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### multiobj_c.c

/* Copyright 2023, Gurobi Optimization, LLC */

/* Want to cover three different sets but subject to a common budget of
* elements allowed to be used. However, the sets have different priorities to
* be covered; and we tackle this by using multi-objective optimization. */

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include "gurobi_c.h"

#define MAXSTR 128

int
main(void)
{
GRBenv   *env   = NULL;
GRBenv   *menv  = NULL;
GRBmodel *model = NULL;
int       error = 0;
int      *cind  = NULL;
double   *cval  = NULL;
char      buffer[MAXSTR];
int e, i, status, nSolutions;
double objn;

/* Sample data */
const int groundSetSize = 20;
const int nSubsets      = 4;
const int Budget        = 12;
double Set[][20] =
{ { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1 },
{ 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0 },
{ 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0 } };
int    SetObjPriority[] = {3, 2, 2, 1};
double SetObjWeight[]   = {1.0, 0.25, 1.25, 1.0};

/* Create environment */
if (error) goto QUIT;

/* Create initial model */
error = GRBnewmodel(env, &model, "multiobj_c", groundSetSize, NULL,
NULL, NULL, NULL, NULL);
if (error) goto QUIT;

/* get model environment */
menv = GRBgetenv(model);
if (!menv) {
fprintf(stderr, "Error: could not get model environment\n");
goto QUIT;
}

/* Initialize decision variables for ground set:
* x[e] == 1 if element e is chosen for the covering. */
for (e = 0; e < groundSetSize; e++) {
sprintf(buffer, "El%d", e);
error = GRBsetcharattrelement(model, "VType", e, GRB_BINARY);
if (error) goto QUIT;

error = GRBsetstrattrelement(model, "VarName", e, buffer);
if (error) goto QUIT;
}

/* Make space for constraint data */
cind = malloc(sizeof(int) * groundSetSize);
if (!cind) goto QUIT;
cval = malloc(sizeof(double) * groundSetSize);
if (!cval) goto QUIT;

/* Constraint: limit total number of elements to be picked to be at most
* Budget */
for (e = 0; e < groundSetSize; e++) {
cind[e] = e;
cval[e] = 1.0;
}
sprintf (buffer, "Budget");
error = GRBaddconstr(model, groundSetSize, cind, cval, GRB_LESS_EQUAL,
(double)Budget, buffer);
if (error) goto QUIT;

/* Set global sense for ALL objectives */
error = GRBsetintattr(model, GRB_INT_ATTR_MODELSENSE, GRB_MAXIMIZE);
if (error) goto QUIT;

/* Limit how many solutions to collect */
error = GRBsetintparam(menv, GRB_INT_PAR_POOLSOLUTIONS, 100);
if (error) goto QUIT;

/* Set and configure i-th objective */
for (i = 0; i < nSubsets; i++) {
sprintf(buffer, "Set%d", i+1);

error = GRBsetobjectiven(model, i, SetObjPriority[i], SetObjWeight[i],
1.0 + i, 0.01, buffer, 0.0, groundSetSize,
cind, Set[i]);
if (error) goto QUIT;
}

/* Save problem */
error = GRBwrite(model, "multiobj_c.lp");
if (error) goto QUIT;
error = GRBwrite(model, "multiobj_c.mps");
if (error) goto QUIT;

/* Optimize */
error = GRBoptimize(model);
if (error) goto QUIT;

/* Status checking */
error = GRBgetintattr(model, "Status", &status);
if (error) goto QUIT;

if (status == GRB_INF_OR_UNBD ||
status == GRB_INFEASIBLE  ||
status == GRB_UNBOUNDED     ) {
printf("The model cannot be solved "
"because it is infeasible or unbounded\n");
goto QUIT;
}
if (status != GRB_OPTIMAL) {
printf("Optimization was stopped with status %i\n", status);
goto QUIT;
}

/* Print best selected set */
error = GRBgetdblattrarray(model, GRB_DBL_ATTR_X, 0, groundSetSize, cval);
if (error) goto QUIT;

printf("Selected elements in best solution:\n\t");
for (e = 0; e < groundSetSize; e++) {
if (cval[e] < .9) continue;
printf("El%d ", e);
}

/* Print number of solutions stored */
error = GRBgetintattr(model, GRB_INT_ATTR_SOLCOUNT, &nSolutions);
if (error) goto QUIT;
printf("\nNumber of solutions found: %d\n", nSolutions);

/* Print objective values of solutions */

if (nSolutions > 10) nSolutions = 10;
printf("Objective values for first %d solutions:\n", nSolutions);
for (i = 0; i < nSubsets; i++) {
error = GRBsetintparam(menv, GRB_INT_PAR_OBJNUMBER, i);
if (error) goto QUIT;

printf("\tSet %d:", i);
for (e = 0; e < nSolutions; e++) {
error = GRBsetintparam(menv, GRB_INT_PAR_SOLUTIONNUMBER, e);
if (error) goto QUIT;

error = GRBgetdblattr(model, GRB_DBL_ATTR_OBJNVAL, &objn);
if (error) goto QUIT;

printf(" %6g", objn);
}
printf("\n");
}

QUIT:

if (cind != NULL)  free(cind);
if (cval != NULL)  free(cval);
if (model != NULL) GRBfreemodel(model);
if (env != NULL)   GRBfreeenv(env);

return error;
}


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