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A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

Author

Listed:
  • Alberto Pajares

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Xavier Blasco

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Juan Manuel Herrero

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Miguel A. Martínez

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

Abstract

In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature ( A r c h i v e U p d a t e P Q , ϵ D x y , A r c h i v e _ n e v M O G A , and t a r g e t S e l e c t ) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:999-:d:545203
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    References listed on IDEAS

    as
    1. Cai Dai & Xiujuan Lei, 2019. "A Multiobjective Brain Storm Optimization Algorithm Based on Decomposition," Complexity, Hindawi, vol. 2019, pages 1-11, January.
    2. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    3. Xiaojun Zhou & Jianpeng Long & Chongchong Xu & Guanbo Jia, 2019. "An External Archive-Based Constrained State Transition Algorithm for Optimal Power Dispatch," Complexity, Hindawi, vol. 2019, pages 1-11, January.
    4. Alberto Pajares & Xavier Blasco & Juan M. Herrero & Gilberto Reynoso-Meza, 2018. "A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA," Complexity, Hindawi, vol. 2018, pages 1-22, October.
    5. 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.
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