A Causal Inference-Based Multi-Objective Evolutionary Algorithm Assisted by Dual-Layer Heterogeneous Graphs☆

In recent years, graph optimization techniques have gained significant attention in multi-objective evolutionary algorithms (MOEAs). However, most existing methods fail to fully leverage the diverse structural and attribute information inherent in graphs. To address this issue, a causal inference-based dual-layer heterogeneous graph-assisted multi-objective evolutionary algorithm (CiDGMO) is proposed. Specifically, the population is represented as a dual-layer heterogeneous graph: the upper layer is a causality-driven directed acyclic graph that captures inter-dimensional dependencies, where dimensions are nodes and causality is represented by edges. The lower layer is an undirected graph based on Euclidean distance, with individuals as nodes and similarity as edges. Meanwhile, a dual-layer node connection strategy based on mutual information fluctuation under random perturbations is introduced to construct robust connections. Furthermore, a causal restricted-based genetic algorithm is presented to avoid undesirable crossover and mutation between individuals and improve search efficiency. In addition, a causal inference-based dot-product attention mechanism is proposed to enhance the model’s capability in node representation learning and further boost the expressive power. Comprehensive experiments conducted on four benchmark suites and six real-world problems demonstrate that CiDGMO significantly outperforms seven state-of-the-art MOEAs, particularly in tackling problems with complex mathematical structures. These findings highlight the promising potential of incorporating causal inference and graph-based modeling into MOEA frameworks for enhanced optimization performance.