Re: [Help-glpk] binary variable

[Andrew Makhorin]

> 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.

You obtained components of lp relaxation, not of mip solution.
You need to call glp_mip_obj_val and glp_mip_col_val rather than
glp_get_obj_val and glp_get_col_prim in statements s32-s36.