Variational graph autoencoder-driven balancing strategy for multimodal multi-objective optimization - Yang, Lei; Zhang, Erlei; Dang, Qianlong (Information sciences, 2025)
Multimodal multi-objective optimization aims to balance the diversity and the convergence to obtain multiple complete and uniform Pareto optimal solution sets. In recent years, using machine learning models to improve the performance of evolutionary algorithms has become a hot topic. However, few studies utilize machine learning models to solve the imbalance problem between the diversity and the convergence in multimodal multi-objective optimization. Therefore, this paper proposes a multimodal multi-objective evolutionary algorithm driven by variational graph autoencoder (VGAE), which can reproduce diversified offspring with good convergence by reconstructing the parent population. In reproduction, the parent population is constructed into graph data, and the VGAE is adopted to map the graph data to the latent space, obtaining the distribution information represented by the low-dimensional vector. By sampling the distribution, the VGAE can generate the offspring with the similar distribution to the parent, which can fill the less dense regions in the decision space and improve the exploitation ability. In archive updating, the convergence state based on the inverted generation distance between the non-dominated solutions and the worst dominated solutions is defined, and the state information of the convergence archive is transferred to the diversity archive to determine the dynamic niche. This niche comprehensively considers the distribution state and convergence degree of solutions in the diversity and convergence archives, which is employed to calculate the local convergence quality, retaining more promising solutions. The results of 48 benchmark problems and a practical application show that the proposed algorithm outperforms eight competitive algorithms.