Progress in presolving for mixed integer programming
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This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 % on affected instances while not degrading the performance on the remaining problems.
Mathematics Subject ClassificationPrimary 90C11 90C10 Secondary 90-04 90-08 90C90
The authors would like to thank the anonymous reviewers for helpful comments on the paper. The work for this article has been partly conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM). Finally, we thank the DFG for their support within Projects A05, B07, and Z02 in CRC TRR 154.
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