Dual-space clustering-guided particle swarm optimization for multi-objective optimization

Abstract

In multi-objective particle swarm optimization (MOPSO) algorithms, the guiding solutions (i.e., pbest and gbest) are usually selected based on neighborhood relationships defined in either the decision space or the objective space. However, the information from these two spaces is complementary, and relying on just one of them might limit optimization performance. This study proposes a dual-space clustering enhanced MOPSO algorithm, called DCPSO. To be specific, in the proposed DCPSO, the density clustering method is performed in the decision space to identify the distribution of particles, and some outliers within the current swarm are distinguished which located in sparse regions. For particles identified as outliers, $K$-means clustering is performed in the objective space, and elite solutions are selected from the corresponding clusters to guide their search. Moreover, for these particles in normal clusters in the decision space, density-reachable information is used to identify neighboring particles for selecting pbest and gbest. In addition, outliers in sparse regions are allowed to serve as gbest candidates which helps maintain population diversity. The developed DCPSO is compared with six representative algorithms on 34 benchmark problems from 4 test suites and 9 real-world problems. The results show that DCPSO obtains the best HV and ${\text{IGD}}^{+}$ values on 26 out of 34 benchmark problems and achieves the highest overall ranking among the compared algorithms.