Fat-tailed distributions for continuous variable neighborhood search

Abstract

Using the Gaussian normal distribution on the whole solution space in the continuous variable neighborhood search method has shown similar success as the use of traditional bounded neighborhoods, but with less parameters to be specified. For unbounded problems with distant optimal solutions, although not limited by bounded geometrical neighborhoods, it showed to be inefficient due to the exponential decrease of the normal density function. In order to reach distant solutions more efficiently, six more “fat-tailed” distributions, which can be easily generated, are tested in this paper. The experiments on test functions showed greater efficiency for most new distributions opposite to a normal distribution. Moreover, following the “less is more approach”, this paper presents a very efficient algorithm for both close and distant optimal solutions. It combines two neighborhood structures: one being efficient for near solutions, and the other more efficient for distant solutions. This approach, with a reduced number of parameters the user must define in advance, has shown to be robust when the position of the optimal point is unknown.