Analyzing and Overcoming Local Optima in Complex Multi-Objective Optimization by Decomposition-Based Evolutionary Algorithms

• URL: http://arxiv.org/abs/2404.08501v1
• Date: Fri, 12 Apr 2024 14:29:45 GMT
• Title: Analyzing and Overcoming Local Optima in Complex Multi-Objective Optimization by Decomposition-Based Evolutionary Algorithms
• Authors: Ting Dong, Haoxin Wang, Hengxi Zhang, Wenbo Ding,
• Abstract summary: Multi-objective Evolutionary Algorithms (MOEADs) often converge to local optima, limiting solution diversity. We introduce an innovative RP selection strategy, the Vector-Guided Weight-Hybrid method, designed to overcome the local optima issue. Our research comprises two main experimental components: an ablation involving 14 algorithms within the MOEADs framework from 2014 to 2022 to validate our theoretical framework, and a series empirical tests to evaluate the effectiveness of our proposed method against both traditional and cutting-edge alternatives.
• Score: 5.153202024713228
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When addressing the challenge of complex multi-objective optimization problems, particularly those with non-convex and non-uniform Pareto fronts, Decomposition-based Multi-Objective Evolutionary Algorithms (MOEADs) often converge to local optima, thereby limiting solution diversity. Despite its significance, this issue has received limited theoretical exploration. Through a comprehensive geometric analysis, we identify that the traditional method of Reference Point (RP) selection fundamentally contributes to this challenge. In response, we introduce an innovative RP selection strategy, the Weight Vector-Guided and Gaussian-Hybrid method, designed to overcome the local optima issue. This approach employs a novel RP type that aligns with weight vector directions and integrates a Gaussian distribution to combine three distinct RP categories. Our research comprises two main experimental components: an ablation study involving 14 algorithms within the MOEADs framework, spanning from 2014 to 2022, to validate our theoretical framework, and a series of empirical tests to evaluate the effectiveness of our proposed method against both traditional and cutting-edge alternatives. Results demonstrate that our method achieves remarkable improvements in both population diversity and convergence.

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