Enhancing Multi-Objective Optimization: A Decomposition-Based Approach Using the Whale Optimization Algorithm

Jorge Ramos-Frutos, Angel Casas-Ordaz, Saúl Zapotecas-Martínez (), Diego Oliva (), Arturo Valdivia-González, Abel García-Nájera and Marco Pérez-Cisneros ()
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Jorge Ramos-Frutos: Departamento de Ingeniería Industrial, Tecnológico Nacional de México, Instituto Tecnológico de Jiquilpan, Jiquilpan 59514, Michoacán, Mexico
Angel Casas-Ordaz: División de Tecnologías para la Integración Ciber-Humana, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Saúl Zapotecas-Martínez: Computer Science Department, Instituto Nacional de Astrofísica Óptica y Electrónica, Luis Enrique Erro No. 1, Sta. María Tonantzintla, San Andrés Cholula 72840, Puebla, Mexico
Diego Oliva: División de Tecnologías para la Integración Ciber-Humana, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Arturo Valdivia-González: División de Tecnologías para la Integración Ciber-Humana, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Abel García-Nájera: Departmento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Unidad Cuajimalpa, Av. Vasco de Quiroga 4871, Santa Fe Cuajimalpa 05348, Ciudad de México, Mexico
Marco Pérez-Cisneros: División de Tecnologías para la Integración Ciber-Humana, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico

Mathematics, 2025, vol. 13, issue 5, 1-25

Abstract: Optimization techniques aim to identify optimal solutions for a given problem. In single-objective optimization, the best solution corresponds to the one that maximizes or minimizes the objective function. However, when dealing with multi-objective optimization, particularly when the objectives are conflicting, identifying the best solution becomes significantly more complex. In such cases, exact or analytical methods are often impractical, leading to the widespread use of heuristic and metaheuristic approaches to identify optimal or near-optimal solutions. Recent advancements have led to the development of various nature-inspired metaheuristics designed to address these challenges. Among these, the Whale Optimization Algorithm (WOA) has garnered significant attention. An adapted version of the WOA has been proposed to handle multi-objective optimization problems. This work extends the WOA to tackle multi-objective optimization by incorporating a decomposition-based approach with a cooperative mechanism to approximate Pareto-optimal solutions. The multi-objective problem is decomposed into a series of scalarized subproblems, each with a well-defined neighborhood relationship. Comparative experiments with seven state-of-the-art bio-inspired optimization methods demonstrate that the proposed decomposition-based multi-objective WOA consistently outperforms its counterparts in both real-world applications and widely used benchmark test problems.

Keywords: multi-objective evolutionary optimization; decomposition-based optimization; whale optimization algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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