraint if separated by at least one space Now you can type in the constraints in the following way st 1 X2 X3 lt 20 1 3x2 x3 lt 30 Constraint Names In this simple example it is easy to keep track of the small number of constraints but for many problems it may be advantageous to name constraints so that they are easier to identify You can do
155. w your own application can call ILOG CPLEX The following chapters give more specific information on the necessary header files for compilation and how to link ILOG CPLEX and Concert Technology libraries into your application Chapter 4 Concert Technology Tutorial for C Users contains information and platform specific instructions for compiling and linking the Concert Technology Library for C users Chapter 5 Concert Technology Tutorial for Java Users contains information and platform specific instructions for compiling and linking the Concert Technology Library for Java users Chapter 6 Concert Technology Tutorial for Users offers an example of a C NET application Chapter 7 Callable Library Tutorial contains information and platform specific instructions for compiling and linking the Callable Library ILOG CPLEX 10 1 GETTING STARTED Part 11 Tutorials This part provides tutorials to introduce you to each of the components of ILOG CPLEX Interactive Optimizer Tutorial on page 35 Concert Technology Tutorial for C Users on page 69 Concert Technology Tutorial for Java Users on page 87 Concert Technology Tutorial for NET Users on page 99 0 Callable Library Tutorial on page 111 Solving an LP with ILOG CPLEX To help you learn which CPLEX component best meets your needs this chapter briefly demonstrates how to create and solve an LP model It shows you at a glance the Interact
156. ws you to model optimization problems independently of the algorithms used to solve the problem It provides an extensible modeling layer adapted to a variety of algorithms ready to use off the shelf This modeling layer enables you to change your model without completely rewriting your application To find a solution to a problem by means of ILOG CPLEX with ILOG Concert Technology for NET users you use a three stage method describe model and solve The first stage is to describe the problem in natural language The second stage is to use the classes and interfaces of ILOG Concert Technology for NET users to model the problem The model is composed of data decision variables and constraints Decision variables are the unknown information in a problem Each decision variable has a domain of possible values The constraints are limits or restrictions on combinations of values for these decision variables The model may also contain an objective an expression that can be maximized or minimized The third stage is to use the classes of ILOG Concert Technology for NET users to solve the problem Solving the problem consists of finding a value for each decision variable while simultaneously satisfying the constraints and maximizing or minimizing an objective if one is included in the model In these tutorials you will describe model and solve a simple problem that also appears elsewhere in C C and Java chapters of this manual e Bui
157. xamples population by rows may seem most straightforward and natural there are some models where population by columns is a more natural or more efficient approach to implement For example problems with network structure typically lend themselves well to modeling by column Readers familiar with matrix algebra may view the method populateByColumn as the transpose of populateByRow In this approach range objects are created for modeling by column with only their lower and upper bound No expressions over variables are given because building them at this point would be impossible since the variables have not been created yet Similarly the objective function is created only with its intended optimization sense and without any expression ILOG CPLEX 10 1 GETTING STARTED 105 106 Next the variables are created and installed in the existing ranges and objective These newly created variables are introduced into the ranges and the objective by means of column objects which are implemented in the class IColumn Objects of this class are created with the methods Cplex Column and can be linked together with the method IColumn And to form aggregate IColumn objects An IColumn object created with the method ICplex Column contains information about how to use this column to introduce a new variable into an existing modeling object For example if obj is an IObjective object cplex Column obj 2 0 creates an IColumn object containing the informatio
158. you need to correct it before you begin real work with ILOG CPLEX For example if you get a message from the compiler such as ilolpex3 cpp 1 Can t find include file ilcplex ilocplex h then you need to verify that your compiler knows where you have installed ILOG CPLEX and its include files that is its header files If you get a message from the linker such as ld lcplex No such file or directory then you need to verify that your linker knows where the ILOG CPLEX library is located on your system If you get a message such as ilm CPLEX no license found for this product or ilm CPLEX invalid encrypted key MNJVUXTDJV82 in usr ilog ilm access ilm run ilmcheck then there is a problem with your license to use ILOG CPLEX Review the ILOG License Manager User s Guide and Reference to see whether you can correct the problem If not call the technical support hotline and repeat the error message there If you successfully compile link and execute one of the examples in the standard distribution then you can be sure that your installation is correct and you can begin to use ILOG CPLEX with ILOG Concert Technology seriously The Anatomy of an ILOG Concert Technology Application 72 ILOG Concert Technology is a C class library and therefore ILOG Concert Technology applications consist of interacting C objects This section gives a short introduction to the most important classes that are usually found in a complet
159. ys to construct a model Modeling by Rows on page 95 Modeling by Columns on page 95 Modeling Nonzeros on page 97 Example LPex1 java is an extension of the example presented in Entering the Example Problem on page 38 Maximize 2X2 3X3 subject to Xp lt 20 X 3X2 lt 30 with these bounds 0 lt lt 40 OS lt OS x3 After an initial check that a valid option string was provided as a calling argument the program begins by enclosing all executable statements that follow in a try catch pair of statements In case of an error ILOG CPLEX Concert Technology will throw an exception of type I1oException which the catch statement then processes In this simple example an exception triggers the printing of aline stating Concert exception e caught where e is the specific exception First create the model object cplex by executing the following statement IloCplex cplex new IloCplex At this point the cplex object represents an empty model that is a model with no variables constraints or other content The model is then populated in one of several ways depending on the command line argument The possible choices are implemented in the methods e populateByRow e populateByColumn e populateByNonzero All these methods pass the same three arguments The first argument is the cplex object to be populated The second and third arguments correspond to the vari

ILOG CPLEX 10.1 Getting Started

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