Improved Particle Swarm Optimization with low-discrepancy sequences

Abstract

Quasirandom or low discrepancy sequences, such as the Van der Corput, Sobol, Faure, Halton (named after their inventors) etc. are less random than a pseudorandom number sequences, but are more useful for computational methods which depend on the generation of random numbers. Some of these tasks involve approximation of integrals in higher dimensions, simulation and global optimization. Sobol, Faure and Halton sequences have already been used [7, 8, 9, 10] for initializing the swarm in a PSO. This paper investigates the effect of initiating the swarm with another classical low discrepancy sequence called Vander Corput sequence for solving global optimization problems in large dimension search spaces. The proposed algorithm called VC-PSO and another PSO using Sobol sequence (SO-PSO) are tested on standard benchmark problems and the results are compared with the Basic Particle Swarm Optimization (BPSO) which follows the uniform distribution for initializing the swarm. The simulation results show that a significant improvement can be made in the performance of BPSO, by simply changing the distribution of random numbers to quasi random sequence as the proposed VC-PSO and SO-PSO algorithms outperform the BPSO algorithm by noticeable percentage, particularly for problems with large search space dimensions.