Re: [Help-glpk] Understanding the LPX_K_TOLOBJ parameter

[Andrew Makhorin]

> I have a binary integer program I'm solving with GLPK.  I've
> noticed excessive Branch Bound time, so thought I would play with the
> tolerance for accepting an integer solution.  In CPLEX, I'd set the
> mipgap value appropriately.  After reading through the GLPK manual, I
> think the parameter that is equivalent is the LPX_K_TOLOBJ.  Am I
> correct?  My C code looks something like this (with lots of stuff left
> out):

> bip = lpx_read_model(argv[INDEX_MODL], argv[INDEX_DATA], NULL);
> lpx_set_real_parm(bip, LPX_TOLOBJ, 0.005); /* 0.5% mipgap */

> If this is wrong please let me know.  For most of my data sets, the
> solution to the relaxation is integer, so this doesn't get exercised
> too much.  But, I think something is wrong because the tail from a run
> on one of my datasets (that is currently still running) looks like
> this:

> +293011: mip =   4.200000000e+02 >=   4.183237456e+02   0.4% (176; 789)
> Time used: 38906.0 secs.  Memory used: 257.4 Mb.
> +293163: mip =   4.200000000e+02 >=   4.183237456e+02   0.4% (177; 789)
> Time used: 38977.0 secs.  Memory used: 257.5 Mb.
> +293273: mip =   4.200000000e+02 >=   4.183237456e+02   0.4% (178; 789)
> Time used: 39047.0 secs.  Memory used: 257.5 Mb.
> |293568:   objval =   4.194444443e+02   infeas =   4.340972026e-14 (37417)
> +293568: mip =   4.200000000e+02 >=   4.183237456e+02   0.4% (178; 790)
> Time used: 39143.0 secs.  Memory used: 257.5 Mb.

> So, I was hoping that it would take the "420" solution and bail
> since the gap is less than 0.5%.  Please help me understand what I am
> missing.  I can provide more info if helpful.

Do not change tol_obj. Set the relative mip gap, say, to 0.01 (that
means 1%) to prematurely stop the search. In this case you obtain
a suboptimal solution. Besides, you can try enabling cutting planes;
sometimes this helps to reduce the solution time.