Particles Initialization of the Polar Particle Swarm Optimizer (Polar PSO) Algorithm in Polar Coordinates

摘要

Polar Particle Swarm Optimizer (Polar PSO) is a modified version of Particle Swarm Optimization (PSO) algorithm that used a mapping function that takes position of particles in polar space and converts them to Cartesian space and vice versa. The conversion is necessary since the particles are initialized and evaluated in Cartesian space while their movements are in polar space. The conversion however distorts the position of particles even though they were initially uniformly distributed. So, this conversion is believed to be the reason behind the Polar PSO performs poorly compared to the original Cartesian PSO, especially in high dimensions. This study proposes an initialization method in polar space for Polar PSO. It uses a distribution function to avoid the points being distributed near the polar origin. This method will reduce the number of conversion and in the same time diverse the position of particles to cover a sufficiently large portion of the search space. The proposed method is tested in Ackley, DeJong, Rastrigin, Rosenbrock, Griewangk, Quartic, Salomon and Dixon benchmark functions. The results show that the polar initialization improves slightly the performance of the Polar PSO. Although, the polar initialization is useful in reducing the distortion during conversion the Polar PSO can be further improved by enhancing its movement in polar space.