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A Numerical Study on MIP Approaches over the Efficient Set

  • Kuan LuEmail author
  • Shinji Mizuno
  • Jianming Shi
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose an equivalent mixed integer programming (MIP) problem and compute an optimal solution by solving the MIP problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes an assumption which lets a more general class of problem can be solved and reduces the size of the MIP problem. By conducting the experiments on a well-known application of the OE problem, the minimum maximal flow problem, we find that the proposed approach is more accurate and faster. The MIP problem can be efficiently solved by current state-of-the-art MIP solvers when the objective function is convex or linear.

Keywords

Gloal optimization Multiobjective programming Efficient set Linear complementarity conditions Mixed integer programming 

Notes

Acknowledgment

This research is supported in part by Grant-in-Aid for Science Research (A) 26242027 and Grant-in-Aid for Scientific Research (C) 17K01272 of Japan Society for the Promotion of Science.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Tokyo University of ScienceTokyoJapan

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