Sampling point extraction based on genetic algorithm and function approximation of a search space

To model a numerical problem space under the limitation of available data, we need to extract sparse but key points form the space and to efficiently approximate the space with them. This study proposes a sampling method based on the search process of genetic algorithm and a space modeling method based on least-squares approximation using the summation of Gaussian functions. We conducted simulations to evaluate them for several kinds of problem spaces: DeJong´s, Schaffer´s and our original one. We then compared the performance between our sampling method and sampling at regular intervals and that between our modeling method and modeling using a polynomial. The results showed that the error between a problem space and its model was the smallest for the combination of our sampling and modeling methods for many problem spaces if the number of samples was considerably small.