A decomposition framework with dual populations and dual stages for constrained multi-objective optimization

The main challenge of constrained multi-objective optimization involves achieving a good balance among feasibility, convergence, and diversity simultaneously. However, most existing methods exhibit an imbalance, making it hard to converge towards Pareto-optimal front (PF) while maintaining the diversity of feasible solutions. To address this issue, this paper proposes a new dual-population and dual-stage constrained multi-objective optimization algorithm, denoted as DD-M2M, based on the multi-objective-to-multi-objective decomposition framework (M2M). In this approach, dual populations, referred to as $CP$ and $DP$, are employed collaboratively. More specifically, in the first stage, the $DP$ evolves independently without considering constraints, focusing solely on convergence towards the unconstrained PF, while the $CP$ evolves with a weak collaboration with the $DP$, driven by feasibility-based environment selection rules. In the second stage, the dual populations are both divided into multiple sub-populations within the M2M framework, generating offspring in a strongly collaborative manner to eventually converge to the constrained PF while ensuring solution diversity. Experimental results on two widely-used test suites fully demonstrate the superiority of DD-M2M compared to seven state-of-the-art methods on most test problems. Additionally, the proposed method is applied to real-world problems, and experimental results confirm its effectiveness in addressing practical challenges.