An indicator-based multi-objective evolutionary algorithm assisted by improved graph convolutional networks

Abstract

Recently, graph convolutional networks (GCN) have attracted significant attention due to their superior performance in handling non-Euclidean spaces, which enables GCN to model and analyze complex data structures that cannot be handled by traditional methods. Neural network-based multi-objective evolutionary algorithms (NNMOEAs) have made significant strides, predominantly focusing on mapping the decision space to the objective space, but may fail to focus on the interconnectedness of solutions within the decision space. To address this problem, this paper proposes a two-stage multi-objective optimization algorithm that utilizes graph convolutional networks to enhance population evolution. In the initial stage, the algorithm employs cosine similarity to represent the population as graph-structured data. A hypervolume-guided self-attention update mechanism is then introduced to balance exploration and exploitation, achieved by establishing an exploratory neighborhood population alongside an expanded neighborhood population. In the subsequent stage, a key node detection strategy is implemented, which considers both the global influence and local mediation roles of nodes. This strategy selects individuals with highly concentrated information to generate new solutions, thereby facilitating a thorough exploration of the solution space. The proposed algorithm is evaluated against five state-of-the-art MOEAs across five benchmark test suites and five real-world problems. The experimental results demonstrate its superior performance in addressing robust, variable linkages and imbalance mapping multi-objective optimization problems, as well as its feasibility in practical problems.