Globally Convergent Particle Swarm Optimization via Branch-and-Bound

Abstract

Particle swarm optimization (PSO) is a recently developed optimization method that has attracted interest of researchers in various areas. PSO has been shown to be effective in solving a variety of complex optimization problems. With properly chosen parameters, PSO can converge to local optima. However, conventional PSO does not have global convergence. Empirical evidences indicate that the PSO algorithm may fail to reach global optimal solutions for complex problems. We propose to combine the branch-and-bound framework with the particle swarm optimization algorithm. With this integrated approach, convergence to global optimal solutions is theoretically guaranteed. We have developed and implemented the BB-PSO algorithm that combines the efficiency of PSO and effectiveness of the branch-and-bound method. The BB-PSO method was tested with a set of standard benchmark optimization problems. Experimental results confirm that BB-PSO is effective in finding global optimal solutions to problems that may cause difficulties for the PSO algorithm.