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Enhanced directed search: a continuation method for mixed-integer multi-objective optimization problems

Author

Listed:
  • Honggang Wang

    (University of La Verne)

  • David Laredo

    (CINVESTAV-IPN)

  • Oliver Cuate

    (CINVESTAV-IPN)

  • Oliver Schütze

    (CINVESTAV-IPN)

Abstract

Multi-objective optimization problems (MOPs) commonly arise in various applications of engineering and management fields. Many real-world MOPs are mixed-integer multi-objective optimization problems (MMOP), where the solution space consists of real and integer decision variables. The research regarding MMOPs is still scarce due to the mixture nature of the solution space and difficulty of finding the set of trade-off solutions. In this work we propose a continuation based method that efficiently solves MMOP problems. Our method, called Enhanced Directed Search (EDS), is capable of steering the search along a predefined direction along the Pareto front in the objective function space. EDS traces the Pareto front by following closest predictor and corrector solutions in the course of optimization. By searching around the objective function boundary, EDS can solve problems with $$k > 2$$ k > 2 objectives. With five example problems widely studied in the literature, we demonstrate that EDS outperforms the recently developed Direct Zig Zag algorithm and the popular NSGA-II method.

Suggested Citation

  • Honggang Wang & David Laredo & Oliver Cuate & Oliver Schütze, 2019. "Enhanced directed search: a continuation method for mixed-integer multi-objective optimization problems," Annals of Operations Research, Springer, vol. 279(1), pages 343-365, August.
    • Handle: RePEc:spr:annopr:v:279:y:2019:i:1:d:10.1007_s10479-018-3060-3
    DOI: 10.1007/s10479-018-3060-3
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    References listed on IDEAS

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    1. Honggang Wang, 2013. "Zigzag Search for Continuous Multiobjective Optimization," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 654-665, November.
    2. Ghodsypour, S. H. & O'Brien, C., 2001. "The total cost of logistics in supplier selection, under conditions of multiple sourcing, multiple criteria and capacity constraint," International Journal of Production Economics, Elsevier, vol. 73(1), pages 15-27, August.
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    Cited by:

    1. Zhe Liu & Shurong Li, 2022. "A numerical method for interval multi-objective mixed-integer optimal control problems based on quantum heuristic algorithm," Annals of Operations Research, Springer, vol. 311(2), pages 853-898, April.

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