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The directed search method for multi-objective memetic algorithms

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Listed:
  • Oliver Schütze
  • Adanay Martín
  • Adriana Lara
  • Sergio Alvarado
  • Eduardo Salinas
  • Carlos Coello

Abstract

We propose a new iterative search procedure for the numerical treatment of unconstrained multi-objective optimization problems (MOPs) which steers the search along a predefined direction given in objective space. Based on this idea we will present two methods: directed search (DS) descent which seeks for improvements of the given model, and a novel continuation method (DS continuation) which allows to search along the Pareto set of a given MOP. One advantage of both methods is that they can be realized with and without gradient information, and if neighborhood information is available the computation of the search direction comes even for free. The latter makes our algorithms interesting candidates for local search engines within memetic strategies. Further, the approach can be used to gain some interesting insights into the nature of multi-objective stochastic local search which may explain one facet of the success of multi-objective evolutionary algorithms (MOEAs). Finally, we demonstrate the strength of the method both as standalone algorithm and as local search engine within a MOEA. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Oliver Schütze & Adanay Martín & Adriana Lara & Sergio Alvarado & Eduardo Salinas & Carlos Coello, 2016. "The directed search method for multi-objective memetic algorithms," Computational Optimization and Applications, Springer, vol. 63(2), pages 305-332, March.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:2:p:305-332
    DOI: 10.1007/s10589-015-9774-0
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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.
    2. Federico Zuiani & Massimiliano Vasile, 2013. "Multi Agent Collaborative Search based on Tchebycheff decomposition," Computational Optimization and Applications, Springer, vol. 56(1), pages 189-208, September.
    3. 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.
    4. Honggang Wang, 2013. "Zigzag Search for Continuous Multiobjective Optimization," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 654-665, November.
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    Cited by:

    1. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.
    2. Alejandro Alvarado-Iniesta & Luis Gonzalo Guillen-Anaya & Luis Alberto Rodríguez-Picón & Raul Ñeco-Caberta, 2020. "Multi-objective optimization of an engine mount design by means of memetic genetic programming and a local exploration approach," Journal of Intelligent Manufacturing, Springer, vol. 31(1), pages 19-32, January.
    3. 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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