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The hypervolume based directed search method for multi-objective optimization problems

Author

Listed:
  • Oliver Schütze

    (CINVESTAV-IPN)

  • Víctor Adrián Sosa Hernández

    (CINVESTAV-IPN)

  • Heike Trautmann

    (University of Münster)

  • Günter Rudolph

    (Technische Universität Dortmund)

Abstract

We present a new hybrid evolutionary algorithm for the effective hypervolume approximation of the Pareto front of a given differentiable multi-objective optimization problem. Starting point for the local search (LS) mechanism is a new division of the decision space as we will argue that in each of these regions a different LS strategy seems to be most promising. For the LS in two out of the three regions we will utilize and adapt the Directed Search method which is capable of steering the search into any direction given in objective space and which is thus well suited for the problem at hand. We further on integrate the resulting LS mechanism into SMS-EMOA, a state-of-the-art evolutionary algorithm for hypervolume approximations. Finally, we will present some numerical results on several benchmark problems with two and three objectives indicating the strength and competitiveness of the novel hybrid.

Suggested Citation

  • Oliver Schütze & Víctor Adrián Sosa Hernández & Heike Trautmann & Günter Rudolph, 2016. "The hypervolume based directed search method for multi-objective optimization problems," Journal of Heuristics, Springer, vol. 22(3), pages 273-300, June.
    • Handle: RePEc:spr:joheur:v:22:y:2016:i:3:d:10.1007_s10732-016-9310-0
    DOI: 10.1007/s10732-016-9310-0
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    References listed on IDEAS

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    1. S. Schäffler & R. Schultz & K. Weinzierl, 2002. "Stochastic Method for the Solution of Unconstrained Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 209-222, July.
    2. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
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    Cited by:

    1. Capitanescu, F. & Marvuglia, A. & Benetto, E. & Ahmadi, A. & Tiruta-Barna, L., 2017. "Linear programming-based directed local search for expensive multi-objective optimization problems: Application to drinking water production plants," European Journal of Operational Research, Elsevier, vol. 262(1), pages 322-334.
    2. Ricardo Landa & Giomara Lárraga & Gregorio Toscano, 2019. "Use of a goal-constraint-based approach for finding the region of interest in multi-objective problems," Journal of Heuristics, Springer, vol. 25(1), pages 107-139, February.
    3. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.

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