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.

翻译：现实世界中的约束多目标优化问题通常包含多个约束，理解并利用这些约束之间的耦合关系对于求解CMOP至关重要。然而，现有的约束多目标进化算法通常忽略这些耦合，将所有约束视为单一聚合体，这缺乏关于约束具体几何作用的可解释性。为应对这一局限，我们首先分析了不同约束如何相互作用，并表明最终的约束帕累托前沿不仅取决于单个约束的帕累托前沿，还取决于不可行区域的边界。这一见解意味着具有不同耦合类型的CMOP必须从不同的搜索方向进行求解。据此，我们提出了一种名为“从两个方向解耦约束”的新算法。该方法周期性地检测约束耦合，并为每个相关约束生成一个具有适当搜索方向的辅助种群。在七个具有挑战性的CMOP基准测试集以及一系列现实世界CMOP上的大量实验表明，DCF2D优于五种先进的CMOEA，包括现有的基于解耦的方法。