Evolutionary Alternating Direction Method of Multipliers for Constrained Multiobjective Optimization With Unknown Constraints
针对约束函数未知或定义不充分的多目标优化问题，提出一种基于交替方向乘子法的进化优化框架，将原问题分解为两个子问题并分配独立种群，通过交替进化方向寻找可行解，在120个基准测试和两个实际工程问题上优于现有算法。
Constrained multiobjective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. Constraint violation (CV) has been a building block in designing evolutionary multiobjective optimization (EMO) algorithms for solving CMOPs. However, in certain scenarios, constraint functions might be unknown or inadequately defined, making CV unattainable and potentially misleading for the conventional constrained EMO 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 toward 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 the five state-of-the-art constrained EMO 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.