A competitive swarm optimizer with probabilistic criteria for many-objective optimization problems

Although multiobjective particle swarm optimizers (MOPSOs) have performed well on multiobjective optimization problems (MOPs) in recent years, there are still several noticeable challenges. For example, the traditional particle swarm optimizers are incapable of correctly discriminating between the personal and global best particles in MOPs, possibly leading to the MOPSOs lacking sufficient selection pressure toward the true Pareto front (PF). In addition, some particles will be far from the PF after updating, this may lead to invalid search and weaken the convergence efficiency. To address the abovementioned issues, we propose a competitive swarm optimizer with probabilistic criteria for many-objective optimization problems (MaOPs). First, we exploit a probability estimation method to select the leaders via the probability space, which ensures the search direction to be correct. Second, we design a novel competition mechanism that uses winner pool instead of the global and personal best particles to guide the entire population toward the true PF. Third, we construct an environment selection scheme with the mixed probability criterion to maintain population diversity. Finally, we present a swarm update strategy to ensure that the next generation particles are valid and the invalid search is avoided. We employ various benchmark problems with 3–15 objectives to conduct a comprehensive comparison between the presented method and several state-of-the-art approaches. The comparison results demonstrate that the proposed method performs well in terms of searching efficiency and population diversity, and especially shows promising potential for large-scale multiobjective optimization problems.