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A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm

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  • Ana Ruiz
  • Rubén Saborido
  • Mariano Luque

Abstract

When solving multiobjective optimization problems, preference-based evolutionary multiobjective optimization (EMO) algorithms introduce preference information into an evolutionary algorithm in order to focus the search for objective vectors towards the region of interest of the Pareto optimal front. In this paper, we suggest a preference-based EMO algorithm called weighting achievement scalarizing function genetic algorithm (WASF-GA), which considers the preferences of the decision maker (DM) expressed by means of a reference point. The main purpose of WASF-GA is to approximate the region of interest of the Pareto optimal front determined by the reference point, which contains the Pareto optimal objective vectors that obey the preferences expressed by the DM in the best possible way. The proposed approach is based on the use of an achievement scalarizing function (ASF) and on the classification of the individuals into several fronts. At each generation of WASF-GA, this classification is done according to the values that each solution takes on the ASF for the reference point and using different weight vectors. These vectors of weights are selected so that the vectors formed by their inverse components constitute a well-distributed representation of the weight vectors space. The efficiency and usefulness of WASF-GA is shown in several test problems in comparison to other preference-based EMO algorithms. Regarding a metric based on the hypervolume, we can say that WASF-GA has outperformed the other algorithms considered in most of the problems. Copyright Springer Science+Business Media New York 2015

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  • Ana Ruiz & Rubén Saborido & Mariano Luque, 2015. "A preference-based evolutionary algorithm for multiobjective optimization: the weighting achievement scalarizing function genetic algorithm," Journal of Global Optimization, Springer, vol. 62(1), pages 101-129, May.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:1:p:101-129
    DOI: 10.1007/s10898-014-0214-y
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    5. Molina, Julin & Santana, Luis V. & Hernandez-Daz, Alfredo G. & Coello Coello, Carlos A. & Caballero, Rafael, 2009. "g-dominance: Reference point based dominance for multiobjective metaheuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 685-692, September.
    6. Figueira, J.R. & Liefooghe, A. & Talbi, E.-G. & Wierzbicki, A.P., 2010. "A parallel multiple reference point approach for multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 205(2), pages 390-400, September.
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    Cited by:

    1. Pinto, F.S. & Figueira, J.R. & Marques, R.C., 2015. "A multi-objective approach with soft constraints for water supply and wastewater coverage improvements," European Journal of Operational Research, Elsevier, vol. 246(2), pages 609-618.
    2. Lu Chen & Kaisa Miettinen & Bin Xin & Vesa Ojalehto, 2023. "Comparing reference point based interactive multiobjective optimization methods without a human decision maker," Journal of Global Optimization, Springer, vol. 85(3), pages 757-788, March.
    3. 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.
    4. Ernestas Filatovas & Algirdas Lančinskas & Olga Kurasova & Julius Žilinskas, 2017. "A preference-based multi-objective evolutionary algorithm R-NSGA-II with stochastic local search," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 859-878, December.
    5. Ana B. Ruiz & Rubén Saborido & José D. Bermúdez & Mariano Luque & Enriqueta Vercher, 2020. "Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences," Journal of Global Optimization, Springer, vol. 76(2), pages 295-315, February.
    6. He, Li-Jun & Ju, Xue-Wei & Zhang, Wei-Bo, 2018. "A fitness assignment strategy based on the grey and entropy parallel analysis and its application to MOEAAuthor-Name: Zhu, Guang-Yu," European Journal of Operational Research, Elsevier, vol. 265(3), pages 813-828.
    7. S. Dutta & B.C. Sahoo & Rajashree Mishra & S. Acharya, 2016. "Fuzzy Stochastic Genetic Algorithm for Obtaining Optimum Crops Pattern and Water Balance in a Farm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4097-4123, September.

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