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

Leticia Amador-Angulo, Oscar Castillo, Patricia Melin and Zong Woo Geem ()
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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

Mathematics, 2024, vol. 12, issue 24, 1-20

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.

Keywords: type-2 fuzzy logic; whale optimization; adaptation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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