The following table summarizes the solutions for the problems found here. Each problem id links to a page where you can download individual files associated with that problem. Follow this link to download all compressed folders each containing a set partitioning problem presented in several forms. The folder also contains the cplex log file associated with the .lp form of the problem. Column n is the number of original variables whose value is between 1 and max_coef, while m is the number of rows and also the number of appended variables to guarantee feasibility (their objective coefficient is 2*max_coef). Therefore, the total number of variables in the set partitioning problem is n + m.
As noted, the Penalty is 100 for all problems, however, if you want to change this penalty or create your own problems to solve and send the results to me, here is a link to my set partitioning problem generator. Although you can run it by clicking on the link, you should probably save it to your computer (it should not crash, or destroy anything). After saving it, simply double-click, answer the questions, and the files will be stored in the directory where you saved the generator.
| Problem id | n | m | n+m |
col density |
max coef |
random seed | Penalty | CPLEX value |
CPLEX time to given value (sec) |
MIP Gap % |
| 1 | 500 | 100 | 600 | 10% | 10 | 0 | 100 | 511 | 4 | 70% |
| 2 | 500 | 100 | 600 | 50% | 10 | 0 | 100 | 768 | 33 | optimal |
| 3 | 500 | 100 | 600 | 90% | 10 | 0 | 100 | 61 | 10 | optimal |
| 4 | 500 | 250 | 750 | 10% | 10 | 0 | 100 | 2905 | 5 | 84% |
| 5 | 500 | 250 | 750 | 50% | 10 | 0 | 100 | 1968 | 218 | optimal |
| 6 | 500 | 250 | 750 | 90% | 10 | 0 | 100 | 224 | 60 | optimal |
| 7 | 500 | 500 | 1000 | 10% | 10 | 0 | 100 | 7073 | 64000 | 74% |
| 8 | 500 | 500 | 1000 | 50% | 10 | 0 | 100 | 4344 | 784 | optimal |
| 9 | 500 | 500 | 1000 | 90% | 10 | 0 | 100 | 628 | 225 | optimal |