Large-Scale Sparse Multimodal Multiobjective Optimization via Multi-Stage Search and RL-Assisted Environmental Selection

Multimodal multiobjective optimization problems (MMOPs) are widely encountered in real-world applications. While numerous evolutionary algorithms have been developed to locate equivalent Pareto-optimal solutions, existing Multimodal Multiobjective Evolutionary Algorithms (MMOEAs) often struggle to handle large-scale decision variables and sparse Pareto sets due to the curse of dimensionality and unknown sparsity. To address these challenges, this paper proposes a novel approach named MASR-MMEA, which stands for Large-scale Sparse Multimodal Multiobjective Optimization via Multi-stage Search and Reinforcement Learning (RL)-assisted Environmental Selection. Specifically, to enhance search efficiency, a multi-stage framework is established incorporating three key innovations. First, a dual-strategy genetic operator based on improved hybrid encoding is designed, employing sparse-sensing dynamic redistribution for binary vectors and a sparse fuzzy decision framework for real vectors. Second, an affinity-based elite strategy utilizing Mahalanobis distance is introduced to pair real vectors with compatible binary vectors, increasing the probability of generating superior offspring. Finally, an adaptive sparse environmental selection strategy assisted by Multilayer Perceptron (MLP) reinforcement learning is developed. By utilizing the MLP-generated Guiding Vector (GDV) to direct the evolutionary search toward efficient regions and employing an iteration-based adaptive mechanism to regulate genetic operators, this strategy accelerates convergence. Furthermore, it dynamically quantifies population-level sparsity and adjusts selection pressure through a modified crowding distance mechanism to filter structural redundancy, thereby effectively balancing convergence and multimodal diversity. Comparative studies against six state-of-the-art methods demonstrate that MASR-MMEA significantly outperforms existing approaches in terms of both solution quality and convergence speed on large-scale sparse MMOPs.