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Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results

Author

Listed:
  • Günter Rudolph

    (TU Dortmund University)

  • Oliver Schütze

    (CINVESTAV IPN)

  • Christian Grimme

    (University of Münster)

  • Christian Domínguez-Medina

    (National Polytechnic Institute)

  • Heike Trautmann

    (University of Münster)

Abstract

One main task in evolutionary multiobjective optimization (EMO) is to obtain a suitable finite size approximation of the Pareto front which is the image of the solution set, termed the Pareto set, of a given multiobjective optimization problem. In the technical literature, the characteristic of the desired approximation is commonly expressed by closeness to the Pareto front and a sufficient spread of the solutions obtained. In this paper, we first make an effort to show by theoretical and empirical findings that the recently proposed Averaged Hausdorff (or $$\Delta _p$$ Δ p -) indicator indeed aims at fulfilling both performance criteria for bi-objective optimization problems. In the second part of this paper, standard EMO algorithms combined with a specialized archiver and a postprocessing step based on the $$\Delta _p$$ Δ p indicator are introduced which sufficiently approximate the $$\Delta _p$$ Δ p -optimal archives and generate solutions evenly spread along the Pareto front.

Suggested Citation

  • Günter Rudolph & Oliver Schütze & Christian Grimme & Christian Domínguez-Medina & Heike Trautmann, 2016. "Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results," Computational Optimization and Applications, Springer, vol. 64(2), pages 589-618, June.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9815-8
    DOI: 10.1007/s10589-015-9815-8
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    References listed on IDEAS

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    1. Beume, Nicola & Naujoks, Boris & Emmerich, Michael, 2007. "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1653-1669, September.
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    Cited by:

    1. 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.
    2. Guerreiro, Andreia P. & Fonseca, Carlos M., 2020. "An analysis of the Hypervolume Sharpe-Ratio Indicator," European Journal of Operational Research, Elsevier, vol. 283(2), pages 614-629.
    3. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
    4. Johan M. Bogoya & Andrés Vargas & Oliver Schütze, 2019. "The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review," Mathematics, MDPI, vol. 7(10), pages 1-35, September.

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