PSO Facing Non-Separable and Ill-Conditioned Problems

Nikolaus Hansen 1, * Raymond Ros 1 Nikolas Mauny 1 Marc Schoenauer 1 Anne Auger 1
* Corresponding author
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : 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.
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[Research Report] RR-6447, INRIA. 2008
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Nikolaus Hansen, Raymond Ros, Nikolas Mauny, Marc Schoenauer, Anne Auger. PSO Facing Non-Separable and Ill-Conditioned Problems. [Research Report] RR-6447, INRIA. 2008. 〈inria-00250078v2〉

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