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A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

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Abstract

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes a strong assumption and reduces the numbers of constraints and binary variables of the MIP problem. By conducting numerical experiments, we find that the proposed approach is more accurate and faster than the previous MIP approach. The proposed MIP problem can be efficiently solved with current state-of-the-art MIP solvers when the objective function is convex or linear.

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Notes

  1. The source code can be found at the author’s website: https://kuanlyu.github.io/otherwise/.

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Acknowledgements

The authors would like to thank the anonymous referees for valuable comments and suggestions. This research is supported in part by Grant-in-Aid for Science Research (A) 19H00808 and Grant-in-Aid for Scientific Research (C) 17K01272 of Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Tokyo Institute of Technology, 2 Chome-12-1 Ookayama, Meguro City, Tokyo, Japan

    Kuan Lu & Shinji Mizuno

  2. Tokyo University of Science, 1 Chome-3 Kagurazaka, Shinjuku City, Tokyo, Japan

    Jianming Shi

Authors
  1. Kuan Lu
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  2. Shinji Mizuno
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  3. Jianming Shi
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Correspondence to Kuan Lu.

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Lu, K., Mizuno, S. & Shi, J. A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem. Optim Lett 14, 2323–2333 (2020). https://doi.org/10.1007/s11590-020-01554-7

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