Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. Constraint violation has been a building block in designing evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, in certain scenarios, constraint functions might be unknown or inadequately defined, making constraint violation unattainable and potentially misleading for conventional constrained evolutionary multi-objective optimization algorithms. To address this issue, we present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. This framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population. Notably, these two populations operate towards complementary evolutionary directions during their optimization processes. In order to minimize discrepancy, their evolutionary directions alternate, aiding the discovery of feasible solutions. Comparative experiments conducted against five state-of-the-art constrained evolutionary multi-objective optimization algorithms, on 120 benchmark test problem instances with varying properties, as well as two real-world engineering optimization problems, demonstrate the effectiveness and superiority of our proposed framework. Its salient features include faster convergence and enhanced resilience to various Pareto front shapes.

翻译：约束多目标优化问题普遍存在于科学、工程与设计领域的实际应用中。约束违反度一直是设计求解约束多目标优化问题的进化多目标优化算法的核心基础。然而，在某些场景中，约束函数可能未知或定义不充分，导致传统约束进化多目标优化算法无法获取约束违反度，甚至可能产生误导性信息。为解决这一难题，我们受交替方向乘子法原理启发，首次提出一种新型进化优化框架。该框架通过将原问题重构为两个子问题的加和形式——每个子问题均分配专属进化种群——来处理含未知约束的约束多目标优化问题。值得关注的是，这两个种群在优化过程中沿互补的进化方向运行。为最小化方向偏差，其进化方向交替切换，从而促进可行解的发现。在120个不同特性的基准测试问题实例及两项实际工程优化问题上，与五种前沿约束进化多目标优化算法的对比实验表明，所提框架具有显著有效性与优越性。其突出特征包括更快的收敛速度，以及对各类帕累托前沿形状更强的适应性。