Masked Genetic Operators with Causal Grouping for Constrained Multi-Objective Optimization

Uncovering the direct causal relationships between decision variables and optimization objectives can significantly simplify the complexity of optimization problems. However, most existing constrained multi-objective evolutionary algorithms (CMOEAs) fail to address constrained multi-objective optimization from this perspective. To bridge this gap, this study introduces a novel algorithm, CI-CMOEA (Causal Intervention-based CMOEA), which leverages causal intervention techniques to enhance optimization performance. CI-CMOEA begins by constructing a causal relationship network that captures the interactions between decision variables and optimization objectives. Using this network, a genetic operator with a causal relationship mask is designed to group decision variables based on their causal impact on the objectives. By focusing genetic operations on key variables with significant causal influence, the algorithm effectively guides the evolutionary optimization process towards better solutions. To further improve performance, CI-CMOEA employs a dual-population collaboration mechanism. One population operates under relaxed epsilon constraints to explore the solution space, while the other disregards constraints to enhance convergence. Preliminary experiments on the LIR-CMOP test suite demonstrate that CI-CMOEA not only accurately identifies the causal relationships between decision variables and objectives but also outperforms eight state-of-the-art CMOEAs in terms of IGD, IGD+ and HV metrics, showcasing its superior optimization performance and reliability.