ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

Recent applications in evolutionary programming have suggested the use of further stable probability distributions, such as Cauchy and Lévy, in the random process associated with the mutations, as an alternative to the traditional, also stable, Normal distribution. This work considers a new self-adaptative class of algorithms in respect to the determination of the more adequate stable distribution parameters for optimization problems. Evaluations that rely upon standard analytical benchmarking functions and comparative performance tests between them were carried out in respect to the baseline defined by a standard algorithm using Normal distribution. Additional comparative studies were made in respect to various self-adaptive approaches, also proposed herein, and an adaptive method drawn from the literature. The results suggest numerical and statistical superiority of the more general stable distribution based approach, when compared with the baseline. However, they show no improvement over the adaptive method available in the literature, possibly due, at least partially, to implementation decisions that had to be made in the present implementation, that were not made explicit therein. Leopoldo Bulgarelli de Carvalho and Pedro P.B. de Oliveira