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 logfreq=10000; run;
The resulting log is shown in Output 11.2.1.
Output 11.2.1: MIPLIB PROC OPTMILP Log
NOTE: The problem BELL3A has 133 variables (39 binary, 32 integer, 0 free, 0 |
fixed). |
NOTE: The problem has 123 constraints (123 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The problem has 347 constraint coefficients. |
NOTE: The MILP presolver value AUTOMATIC is applied. |
NOTE: The MILP presolver removed 33 variables and 37 constraints. |
NOTE: The MILP presolver removed 92 constraint coefficients. |
NOTE: The MILP presolver modified 3 constraint coefficients. |
NOTE: The presolved problem has 100 variables, 86 constraints, and 255 |
constraint coefficients. |
NOTE: The MILP solver is called. |
Node Active Sols BestInteger BestBound Gap Time |
0 1 0 . 866240 . 0 |
0 1 0 . 866240 . 0 |
801 49 1 916564 874287 4.84% 0 |
881 108 2 916327 874287 4.81% 0 |
947 159 3 915158 874287 4.67% 0 |
979 165 4 898096 874287 2.72% 0 |
1002 123 5 887234 874287 1.48% 0 |
1088 122 6 883066 874287 1.00% 0 |
1978 381 7 880717 874502 0.71% 0 |
6093 1902 8 878430 875484 0.34% 0 |
10000 2382 8 878430 876000 0.28% 1 |
20000 1703 8 878430 876961 0.17% 2 |
23321 2 8 878430 878365 0.01% 2 |
NOTE: Optimal within relative gap. |
NOTE: Objective = 878430.316. |
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 logfreq=5000 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.
Output 11.2.2: MIPLIB PROC OPTMILP Log with TARGET= Option
NOTE: The problem BELL3A has 133 variables (39 binary, 32 integer, 0 free, 0 |
fixed). |
NOTE: The problem has 123 constraints (123 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The problem has 347 constraint coefficients. |
NOTE: The MILP presolver value AUTOMATIC is applied. |
NOTE: The MILP presolver removed 33 variables and 37 constraints. |
NOTE: The MILP presolver removed 92 constraint coefficients. |
NOTE: The MILP presolver modified 3 constraint coefficients. |
NOTE: The presolved problem has 100 variables, 86 constraints, and 255 |
constraint coefficients. |
NOTE: The MILP solver is called. |
Node Active Sols BestInteger BestBound Gap Time |
0 1 0 . 866240 . 0 |
0 1 0 . 866240 . 0 |
801 49 1 916564 874287 4.84% 0 |
881 108 2 916327 874287 4.81% 0 |
947 159 3 915158 874287 4.67% 0 |
979 165 4 898096 874287 2.72% 0 |
1002 123 5 887234 874287 1.48% 0 |
1088 122 6 883066 874287 1.00% 0 |
1978 381 7 880717 874502 0.71% 0 |
5000 1476 7 880717 875311 0.62% 0 |
6093 2011 8 878430 875484 0.34% 0 |
NOTE: Target reached. |
NOTE: Objective of the best integer solution found = 878430.32. |
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.
Output 11.2.3: MIPLIB PROC OPTMILP Log with RELOBJGAP= Option
NOTE: The problem BELL3A has 133 variables (39 binary, 32 integer, 0 free, 0 |
fixed). |
NOTE: The problem has 123 constraints (123 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The problem has 347 constraint coefficients. |
NOTE: The MILP presolver value AUTOMATIC is applied. |
NOTE: The MILP presolver removed 33 variables and 37 constraints. |
NOTE: The MILP presolver removed 92 constraint coefficients. |
NOTE: The MILP presolver modified 3 constraint coefficients. |
NOTE: The presolved problem has 100 variables, 86 constraints, and 255 |
constraint coefficients. |
NOTE: The MILP solver is called. |
Node Active Sols BestInteger BestBound Gap Time |
0 1 0 . 866240 . 0 |
0 1 0 . 866240 . 0 |
100 85 0 . 873180 . 0 |
200 166 0 . 873577 . 0 |
300 243 0 . 873730 . 0 |
400 317 0 . 873867 . 0 |
500 379 0 . 874141 . 0 |
600 460 0 . 874247 . 0 |
700 544 0 . 874262 . 0 |
800 50 0 . 874287 . 0 |
801 49 1 916564 874287 4.84% 0 |
881 108 2 916327 874287 4.81% 0 |
900 125 2 916327 874287 4.81% 0 |
947 159 3 915158 874287 4.67% 0 |
979 165 4 898096 874287 2.72% 0 |
1000 185 4 898096 874287 2.72% 0 |
1002 123 5 887234 874287 1.48% 0 |
1088 122 6 883066 874287 1.00% 0 |
1100 129 6 883066 874287 1.00% 0 |
1200 168 6 883066 874287 1.00% 0 |
1300 199 6 883066 874287 1.00% 0 |
1400 238 6 883066 874287 1.00% 0 |
1500 266 6 883066 874287 1.00% 0 |
1600 302 6 883066 874287 1.00% 0 |
1700 327 6 883066 874314 1.00% 0 |
1736 341 6 883066 874325 1.00% 0 |
NOTE: Optimal within relative gap. |
NOTE: Objective = 883066.108. |
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.
Output 11.2.4: MIPLIB PROC OPTMILP Log with MAXTIME= Option
NOTE: The problem BELL3A has 133 variables (39 binary, 32 integer, 0 free, 0 |
fixed). |
NOTE: The problem has 123 constraints (123 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The problem has 347 constraint coefficients. |
NOTE: The MILP presolver value AUTOMATIC is applied. |
NOTE: The MILP presolver removed 33 variables and 37 constraints. |
NOTE: The MILP presolver removed 92 constraint coefficients. |
NOTE: The MILP presolver modified 3 constraint coefficients. |
NOTE: The presolved problem has 100 variables, 86 constraints, and 255 |
constraint coefficients. |
NOTE: The MILP solver is called. |
Node Active Sols BestInteger BestBound Gap Time |
0 1 0 . 866240 . 0 |
0 1 0 . 866240 . 0 |
100 85 0 . 873180 . 0 |
200 166 0 . 873577 . 0 |
203 167 0 . 873577 . 0 |
NOTE: CPU time limit reached. |
NOTE: No integer solutions found. |
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.
Output 11.2.5: MIPLIB PROC OPTMILP Log with MAXNODES= Option
NOTE: The problem BELL3A has 133 variables (39 binary, 32 integer, 0 free, 0 |
fixed). |
NOTE: The problem has 123 constraints (123 LE, 0 EQ, 0 GE, 0 range). |
NOTE: The problem has 347 constraint coefficients. |
NOTE: The MILP presolver value AUTOMATIC is applied. |
NOTE: The MILP presolver removed 33 variables and 37 constraints. |
NOTE: The MILP presolver removed 92 constraint coefficients. |
NOTE: The MILP presolver modified 3 constraint coefficients. |
NOTE: The presolved problem has 100 variables, 86 constraints, and 255 |
constraint coefficients. |
NOTE: The MILP solver is called. |
Node Active Sols BestInteger BestBound Gap Time |
0 1 0 . 866240 . 0 |
0 1 0 . 866240 . 0 |
100 85 0 . 873180 . 0 |
200 166 0 . 873577 . 0 |
300 243 0 . 873730 . 0 |
400 317 0 . 873867 . 0 |
499 378 0 . 874141 . 0 |
NOTE: Node limit reached. |
NOTE: No integer solutions found. |