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TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem

Author

Listed:
  • Máximo Méndez

    (Instituto Universitario SIANI, Universidad de Las Palmas de Gran Canaria (ULPGC), 35017 Las Palmas de G.C., Spain
    These authors contributed equally to this work.)

  • Mariano Frutos

    (Department of Engineering, Universidad Nacional del Sur and CONICET, Bahía Blanca 8000, Argentina
    These authors contributed equally to this work.)

  • Fabio Miguel

    (Universidad Nacional de Río Negro, Sede Alto Valle y Valle Medio, Villa Regina 8336, Argentina
    These authors contributed equally to this work.)

  • Ricardo Aguasca-Colomo

    (Instituto Universitario SIANI, Universidad de Las Palmas de Gran Canaria (ULPGC), 35017 Las Palmas de G.C., Spain
    These authors contributed equally to this work.)

Abstract

A common technique used to solve multi-objective optimization problems consists of first generating the set of all Pareto-optimal solutions and then ranking and/or choosing the most interesting solution for a human decision maker (DM). Sometimes this technique is referred to as generate first–choose later. In this context, this paper proposes a two-stage methodology: a first stage using a multi-objective evolutionary algorithm (MOEA) to generate an approximate Pareto-optimal front of non-dominated solutions and a second stage, which uses the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) devoted to rank the potential solutions to be proposed to the DM. The novelty of this paper lies in the fact that it is not necessary to know the ideal and nadir solutions of the problem in the TOPSIS method in order to determine the ranking of solutions. To show the utility of the proposed methodology, several original experiments and comparisons between different recognized MOEAs were carried out on a welded beam engineering design benchmark problem. The problem was solved with two and three objectives and it is characterized by a lack of knowledge about ideal and nadir values.

Suggested Citation

  • Máximo Méndez & Mariano Frutos & Fabio Miguel & Ricardo Aguasca-Colomo, 2020. "TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2072-:d:448110
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    1. A. Charnes & W. W. Cooper & R. O. Ferguson, 1955. "Optimal Estimation of Executive Compensation by Linear Programming," Management Science, INFORMS, vol. 1(2), pages 138-151, January.
    2. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    3. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    4. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    5. Khalil Amine, 2019. "Multiobjective Simulated Annealing: Principles and Algorithm Variants," Advances in Operations Research, Hindawi, vol. 2019, pages 1-13, May.
    6. Irina Vinogradova, 2019. "Multi-Attribute Decision-Making Methods as a Part of Mathematical Optimization," Mathematics, MDPI, vol. 7(10), pages 1-21, October.
    7. Octavio Camarena & Erik Cuevas & Marco Pérez-Cisneros & Fernando Fausto & Adrián González & Arturo Valdivia, 2018. "Ls-II: An Improved Locust Search Algorithm for Solving Optimization Problems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-15, October.
    8. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    9. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
    10. Garg, Harish, 2016. "A hybrid PSO-GA algorithm for constrained optimization problems," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 292-305.
    11. Rezaei, Jafar, 2015. "Best-worst multi-criteria decision-making method," Omega, Elsevier, vol. 53(C), pages 49-57.
    12. Cui, Yunfei & Geng, Zhiqiang & Zhu, Qunxiong & Han, Yongming, 2017. "Review: Multi-objective optimization methods and application in energy saving," Energy, Elsevier, vol. 125(C), pages 681-704.
    13. Lin, Yi-Kuei & Yeh, Cheng-Ta, 2012. "Multi-objective optimization for stochastic computer networks using NSGA-II and TOPSIS," European Journal of Operational Research, Elsevier, vol. 218(3), pages 735-746.
    14. Li, Zhaojun & Liao, Haitao & Coit, David W., 2009. "A two-stage approach for multi-objective decision making with applications to system reliability optimization," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1585-1592.
    15. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    16. Mi, Xiaomei & Tang, Ming & Liao, Huchang & Shen, Wenjing & Lev, Benjamin, 2019. "The state-of-the-art survey on integrations and applications of the best worst method in decision making: Why, what, what for and what's next?," Omega, Elsevier, vol. 87(C), pages 205-225.
    17. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    18. 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.
    19. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
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