Multi-indicator collaborative evolutionary algorithm for many-objective optimization

Most algorithms based on non-dominated relationships struggle to converge to the Pareto front when solving many-objective optimization problems. This is primarily due to the rapid increase in the number of non-dominated solutions with the number of objectives, leading to a small number of dominance-resistant solutions being produced by the algorithm. These dominance-resistant solutions significantly impact algorithm performance, slow down convergence speed, and may even prevent convergence. To address these problems and enhance the algorithm's ability to approach the Pareto optimal front, a multi-indicator collaborative evolutionary (MICE) algorithm is proposed in this paper. When the combined population contains fewer non-dominated individuals than its size allows, a dominated frequency indicator is proposed to compare fitness among these individuals and select more fit candidates for the next generation. Additionally, we employ a ratio indicator to construct a promising region and eliminate individuals located outside this region in order to accelerate convergence speed and improve stability. In pursuit of well-distributed solutions in the objective space, our MICE algorithm combines "large-vector-angle-first" criterion with ISDE+ indicator to maintain balance between population diversity and algorithm convergence by removing high-density individuals with poor convergence. Experimental results demonstrate promising performance of our proposed MICE algorithm which not only identifies a set of well-distributed points on the entire Pareto-optimal front but also effectively maintains boundary solutions.