Burglar - Use of index sets, formulating logical constraints

• 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

/********************************************************
  BCL Example Problems
  ====================

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

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

#include 
#include "xprb.h"

#define NItems 8                        /* Number of items */

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

int main(int argc, char **argv)
{
 XPRBvar x[NItems];  
 XPRBctr cobj,ctr;  
 int i;
 XPRBprob prob;
 
 prob=XPRBnewprob("Burglar");           /* Initialize a new problem in BCL */
 
/****VARIABLES****/
                /* 1 if we take item i; 0 otherwise */
 for(i=0;i

/********************************************************
  BCL Example Problems
  ====================

  file xbburgi.c
  ``````````````
  Burglar problem.
  Binary variable formulation with index sets.

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

#include 
#include 
#include "xprb.h"

/****DATA****/
/* Item:           ca  ne  va  pi  tv  vi  ch  br */
double VALUE[]  = {15,100, 90, 60, 40, 15, 10,  1}; /* Value of items */
double WEIGHT[] = { 2, 20, 20, 30, 40, 30, 60, 10}; /* Weight of items */
double WTMAX    = 102;                  /* Max weight allowed for haul */

char *ITEMNAMES[] = {"camera", "necklace", "vase", "picture", "tv", "video", 
            "chest", "brick"};
            
int NItems;                             /* Number of items */

int main(int argc, char **argv)
{
 XPRBvar *x;     
 XPRBidxset ITEMS;                     /* Set of items */
 int i;
 XPRBctr ctr,cobj;
 XPRBprob prob;
 
 prob=XPRBnewprob("Burglari");          /* Initialize a new problem in BCL */
 
/****INDICES****/
 ITEMS=XPRBnewidxset(prob,"Items",8);   /* Create the index set */
 for(i=0;i<8;i++) XPRBaddidxel(ITEMS, ITEMNAMES[i]);
 
 NItems=XPRBgetidxsetsize(ITEMS);       /* Get the size of the index set */
 
/****VARIABLES****/
 x = (XPRBvar *)malloc(NItems*sizeof(XPRBvar));
 for(i=0;i0) 
   printf("%s : %g\n", XPRBgetidxelname(ITEMS, i), XPRBgetsol(x[i]));
                                        /* Print out the chosen items */
 return 0;
} 

/********************************************************
  BCL Example Problems
  ====================

  file xbburgl.c
  ``````````````
  Burglar problem.
  Binary variable formulation with index sets.
  -- Formulating logical conditions 
     with indicator constraints --

  (c) 2009 Fair Isaac Corporation
      author: S.Heipcke, June 2009, rev. Mar. 2011
********************************************************/

#include 
#include 
#include "xprb.h"

/****DATA****/
/* Item:           ca  ne  va  pi  tv  vi  ch  br */
double VALUE[]  = {15,100, 90, 60, 40, 15, 10,  1}; /* Value of items */
double WEIGHT[] = { 2, 20, 20, 30, 40, 30, 60, 10}; /* Weight of items */
double WTMAX    = 102;                  /* Max weight allowed for haul */

char *ITEMNAMES[] = {"camera", "necklace", "vase", "picture", "tv", "video", 
            "chest", "brick"};
            
int NItems;                             /* Number of items */

int main(int argc, char **argv)
{
 XPRBvar *x;     
 XPRBidxset ITEMS;                     /* Set of items */
 int i;
 XPRBctr ctr,cobj,Log3a,Log3b;
 XPRBprob prob;
 
 prob=XPRBnewprob("BurglarL");          /* Initialize a new problem in BCL */
 
/****INDICES****/
 ITEMS=XPRBnewidxset(prob,"Items",8);   /* Create the index set */
 for(i=0;i<8;i++) XPRBaddidxel(ITEMS, ITEMNAMES[i]);
 
 NItems=XPRBgetidxsetsize(ITEMS);       /* Get the size of the index set */
 
/****VARIABLES****/
 x = (XPRBvar *)malloc(NItems*sizeof(XPRBvar));
 for(i=0;i= 2 */
 XPRBaddterm(Log3b, x[XPRBgetidxel(ITEMS,"tv")], 1);
 XPRBaddterm(Log3b, x[XPRBgetidxel(ITEMS,"video")], 1);
 XPRBaddterm(Log3b, NULL, 2);

/* Turn the 2 constraints into indicator constraints */
 XPRBsetindicator(Log3a, 1, x[XPRBgetidxel(ITEMS,"vase")]);
                                  /* x["vase"]=1 -> x["tv"]+x["video"]=0 */
 XPRBsetindicator(Log3b, -1, x[XPRBgetidxel(ITEMS,"vase")]);
                                  /* x["vase"]=0 -> x["tv"]+x["video"]=2 */

/* Alternative MIP formulation (instead of Log3a and Log3b) */
/*
 ctr = XPRBnewctr(prob, "Log3", XPRB_E);      // x["tv"] = 1 - x["vase"] 
 XPRBaddterm(ctr, x[XPRBgetidxel(ITEMS,"tv")], 1);
 XPRBaddterm(ctr, x[XPRBgetidxel(ITEMS,"vase")], 1);
 XPRBaddterm(ctr, NULL, 1);
*/
 
/****SOLVING + OUTPUT****/
 XPRBsetsense(prob,XPRB_MAXIM);         /* Choose the sense of optimization */
 XPRBmipoptimize(prob,"");              /* Solve the MIP-problem */
 printf("Objective: %g\n",XPRBgetobjval(prob));   /* Get objective value */

 for(i=0;i0) 
   printf("%s : %g\n", XPRBgetidxelname(ITEMS, i), XPRBgetsol(x[i]));
                                        /* Print out the chosen items */
 return 0;
}