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Decoupling Constraint from Two Direction in Evolutionary Constrained Multi-objective Optimization

Real-world Constrained Multi-objective Optimization Problems (CMOPs) often contain multiple constraints, and understanding and utilizing the coupling between these constraints is crucial for solving CMOPs. However, existing Constrained Multi-objective Evolutionary Algorithms (CMOEAs) typically ignore these couplings and treat all constraints as a single aggregate, which lacks interpretability regarding the specific geometric roles of constraints. To address this limitation, we first analyze how different constraints interact and show that the final Constrained Pareto Front (CPF) depends not only on the Pareto fronts of individual constraints but also on the boundaries of infeasible regions. This insight implies that CMOPs with different coupling types must be solved from different search directions. Accordingly, we propose a novel algorithm named Decoupling Constraint from Two Directions (DCF2D). This method periodically detects constraint couplings and spawns an auxiliary population for each relevant constraint with an appropriate search direction. Extensive experiments on seven challenging CMOP benchmark suites and on a collection of real-world CMOPs demonstrate that DCF2D outperforms five state-of-the-art CMOEAs, including existing decoupling-based methods.