The OPTMILP Procedure

The following example illustrates the conversion of a standard MPS-format file into an MPS-format data table. The problem is re-solved several times, each time by using a different control option. For such a small example, it is helpful to disable cuts and heuristics in order to see the computational savings gained by using other options. For larger or more complex examples, the benefits of using the various control options are more pronounced.

The standard set of MILP benchmark cases are the various versions of MIPLIB (Bixby et al. 1998, Achterberg, Koch, and Martin 2003) and can be found at http://miplib.zib.de/. The following statement uses the %MPS2SASD macro to convert an example from MIPLIB to a data table:

%mps2sasd(mpsfile="bell3a.mps", outdata=mycas.mpsdata);

The problem can then be solved using PROC OPTMILP on the data table uploaded to CAS:

proc optmilp data=mycas.mpsdata allcuts=none heuristics=none;
run;

The resulting log is shown in Output 7.2.1.

If there is an objective value that, even if it is not optimal, satisfies your requirements, then you can save time by using the TARGET= option. The following PROC OPTMILP call solves the problem with a target value of 880,000:

proc optmilp data=mycas.mpsdata allcuts=none heuristics=none
   target=880000;
run;

The relevant results from this run are displayed in Output 7.2.2. In this case, there is a decrease in the number of nodes processed, but the objective value has increased.

When the objective value of a solution is within a certain relative gap of the optimal objective value, the procedure stops. The acceptable relative gap can be changed using the RELOBJGAP= option, as demonstrated in the following example:

proc optmilp data=mycas.mpsdata allcuts=none heuristics=none
   relobjgap=0.3;
run;

The relevant results from this run are displayed in Output 7.2.3. In this case, since the specified RELOBJGAP= value is larger than the default value, the number of nodes processed has decreased from their values in the original run. Note that these savings are possible because PROC OPTMILP makes a weaker statement about how good the solution found is, which is indicated by the decreased best bound value.

The MAXTIME= option enables you to accept the best solution produced by PROC OPTMILP in a specified amount of time. The following example illustrates the use of the MAXTIME= option:

proc optmilp data=mycas.mpsdata allcuts=none heuristics=none
   maxtime=0.5;
run;

The relevant results from this run are displayed in Output 7.2.4. In this case the solution process stopped early because the time limit was reached.

The MAXNODES= option enables you to limit the number of nodes generated by PROC OPTMILP. The following example illustrates the use of the MAXNODES= option:

proc optmilp data=mycas.mpsdata allcuts=none heuristics=none
   maxnodes=1000;
run;

The relevant results from this run are displayed in Output 7.2.5. PROC OPTMILP displays the best objective value of all the solutions produced within the first 1000 nodes.