Evolutionary Alternating Direction Method of Multipliers for Constrained Multiobjective Optimization With Unknown Constraints

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.