Multi-agent cooperation-based bi-criteria evolutionary many-objective optimization

Many-objective evolutionary algorithms (MaOEAs) excel in solving many-objective optimization problems (MaOPs), which are mainly classified into two frameworks: the Pareto domination and the non-Pareto domination. The Pareto criterion (PC) obtains a well-converged solution set in multi-objective spaces through the Pareto dominance relationship between solutions. However, insufficient environmental selection pressure in many-objective spaces leads to slow convergence. The non-Pareto criterion (NPC) enhances the selection pressure by evaluating the solution set with a set of sortable scalar values. However, it is difficult to ensure the Pareto-optimal consistency of convergence and distribution when facing highly irregular Pareto fronts (PFs). Therefore, combining the two sets of criteria can satisfy the demand for uniform distribution while bringing significant selection pressure. A multi-agent cooperative strategy is proposed in this study to realize the combination of the two criteria. This strategy controls the evolutionary direction of two populations separately by deploying two agents, and promotes cooperative evolution between these populations through the exchange and flow of large amounts of information. In order to better realize the cooperative effect, we adopt the multi-agent reinforcement learning (MARL) strategy to accurately regulate the variation operator and parameter configurations of the bi-population. In addition, the effectiveness of the proposed method is validated on 74 test problems (DTLZ, WFG, and UF) and 3 real-world problems. The results show that the proposed algorithm is more competitive than 6 state-of-the-art algorithms.