A study of optimal topologies in swarm intelligence

The Particle Swarm Optimization (PSO) algorithm was proposed by Kennedy and Eberhart to solve unconstrained, nonlinear optimization problems. This paper examines the merits of different neighbourhood topologies using the original PSO algorithm. The global, ring, star, torus, trees, and a newly proposed hierarchical topologies are tested against the Sphere, Rosenbrock, Rastrigin, and Griewank functions. The study looks at the number of iterations until the function converges (when the fitness function does not change by more than a convergence error for 50 iterations) and the mean fitness achieved by each test. The results indicate that the torus and a Gov-7 topologies performs well for all functions tested due to the degrees of separation and multiple paths for information flow that allow information about a good solution to be propagated to the rest of the particles. This work also shows how special nodes can serve as filters that reject local solutions in swarm topologies. This work furthers the understanding of swarms and the information flow through the network.