Hierarchical Multi-Population Cooperative Evolutionary Approach for Constrained Multi-Objective Optimization

To address the complexity of multi-constraint multi-objective optimization problems (mCMOPs), this paper proposes a novel multi-population evolutionary algorithm (MOEA). Multi-objective optimization problems (MOPs) are ubiquitous in scientific and engineering fields, while the introduction of multiple complex constraints significantly increases the difficulty of finding solutions. To tackle this challenge, this work systematically analyzes the intrinsic relationships among the Single-Constraint Pareto Front (SCPF), Sub-Constraint Pareto Front (SSCPF), Unconstrained Pareto Front (UPF), and the Final Constrained Pareto Front (FCPF), and it investigates how these relationships can be leveraged to effectively enhance optimization performance. Based on this analysis, a Hierarchical Multi-Population Cooperative Evolutionary Approach (HMP-CE) is proposed. The approach constructs C+2 populations (where C represents the number of constraints) to search the UPF, SCPF, and SSCPF at appropriate stages, thereby driving the final solution approximation in a hierarchical manner. Meanwhile, HMP-CE introduces the following two key mechanisms: (1) the Population Activation–Dormancy Regulation (PADR) mechanism, which adaptively regulates the activation and dormancy of populations to reduce computational cost and accelerate convergence; (2) the Constraint Combination Timing Identification (CCTI) mechanism, which identifies suitable moments to jointly solve selected constraints in SSCPF, thereby enhancing cooperative efficiency among populations. Experimental results on 37 benchmark mCMOPs, and six real-world engineering problems demonstrate that the proposed algorithm exhibits superior performance in terms of convergence, feasibility, and solution diversity, providing a competitive approach for solving complex multi-constraint optimization problems.