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Generalized Type-2 Fuzzy Approach for Parameter Adaptation in the Whale Optimization Algorithm

Author

Listed:
  • Leticia Amador-Angulo

    (Division of Graduate Studies and Research, Tijuana Institute of Technology, TecNM, Tijuana 22379, Mexico)

  • Oscar Castillo

    (Division of Graduate Studies and Research, Tijuana Institute of Technology, TecNM, Tijuana 22379, Mexico)

  • Patricia Melin

    (Division of Graduate Studies and Research, Tijuana Institute of Technology, TecNM, Tijuana 22379, Mexico)

  • Zong Woo Geem

    (College of IT Convergence, Gachon University, Seongnam 13120, Republic of Korea)

Abstract

An enhanced whale optimization algorithm (WOA) through the implementation of a generalized type-2 fuzzy logic system (GT2FLS) is outlined. The initial idea is to improve the efficacy of the original WOA using a GT2FLS to find the optimal values of the r → 1 and r → 2 parameters of the WOA, for the case of optimizing mathematical functions. In the WOA algorithm, r → 1 is a variable that affects the new position of the whale in the search space, in this case, affecting the exploration, and r → 2 is a variable that has an effect on finding the local optima, which is an important factor for the exploration. The efficiency of a fuzzy WOA with a GT2FLS (FWOA-GT2FLS) is highlighted by presenting the excellent results of the case study of the benchmark function optimization. A relevant analysis and comparison with a bio-inspired algorithm based on artificial bees is also presented. Statistical tests and comparisons with other bio-inspired algorithms and the initial WOA, with type-1 FLS (FWOA-T1FLS) and interval type-2 FLS (FWOA-IT2FLS), are presented. For each of the methodologies, the metric for evaluation is the average of the minimum squared errors.

Suggested Citation

  • Leticia Amador-Angulo & Oscar Castillo & Patricia Melin & Zong Woo Geem, 2024. "Generalized Type-2 Fuzzy Approach for Parameter Adaptation in the Whale Optimization Algorithm," Mathematics, MDPI, vol. 12(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:4031-:d:1549993
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    References listed on IDEAS

    as
    1. Zoubida Benmamoun & Khaoula Khlie & Mohammad Dehghani & Youness Gherabi, 2024. "WOA: Wombat Optimization Algorithm for Solving Supply Chain Optimization Problems," Mathematics, MDPI, vol. 12(7), pages 1-61, April.
    2. Lu Zhao & Jiangjun Liu & Yuan Li & Tudor Barbu, 2024. "Application of Improved WOA in Hammerstein Parameter Resolution Problems under Advanced Mathematical Theory," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-11, February.
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