Constraint-tightening based adaptive two-stage evolutionary algorithm for constrained multi-objective optimization

Constrained multi-objective optimization problems (CMOPs) are prevalent in practical applications, yet existing methods often struggle to handle their diverse characteristics, such as disconnected feasible regions and infeasible solutions near the true constraints Pareto front (CPF). To address these challenges, this paper proposes a constraint-tightening based adaptive two-stage evolutionary algorithm (CT-TSEA) for CMOPs, incorporating a constraint boundary tightening strategy and parameter dynamic adjustment strategy. In the first stage, a constraint boundary tightening strategy based on evaluation counts guides the population toward feasible regions. Initially, constraint boundaries are relaxed to explore the solution space thoroughly, identifying promising solutions. As evaluations increase, the search boundaries shrink, enhancing the feasibility of solutions. Additionally, a step-size adaptive adjustment method improves infeasible solutions using their information, boosting search efficiency and solution diversity. The second stage introduces a dynamic adjustment method for crossover probability and scaling factor, balancing exploration and exploitation. It better balances the exploration and exploitation capabilities of the population. The proposed method is validated via comparing with seven state-of-the-art peer competitors across 59 test instances from four benchmark suites and 21 real-world problems. The corresponding results demonstrate that CT-TSEA has the higher competitiveness in addressing complex CMOPs.