Data-Driven Evolutionary Algorithm Based on Inductive Graph Neural Networks for Multimodal Multi-Objective Optimization

In multimodal multi-objective optimization problems (MMOPs), multiple solutions on different Pareto optimal solution sets (PSs) are mapped to the same point on the Pareto front. Considering these different solutions can provide users with richer decisions, the search of multiple PSs is crucial when solving MMOPs. To this end, many multimodal multi-objective evolutionary algorithms (MMOEAs) often employ intricate mechanisms to maintain the diversity of the offspring in mating selection, but ignore to learn PSs. In this paper, a data-driven evolutionary algorithm based on inductive graph neural networks (DEA-IGNN) is proposed to solve MMOPs, which successfully learns the PSs topology by the graph structure to generate offspring with good performance. Specifically, a graph topology construction method based on Euclidean distance in the decision space is designed. It determines the neighborhood by calculating the Euclidean distance of individuals in the decision space and establishes the topological relationships to construct the graphs representing of population distribution. On this basis, a model based on inductive graph neural networks is constructed to assist offspring reproduction, which can learn unknown nodes by sampling and aggregating existing information. Moreover, a data-driven reproduction strategy is proposed to predict offspring with the good diversity and convergence, which uses the traditional variation operators to generate training data and adopts these data to train the model. The proposed DEA-IGNN is implemented and compared with eleven competitive MMOEAs on three test suites and a practical problem. The experimental results show that DEA-IGNN has good performance.