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

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

Découverte à Nouakchott d'un denier d'Alexandre

Mauny Raymond. Découverte à Nouakchott d'un denier d'Alexandre. In: Journal des africanistes, 1983, tome 53, fascicule 1-2. pp. 181-184

Levtzion, Nehemia. Ancient Ghana and Mali

Mauny Raymond. Levtzion, Nehemia. Ancient Ghana and Mali . In: Journal de la Société des Africanistes, 1973, tome 43, fascicule 2. pp. 281-282

J.-D. Devisse & S. Robert, Tegdaoust III. Recherches sur Aoudaghost Campagnes 1960-65. Enquêtes générales.

Mauny Raymond. J.-D. Devisse & S. Robert, Tegdaoust III. Recherches sur Aoudaghost Campagnes 1960-65. Enquêtes générales. . In: Journal des africanistes, 1983, tome 53, fascicule 1-2. pp. 217-219

Willett (Frank) : Ifé, une civilisation africaine

Mauny Raymond. Willett (Frank) : Ifé, une civilisation africaine. In: Revue française d'histoire d'outre-mer, tome 59, n°217, 4e trimestre 1972. p. 720

Levtzion, Nehemia. Ancient Ghana and Mali

Mauny Raymond. Levtzion, Nehemia. Ancient Ghana and Mali . In: Journal de la Société des Africanistes, 1973, tome 43, fascicule 2. pp. 281-282

Summers (Roger) : Zimbabwe, mystère rhodésien, Trad. de l'anglais par P. Chwa

Mauny Raymond. Summers (Roger) : Zimbabwe, mystère rhodésien, Trad. de l'anglais par P. Chwa. In: Revue française d'histoire d'outre-mer, tome 59, n°217, 4e trimestre 1972. pp. 720-721

Chittick, Neville, Kilwa. An Islamic trading city on the East African coast.

Mauny Raymond. Chittick, Neville, Kilwa. An Islamic trading city on the East African coast.. In: Journal de la Société des Africanistes, 1975, tome 45, fascicule 1-2. p. 223

Kiethega (J. B.) : L'or de la Volta Noire. Archéologie et histoire de l'exploitation (Région de Poura, Haute-Volta)

Mauny Raymond. Kiethega (J. B.) : L'or de la Volta Noire. Archéologie et histoire de l'exploitation (Région de Poura, Haute-Volta). In: Revue française d'histoire d'outre-mer, tome 72, n°266, 1er trimestre 1985. p. 111