Exact Analysis of the Sampling Distribution for the Canonical.pdfVIP

Exact Analysis of the Sampling Distribution for the Canonical Particle Swarm Optimiser and its Convergence during Stagnation Riccardo Poli David Broomhead Department of Computer Science School of Mathematics University of Essex, UK University of Manchester, UK rpoli@essex.ac.uk D.S.Broomhead@manchester.ac.uk ABSTRACT Algorithm 1 Classical PSO. Several theoretical analyses of the dynamics of particle 1: Initialize a population array of particles with random swarms have been offered in the literature over the last positions and velocities on D dimensions in the problem decade. Virtually all rely on substantial simplifications, in- space. cluding the assumption that the particles are deterministic. 2: loop This has prevented the exact characterisation of the sam- 3: For each particle, evaluate the desired optimization pling distribution of the PSO. In this paper we introduce fitness function in D variables. a novel method, which allows one to exactly determine all 4: Compare particle’s fitness evaluation with its personal the characteristics of a PSO’s sampling distribution and ex- best fitness pbest i . If current value is better than plain how they change over any number of generations, in pbest i , then set pbest i equal to the current value, and