Particle swarm optimization (PSO) algorithm: Analysis, improvements, and applications

Abstract

In this dissertation, we present a theoretical analysis, improvement strategies, and applications of the PSO algorithm. On the theoretical front, we provide a deterministic and stochastic convergence analysis of the standard PSO algorithm using contraction mapping principles. Our analysis is more general and removes the stagnation assumptions that were used in the previous studies. The theoretical findings are illustrated by constructing an example problem. In an effort to improve the PSO algorithm, it is implemented with the multi-start approach and is combined with the Cyclic Coordinate Descent (CCD) local optimizer to develop a hybrid algorithm MPSO-CCD. The MPSO-CCD algorithm not only increases the exploration ability of the standard PSO but also enhances the local search capability. The MPSO-CCD algorithm is further implemented in a parallel environment to construct a parallel PSO version PMPSO-CCD. The PMPSO-CCD is a highly scalable algorithm which provides a better overall performance in the benchmark test functions. Finally, we apply the improved PSO algorithm in molecular dynamics to fit an analytic potential energy function to I-(H2O) intermolecular potential energy curves calculated with DFT/B97-1 theory. The analytic function is a sum of two-body terms, each written as a generalized sum of Buckingham and Lennard-Jones terms. Two models are used to describe the two-body terms between I- and H2O: (i) a three-site model H2O and (ii) a four-site model including a ghost atom. Fitting results are compared with that were found using the genetic/nonlinear least-squares algorithm. The PSO algorithm performs better than the genetic/nonlinear least-squares algorithm in terms of the quality of the solution and computation time complexity.