Upsampling graph convolutional neural networks enhanced multimodal multi-objective evolutionary algorithm

In recent years, neural networks have been widely adopted to solve multimodal multi-objective optimization problems (MMOPs) due to their good learning ability. However, general neural networks are not good at dealing with population data with non-Euclidean structure. Therefore, this paper proposes a graph convolutional networks (GCN) enhanced multimodal multi-objective evolutionary algorithm, which can utilize GCN to learn the complex distribution of Pareto optimal solution set in the decision space and generate diversified offspring with good convergence through upsampling operation to balance the diversity and the convergence. Specifically, the population is represented as the graph-structured data based on the Euclidean distance in the decision space, and GCN is employed to aggregate the features of solutions and neighbors. Moreover, a linear interpolation is utilized to upsample the aggregation results of GCN, and the offspring with good exploitation performance are obtained. Subsequently, a maximum difference selection mechanism is designed to select solutions in the less dense regions by measuring the distribution similarity between the parent and the offspring, thereby enhancing the diversity. The proposed algorithm is compared with eight advanced algorithms on 56 MMOPs and the location planning problem. The results show that the proposed algorithm performs well in maintaining the diversity and the convergence and finds many best locations in the location planning problem.

Authors

• Lei Yang
• Qianlong Dang
• Erlei Zhang

Keywords

• Multimodal multi-objective optimization
• Graph convolutional network
• Upsampling operation
• Maximum difference selection
• Location planning problem