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.
翻译:现有针对约束多目标优化问题的进化算法通常统一处理所有约束,忽视了它们与真实约束帕累托前沿(CPF)之间不同的几何关系。实际上,约束扮演着不同角色:有些直接塑造最终CPF,有些造成不可行障碍,而其他则无关紧要。为利用这一洞察,我们提出一种名为RCCMO的新算法,该算法依次执行无约束探索、单约束利用和全约束精炼。RCCMO的核心创新在于一种基于这些几何洞察导出的约束优先级方法,并与独特的双向搜索机制无缝耦合。具体地,RCCMO首先对构成最终CPF的约束进行优先级排序,从进化方向(优化目标)接近这些约束,以定位由单约束边界直接塑造的CPF。随后,对于仅阻碍种群进步的约束,RCCMO从反进化方向(瞄准阻碍约束与CPF相交处的不可行边界)进行搜索,以有效发现这些约束如何阻碍并形成最终CPF。同时,无关约束被有意绕过。此外,提出了一系列专门机制以加速算法执行、减少启发式误判并实时动态调整搜索方向。在5个基准测试套件和29个真实世界CMOP上的广泛实验表明,RCCMO显著优于七种最先进算法。