Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints

Constrained multi-objective optimization problems (CMOPs) pervade real-worldapplications in science, engineering, and design. Constraint violation has beena building block in designing evolutionary multi-objective optimizationalgorithms for solving constrained multi-objective optimization problems.However, in certain scenarios, constraint functions might be unknown orinadequately defined, making constraint violation unattainable and potentiallymisleading for conventional constrained evolutionary multi-objectiveoptimization algorithms. To address this issue, we present the first of itskind evolutionary optimization framework, inspired by the principles of thealternating direction method of multipliers that decouples objective andconstraint functions. This framework tackles CMOPs with unknown constraints byreformulating the original problem into an additive form of two subproblems,each of which is allotted a dedicated evolutionary population. Notably, thesetwo populations operate towards complementary evolutionary directions duringtheir optimization processes. In order to minimize discrepancy, theirevolutionary directions alternate, aiding the discovery of feasible solutions.Comparative experiments conducted against five state-of-the-art constrainedevolutionary multi-objective optimization algorithms, on 120 benchmark testproblem instances with varying properties, as well as two real-worldengineering optimization problems, demonstrate the effectiveness andsuperiority of our proposed framework. Its salient features include fasterconvergence and enhanced resilience to various Pareto front shapes.