Ranking Constraints via Topological Dual-Directional Search in Evolutionary Multi-Objective Optimization

Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In reality, constraints play different roles: some directly shape the final CPF, some create infeasible obstacles, while others are irrelevant. To exploit this insight, we propose a novel algorithm named RCCMO, which sequentially performs unconstrained exploration, single-constraint exploitation, and full-constraint refinement. The core innovation of RCCMO lies in a constraint prioritization method derived from these geometric insights, seamlessly coupled with a unique dual-directional search mechanism. Specifically, RCCMO first prioritizes constraints that constitute the final CPF, approaching them from the evolutionary direction (optimizing objectives) to locate the CPF directly shaped by single-constraint boundaries. Subsequently, for constraints that merely hinder the population's progress, RCCMO searches from the anti-evolutionary direction (targeting the infeasible boundaries where hindering constraints intersect with the CPF) to effectively discover how these constraints obstruct and form the final CPF. Meanwhile, irrelevant constraints are intentionally bypassed. Furthermore, a series of specialized mechanisms are proposed to accelerate the algorithm's execution, reduce heuristic misjudgments, and dynamically adjust search directions in real time. Extensive experiments on 5 benchmark test suites and 29 real-world CMOPs demonstrate that RCCMO significantly outperforms seven state-of-the-art algorithms.

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.