A Chaotic Decomposition-Based Approach for Enhanced Multi-Objective Optimization

Javad Alikhani Koupaei () and Mohammad Javad Ebadi ()
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Javad Alikhani Koupaei: Department of Mathematics, Payame Noor University, Tehran P.O. Box 19395-3697, Iran
Mohammad Javad Ebadi: Department of Mathematics, Chabahar Maritime University, Chabahar 9971778631, Iran

Mathematics, 2025, vol. 13, issue 5, 1-20

Abstract: Multi-objective optimization problems often face challenges in balancing solution accuracy, computational efficiency, and convergence speed. Many existing methods struggle with achieving an optimal trade-off between exploration and exploitation, leading to premature convergence or excessive computational costs. To address these issues, this paper proposes a chaotic decomposition-based approach that leverages the ergodic properties of chaotic maps to enhance optimization performance. The proposed method consists of three key stages: (1) chaotic sequence initialization, which generates a diverse population to enhance the global search while reducing computational costs; (2) chaos-based correction, which integrates a three-point operator (TPO) and a local improvement operator (LIO) to refine the Pareto front and balance the exploration–exploitation trade-offs; and (3) Tchebycheff decomposition-based updating, ensuring efficient convergence toward optimal solutions. To validate the effectiveness of the proposed method, we conducted extensive experiments on a suite of benchmark problems and compared its performance with several state-of-the-art methods. The evaluation metrics, including inverted generational distance (IGD), generational distance (GD), and spacing (SP), demonstrated that the proposed method achieves competitive optimization accuracy and efficiency. While maintaining computational feasibility, our approach provides a well-balanced trade-off between exploration and exploitation, leading to improved solution diversity and convergence stability. The results establish the proposed algorithm as a promising alternative for solving multi-objective optimization problems.

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