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Progressively strengthening and tuning MIP solvers for reoptimization

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Abstract

This paper explores reoptimization techniques for solving sequences of similar mixed integer programs (MIPs) more effectively. Traditionally, these MIPs are solved independently, without capitalizing on information from previously solved instances. Our approach focuses on primal bound improvements by reusing the solutions of the previously solved instances, as well as dual bound improvements by reusing the branching history and automating parameter tuning. We also describe ways to improve the solver performance by extending ideas from reliability branching to generate better pseudocosts. Our reoptimization approach, crafted for the MIP 2023 workshop computational competition, was honored with the first prize. In this paper, we thoroughly analyze the performance of each technique and their combined impact on the solver’s performance. Finally, we present ways to extend our techniques in practice for further improvements.

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Data availability

The datasets analysed for the current study are available in the github repository, https://github.com/krooonal/mipcc2023/tree/MPCPaper.

Code availability

The code used for the current study is available in the github repository, https://github.com/krooonal/mipcc2023/tree/MPCPaper.

Notes

  1. For the series RHS 2 and RHS 4, the shifted geometric means of solving times are higher than the time limit. This indicates that SCIP could not solve most of these instances in the given time limit.

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Acknowledgements

The author received financial support from the Canada Excellence Research Chair (CERC), Polytechnique Montreal and the computational resources for experimental evaluation were provided by CERC. The author would also like to thank Prof. Andrea Lodi, Prof. Guy Desaulniers, and the anonymous reviewers for their helpful comments.

Funding

Partial financial support was received from Canada Excellence Research Chair (CERC), Polytechnique Montreal. The computational resources for experimental evaluation were provided by CERC.

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  1. CERC, Polytechnique Montréal, Montreal, QC, Canada

    Krunal Kishor Patel

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  1. Krunal Kishor Patel
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Krunal Kishor Patel designed, implemented, and tested the ideas presented in this paper.

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Correspondence to Krunal Kishor Patel.

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Appendix: Detailed results

Appendix: Detailed results

See Tables 13, 14, 15, 16.

Table 13 Effects of providing solution hints on total scores
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Table 14 Effects of reusing branching history and strong branching for the first instance on total scores
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Table 15 Effects of automated parameter tuning on total scores
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Table 16 Effects of turning off inefficient solver parts on total scores
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We present the aggregated statistics for techniques presented in this paper in Table 17 (grouped by changing component), Table 18 (grouped by geometric mean of solve time in BASE), and Table 19 (grouped by BASE score). Each table shows the aggregated BASE total score and percentage improvements caused by each technique. Since the number of series for each group is too small, we advise readers to be cautious while making generalized conclusions based on these tables (e.g., TURNOFF works best when RHS is changing).

Table 17 Aggregated results for changing components
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Table 18 Aggregated results for series grouped by geometric means of solving time in BASE
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Table 19 Aggregated results for series grouped by average BASE scores
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Patel, K.K. Progressively strengthening and tuning MIP solvers for reoptimization. Math. Prog. Comp. (2024). https://doi.org/10.1007/s12532-024-00253-z

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