Particle Swarm Optimization Simulation via Optimal Halton Sequences

Inspired by the social behavior of the bird flocking or fish schooling, the particle swarm optimization (PSO) is a population based stochastic optimization method developed by Eberhart and Kennedy in 1995. It has been used across a wide range of applications. Faure, Halton and Vander Corput sequences have been used for initializing the swarm in PSO. Quasirandom(or low-discrepancy) sequences such as Faure, Halton, Vander Corput etc are deterministic and suffers from correlations between radical inverse functions with different bases used for different dimensions. In this paper, we investigate the effect of initializing the swarm with scrambled optimal Halton sequence, which is a randomized quasirandom sequence. This ensures that we still have the uniformity properties of quasirandom sequences while preserving the stochastic behavior for particles in the swarm. Numerical experiments are conducted with benchmark objective functions with high dimensions to verify the convergence and effectiveness of the proposed initialization of PSO.