Dimensions cooperate by Euclidean metric in Particle Swarm Optimization

Since Particle Swarm Optimization (PSO) was introduced, variants of PSO have usually updated velocities of particles in each dimension independently in the high-dimensional space. This paper proposes a Dimensionally Cooperative PSO (DCPSO), in which dimensions cooperate to update velocities of particles through Euclidean metric. The Euclidean metric first builds pbest-centered and gbest-centered hyperspheres. And then, velocity vectors of particles are derived from stochastic points obeying a distribution within the hyperspheres for dimensions cooperating. DCPSO investigates such cooperation of dimensions through Euclidean metric, instead of updating each dimension independently. Compared with the traditional PSO, DCPSO is validated by simulations on the 20 standard benchmark problems from CEC 2013. Furthermore, DCPSO shows more rotationally-invariant than the traditional PSO from the results. Additionally, the differences between the behaviors of the traditional PSO and the proposed DCPSO are analyzed from the aspect of the search space. Meanwhile, the curse of dimensionality is illustrated by comparisons between the traditional PSO and DCPSO in distinct dimensions.