Reinforcement learning based multi-population co-evolution algorithm with indicator preference guidance for multiobjective optimization

Multiobjective optimization problems (MOPs) require a delicate balance between convergence to the Pareto front (PF) and diversity maintenance. Traditional algorithms often struggle with high-dimensional objectives and a complex PF. This paper introduces a reinforcement learning (RL)-based multi-population co-evolution algorithm with indicator preference guidance (MPCEP), in which each subpopulation plays a specific role. The first subpopulation focuses on improving solution quality through a convergent external archive and a preference evolution strategy, utilizing preference guidance based on solution similarity and reverse evolution to direct solutions towards the true PF. The second subpopulation encourages exploration and ensures diversity by employing a dynamic penalty strategy that prevents premature convergence. The third subpopulation integrates reinforcement learning with a reward–penalty mechanism to promote the emergence of suboptimal solutions, allowing for adaptive preference adjustments during the search process. This co-evolutionary structure facilitates dynamic adjustment for efficient exploration and exploitation of the decision space, while promoting collaboration between subpopulations. Extensive experiments on benchmark problems and real-world problems demonstrate that MPCEP consistently outperforms existing algorithms in terms of both convergence and diversity, highlighting its robustness and adaptability in solving multiobjective optimization problems across various domains.