Lianghao Li | Searcharxiv

arXiv2026

Decoupling Constraints from Two Directions for Evolutionary Constrained Multi-objective Optimization

Real-world constrained multi-objective optimization problems (CMOPs) commonly involve multiple constraints, and understanding and exploiting their coupling relationships is crucial for efficient optimization. Recent constraint-decoupling methods handle individual constraints separately, but they generally search only in the evolutionary direction to approximate single-constraint Pareto fronts (SCPFs). In this study, we show that part or all of the constrained Pareto front (CPF) may be unrelated to any SCPF and instead be shaped by the boundaries of infeasible regions. We refer to such a portion as the independent CPF (ICPF) and introduce the reverse CPF (RCPF) to characterize its associated informative infeasible boundaries. Based on these observations, we propose a bidirectional constraint-decoupling coevolutionary algorithm named DCF2D. DCF2D dynamically identifies the constraints obstructing the main population and activates constraint-specific auxiliary populations. These populations adaptively search in the evolutionary direction for the corresponding SCPFs or in the reverse evolutionary direction for the corresponding RCPFs. Its three-stage framework integrates unconstrained global exploration, event-driven bidirectional coevolution, and final convergence refinement. Experiments on 87 benchmark instances from seven test suites and 28 real-world engineering CMOPs demonstrate that DCF2D achieves the best overall performance among nine algorithms. Code available at: https://github.com/RuiqingS/DCF2D.

cs.NE↗

arXiv2026

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.

cs.NE↗