[Help-glpk] binary variable

[Bayrem Chelly]

i have this example to do and here my code


maximize  x1 + x2 + 3* x3 + 4* x4;

           x4 <= x2
           x3 <= x1
           x1 + x2 + x3 + x4 <= 3

 
           xi : binary variable so xi = 0 or xi =1

i do my code as follow :

/* myexp.c */

#include <stdio.h>
#include <stdlib.h>
//extern "C" {
#include <glpk.h>
//}


int main(void)
{     glp_prob *lp;
    
        double Z, x1, x2, x3,x4;
s1:   lp = glp_create_prob();


s2:   glp_set_prob_name(lp, "sample");
s3:   glp_set_obj_dir(lp, GLP_MAX);
s4:   glp_add_rows(lp, 3);
s5:   glp_set_row_name(lp, 1, "p");
s6:   glp_set_row_bnds(lp, 1, GLP_UP, 0, 0);
s7:   glp_set_row_name(lp, 2, "q");
s8:   glp_set_row_bnds(lp, 2, GLP_UP, 0, 0);
s9:   glp_set_row_name(lp, 3, "r");
s10:  glp_set_row_bnds(lp, 3, GLP_UP, 0, 3);
s11:  glp_add_cols(lp, 4);

glp_set_col_kind(lp,1,GLP_BV);
s12:  glp_set_col_name(lp, 1, "x1");
s13:  glp_set_col_bnds(lp, 1, GLP_DB, 0, 1);
s14:  glp_set_obj_coef(lp, 1, 1);

glp_set_col_kind(lp,2,GLP_BV);
s15:  glp_set_col_name(lp, 2, "x2");
s16:  glp_set_col_bnds(lp, 2, GLP_DB, 0, 1);
s17:  glp_set_obj_coef(lp, 2, 1);

glp_set_col_kind(lp,3,GLP_BV);
s18:  glp_set_col_name(lp, 3, "x3");
s19:  glp_set_col_bnds(lp, 3, GLP_DB, 0,1);
s20:  glp_set_obj_coef(lp, 3, 3);

glp_set_col_kind(lp,4,GLP_BV);
glp_set_col_name(lp, 4, "x4");
glp_set_col_bnds(lp, 4, GLP_DB, 0,1);
glp_set_obj_coef(lp, 4, 4);

int ia[9]={0,1,1,2,2,3,3,3,3};
int ja[9]={0,2,4,1,3,1,2,3,4};
double ar[9]={0,-1,1,-1,1,1,1,1,1};

s30:  glp_load_matrix(lp, 8, ia, ja, ar);
        glp_simplex(lp,NULL);
s31:  glp_intopt(lp,NULL);
s32:  Z = glp_get_obj_val(lp);
s33:  x1 = glp_get_col_prim(lp, 1);
s34:  x2 = glp_get_col_prim(lp, 2);
s35:  x3 = glp_get_col_prim(lp, 3);
        x4 = glp_get_col_prim(lp, 4);
s36:  printf("\nZ = %g; x1 = %g; x2 = %g; x3 = %g; x4
= %g\n", Z, x1, x2, x3, x4);
s37:  glp_delete_prob(lp);
      return 0;
}

/* eof */


my problem is that i have an inexpected result : 



*     0:   objval =   0.000000000e+00   infeas =  
0.000000000e+00 (0)
*     4:   objval =   7.000000000e+00   infeas =  
0.000000000e+00 (0)
OPTIMAL SOLUTION FOUND
Integer optimization begins...
+     4: mip =     not found yet <=              +inf 
      (1; 0)
+     6: >>>>>   6.000000000e+00 <=   7.000000000e+00 
16.7% (3; 0)
+     6: mip =   6.000000000e+00 <=     tree is empty 
 0.0% (0; 5)
INTEGER OPTIMAL SOLUTION FOUND

Z = 7; x1 = 0.5; x2 = 1; x3 = 0.5; x4 = 1


====> we can see here than xi even if are binary we
have x3 = 0.5 and also for x1 = 0.5 so i wonder that
there is something wrong with binary variable or may
be i did a mistake in my code.


      
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