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Deep reinforcement learning assisted adaptive guided vectors for large-scale multimodal multi-objective optimization
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DOI：10.1016/j.swevo.2026.102485.png)
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Abstract
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Multimodal multi-objective optimization problems (MMOPs) aim to identify multiple equivalent Pareto solution sets (PSs) in the decision space with the same Pareto front (PF) in the objective space. As the number of decision vectors increases, traditional multimodal multi-objective evolutionary algorithms (MMEAs) often become ineffective because distance-based diversity measures lose their discriminative ability in large-scale MMOPs (LMMOPs) with high-dimensional decision vectors. To address this challenge, we propose an adaptive guided vector assisted large-scale multimodal multi-objective evolutionary using deep reinforcement learning, termed as AGVLMMEA, for solving LMMOPs. A deep Q-network is designed in AGVLMMEA to adaptively select distinct guided vectors for guiding the direction of evolutionary search. Subsequently, a dimension-analysis two complementary operator including a global exploration operator and a local exploitation operator is designed, where a global exploration operator performs full-dimensional variation to improve global exploration and a local refinement operator focuses on important dimensions identified through guided-vector analysis to amplify local search. Finally, a similarity-based dynamic dividing and merging evolutionary mechanism (DAM) is incorporated into a multi-population co-evolutionary framework, and it dynamically adjusts the number of subpopulations to preserve multiple equivalent PSs. Experimental results on 15 LMMOPs test problems demonstrate that AGVLMMEA consistently achieves superior decision space diversity while maintaining competitive convergence in the objective space. Compared with seven state-of-the-art algorithms, AGVLMMEA more effectively discovers and preserves multiple equivalent PSs, particularly in high-dimensional space.
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