The OPTMILP Procedure

Example 11.2 MIPLIB Benchmark Instance

The following example illustrates the conversion of a standard MPS-format file into an MPS-format SAS data set. The problem is re-solved several times, each time by using a different control option. For such a small example, it is necessary 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 is called 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 SAS data set:

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

The problem can then be solved using PROC OPTMILP on the data set created by the conversion:

                                                                                                  
proc optmilp data=mpsdata allcuts=none heuristics=none printfreq=10000;                                                                                                          
run;                                                                                                                                

The resulting log is shown in Output 11.2.1.

Suppose you do not have a bound for the solution. 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=mpsdata allcuts=none heuristics=none target=880000;                                                                                            
run;

The relevant results from this run are displayed in Output 11.2.2. In this case, there is a decrease in CPU time, 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=mpsdata allcuts=none heuristics=none relobjgap=0.01;                                                                                           
run;                                                                                                                                

The relevant results from this run are displayed in Output 11.2.3. In this case, since the specified RELOBJGAP= value is larger than the default value, the number of nodes and the CPU time have decreased from their values in the original run. Note that these savings are exchanged for an increase in the objective value of the solution.

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=mpsdata allcuts=none heuristics=none maxtime=0.1;                                                                                                
run;                                                                                                                                

The relevant results from this run are displayed in Output 11.2.4. Once again, a reduction in solution time is traded for an increase in objective value.

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=mpsdata allcuts=none heuristics=none maxnodes=500;                                                                                  
run;                                                                                                                                

The relevant results from this run are displayed in Output 11.2.5. PROC OPTMILP displays the best objective value of all the solutions produced.