A Constrained Learning-Based Competitive Swarm Optimizer for Large-Scale Multiobjective Optimization

competitive swarm optimizer (CSO) is considered as a prominent paradigm for solving large-scale multiobjective optimization problems (LMOPs). However, the pairwise random competition (PRC) mechanism used in most existing CSOs may limit their performance in solving LMOPs due to the following reasons. First, when the winner particle obtained by PRC is of poor quality, it may limit the learning effect of its corresponding loser particle. Second, due to the stochastic nature of PRC, the evolutionary direction of the loser particles may be drastically perturbed over the iterations, thus slowing down their convergence speed. To alleviate the above issues, this article proposes a constrained learning (CL)-based CSO for tackling LMOPs, called CL-CSO. First, CL-CSO adopts a set of reference vectors to divide the original objective space into several subregions. Second, CL-CSO designs a CL-based strategy, including the intra-subregion learning and cross-subregion learning strategy, which let the loser particles only learn from the winner particles in their intra-subregions or neighboring subregions, respectively. Moreover, CL-CSO designs a Gaussian model assisted evolutionary strategy to help the evolution of winner particles, aiming to further improve the diversity and quality of winner particles. This way, the learning effect of particles and the overall convergence speed can be significantly enhanced. Compared to several competitive algorithms for tackling LMOPs, experimental results show that CL-CSO performs well in solving two well-known benchmark LMOPs (containing 2-3 objectives and 500-5000 decision variables), as well as real-world instance selection problems.