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Burglar - Use of index sets, formulating logical constraints

Description
Several versions of a simple knapsack problem:
  • xbburg: standard formlation
  • xbburgi: shows how to index an array of variables by an index set
  • xbburgl: adds several indicator constraints to state logical conditions
Further explanation of this example: Quick reference guide 'MIP formulations and linearizations', Section 4 Indicator constraints

xbburgjava.zip[download all files]

Source Files





xbburg.java

/********************************************************
  Xpress-BCL Java Example Problems
  ================================

  file xbburg.java
  ````````````````
  Burglar problem, binary variable formulation.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Jan. 2000, rev. Mar. 2011
********************************************************/

import com.dashoptimization.*;

public class xbburg
{
 static final int NItems = 8;        /* Number of items */

/****DATA****/
/* Item:                           1   2   3   4   5   6   7   8 */
 static final double[] VALUE  =  {15,100, 90, 60, 40, 15, 10,  1};
                                     /* Value of items */
 static final double[] WEIGHT =  { 2, 20, 20, 30, 40, 30, 60, 10};
                                     /* Weight of items */
 static final double WTMAX = 102;    /* Max weight allowed for haul */

 public static void main(String[] args)
 { 
  XPRB bcl;
  XPRBvar[] x;  
  XPRBexpr lobj, kn;  
  int i;
  XPRBprob p;
  
  bcl = new XPRB();                  /* Initialize BCL */
  p = bcl.newProb("Burglar");        /* Create a new problem in BCL */
 
/****VARIABLES****/
  x = new XPRBvar[NItems];           /* 1 if we take item i; 0 otherwise */
  for(i=0;i<NItems;i++)  x[i]=p.newVar("x", XPRB.BV);
 
/****OBJECTIVE****/
  lobj = new XPRBexpr();
  for(i=0;i<NItems;i++)  lobj.add(x[i].mul(VALUE[i])); 
  p.setObj(lobj);                    /* Set objective: maximize total value */ 

/****CONSTRAINTS****/
  kn = new XPRBexpr();
  for(i=0;i<NItems;i++)  kn.add(x[i].mul(WEIGHT[i]));  
  p.newCtr("WtMax", kn.lEql(WTMAX) );   /* Weight restriction */

/****SOLVING + OUTPUT****/
  p.setSense(XPRB.MAXIM);            /* Choose the sense of the optimization */
  p.mipOptimize("");                 /* Solve the MIP-problem */
  System.out.println("Objective: " + p.getObjVal());  /* Get objective value */

  for(i=0;i<NItems;i++)              /* Print out the solution */
   System.out.print(x[i].getName()+ ":" + x[i].getSol() + " ");
  System.out.println();
 }
} 


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