Fourier analysis and swarm intelligence for stochastic optimization of discrete functions

Abstract

A new methodology for solving discrete optimization problems by the continuous approach has been developed in this study. A discrete Fourier series method was derived and used for re-formulation of discrete objective functions as continuous functions. Particle Swarm Optimization (PSO) was then applied to locate the global optimal solutions of the continuous functions derived. The continuous functions generated by the proposed discrete Fourier series method correlated almost exactly with their original model functions. The PSO algorithm was observed to be highly successful in achieving global optimization of all such objective functions considered in this study. The results obtained indicated that the discrete Fourier series method coupled to the PSO algorithm is indeed a promising methodology for solving discrete optimization problems via the continuous approach. © Springer-Verlag Berlin Heidelberg 2010.