PSO Facing Non-Separable and Ill-Conditioned Problems

This report investigates the behavior of particle swarm optimization (PSO) on ill-conditioned functions. We find that PSO performs very well on separable, ill-conditioned functions. If the function is rotated such that it becomes non-separable, the performance declines dramatically. On non-separable, ill-conditioned functions we find the search costs (number of function evaluations) of PSO increasing roughly proportional with the condition number. We never observe premature convergence, but on non-separable, ill-conditioned problems PSO is outperformed by a contemporary evolution strategy by orders of magnitude. The strong dependency of PSO on rotations originates from random events that are only independent within the given coordinate system. We argue that invariance properties, like rotational invariance, are desirable, because they increase the predictive power of performance results. Key-words: Particle Swarm Optimization, performance assessment, ill-conditioned problems, non-separable problems, invariance ∗ Raymond Ros is with LRI, Project-team TAO, Université Paris-Sud, 91405 Orsay Cedex, France. All other authors are with INRIA Saclay, Project-team TAO, LRI, Université Paris-Sud, 91405 Orsay Cedex, France. For 1st, 4th and 5th author mail to [email protected], for 2nd and 3rd author mail to [email protected]. OEP face à des problèmes non-séparables et mal conditionnés Résumé : Pas de résumé Mots-clés : Pas de motclef PSO Facing Non-Separable and Ill-Conditioned Problems 3