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Archivers for the representation of the set of approximate solutions for MOPs

Author

Listed:
  • O. Schütze

    (Cinvestav-IPN)

  • C. Hernández

    (Cinvestav-IPN)

  • E-G. Talbi

    (University of Lille 1)

  • J. Q. Sun

    (University of California)

  • Y. Naranjani

    (University of California)

  • F.-R. Xiong

    (Tianjin University)

Abstract

In this paper we address the problem of computing suitable representations of the set of approximate solutions of a given multi-objective optimization problem via stochastic search algorithms. For this, we will propose different archiving strategies for the selection of the candidate solutions maintained by the generation process of the stochastic search process, and investigate them further on analytically and empirically. For all archivers we will provide upper bounds on the approximation quality as well as on the cardinality of the limit solution set. We conclude this work by a comparative study on some test problems in order to visualize the effect of all novel archiving strategies.

Suggested Citation

  • O. Schütze & C. Hernández & E-G. Talbi & J. Q. Sun & Y. Naranjani & F.-R. Xiong, 2019. "Archivers for the representation of the set of approximate solutions for MOPs," Journal of Heuristics, Springer, vol. 25(1), pages 71-105, February.
    • Handle: RePEc:spr:joheur:v:25:y:2019:i:1:d:10.1007_s10732-018-9383-z
    DOI: 10.1007/s10732-018-9383-z
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    References listed on IDEAS

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    2. Engau, Alexander & Wiecek, Margaret M., 2007. "Generating [epsilon]-efficient solutions in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1566-1579, March.
    3. White, D.J., 1998. "Epsilon-dominating solutions in mean-variance portfolio analysis," European Journal of Operational Research, Elsevier, vol. 105(3), pages 457-466, March.
    4. 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.
    5. Laumanns, Marco & Zenklusen, Rico, 2011. "Stochastic convergence of random search methods to fixed size Pareto front approximations," European Journal of Operational Research, Elsevier, vol. 213(2), pages 414-421, September.
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    Cited by:

    1. Alberto Pajares & Xavier Blasco & Juan Manuel Herrero & Miguel A. Martínez, 2021. "A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization," Mathematics, MDPI, vol. 9(9), pages 1-28, April.
    2. Nicolas Dupin & Frank Nielsen & El-Ghazali Talbi, 2021. "Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front," Mathematics, MDPI, vol. 9(4), pages 1-30, February.
    3. Carlos Ignacio Hernández Castellanos & Oliver Schütze & Jian-Qiao Sun & Guillermo Morales-Luna & Sina Ober-Blöbaum, 2020. "Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping," Mathematics, MDPI, vol. 8(11), pages 1-18, November.

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