Matrix input

In this chapter we show how to

• initialize Xpress Optimizer,
• load matrices in MPS or LP format into the Optimizer,
• solve a problem, and
• write out the solution to a file.

Matrix files

With Xpress, the user has the choice between two matrix formats: extended MPS and extended LP format, the latter being in general more easily human-readable since constraints are printed in algebraic form. Such matrices may be written out by Xpress Optimizer, but more likely they will have been generated by some other tool.

If the optimization process with Xpress Optimizer is started from within a Mosel or BCL program, then the problem matrix is loaded in memory into the solver without writing it out to a file (which would be expensive in terms of running time). However, both tools may also be used to produce matrix files (see Chapter 9 for matrix generation with Mosel and Chapter 10 for BCL).

Implementation

To load a matrix into Xpress Optimizer we need to perform the following steps:

1. Initialize Xpress Optimizer.
2. Create a new problem.
3. Read the matrix file.

The following C program folioinput.c (similar interfaces exist for Java and C#) shows how to load a matrix file, solve it, and write out the results. For clarity's sake we have omitted all error checking in this program. In general it is recommended to test the return value of the initialization function and also whether the problem has been created and read correctly.

To use Xpress Optimizer, we need to include the header file xprs.h.

#include <stdio.h>
#include "xprs.h"

int main(int argc, char **argv)
{
 XPRSprob prob;

 XPRSinit(NULL);                      /* Initialize Xpress Optimizer */
 XPRScreateprob(&prob);               /* Create a new problem */

 XPRSreadprob(prob, "Folio", "");     /* Read the problem matrix */

 XPRSchgobjsense(prob, XPRS_OBJ_MAXIMIZE);   /* Set sense to maximization */
 XPRSlpoptimize(prob, "");            /* Solve the problem */

 XPRSwriteprtsol(prob, "Folio.prt", "");  /* Write results to `Folio.prt' */

 XPRSdestroyprob(prob);               /* Delete the problem */
 XPRSfree();                          /* Terminate Xpress */

 return 0;
}

Compilation and program execution

If you have followed the standard installation procedure of Xpress Optimizer, you may compile this file with the following command under Windows:

cl /MD /I%XPRESSDIR%\include %XPRESSDIR%\lib\xprs.lib folioinput.c

For Linux or Solaris use

cc -D_REENTRANT -I${XPRESSDIR}/include -L${XPRESSDIR}/lib folioinput.c -o folioinput -lxprs

For other systems please refer to the example makefile provided with the corresponding distribution.

If we run this program with the matrix Folio.mat produced by BCL for the LP example problem of Chapter 2, then we obtain an output file Folio.prt with the following contents:

Problem Statistics
Matrix FolioLP
Objective *OBJ*

RHS *RHS*
Problem has      4 rows and     10 structural columns

Solution Statistics
Maximization performed
Optimal solution found after      5 iterations
Objective function value is    14.066659

Rows Section
   Number    Row     At     Value      Slack Value   Dual Value      RHS
 N      1  *OBJ*     BS    14.066659    -14.066659       .000000     .000000
 E      2  Cap       EQ     1.000000       .000000      8.000000    1.000000
 G      3  NA        LL      .500000       .000000     -5.000000     .500000
 L      4  Risk      UL      .333333       .000000     23.000000     .333333

Columns Section
   Number   Column   At     Value      Input Cost   Reduced Cost
 C      5  frac      UL      .300000      5.000000      2.000000
 C      6  frac_1    LL      .000000     17.000000     -9.000000
 C      7  frac_2    BS      .200000     26.000000       .000000
 C      8  frac_3    LL      .000000     12.000000    -14.000000
 C      9  frac_4    BS      .066667      8.000000       .000000
 C     10  frac_5    UL      .300000      9.000000      1.000000
 C     11  frac_6    LL      .000000      7.000000     -1.000000
 C     12  frac_7    LL      .000000      6.000000     -2.000000
 C     13  frac_8    BS      .133333     31.000000       .000000
 C     14  frac_9    LL      .000000     21.000000    -10.000000      

The upper half contains some statistics concerning the problem size and the solution algorithm: the optimal LP solution found has a value of 14.066659. The Rows Section gives detailed solution information for the constraints in the problem. The solution values for the decision variables are located in the column labeled Value of the Columns Section.