The use of fuzzy sets to determine the parameters of genetic algorithms that provide approximately the same execution time on the CPU and GPU

Abstract

The problem under consideration consists in choosing the number of k individuals, so that the time for processing k individuals by the genetic algorithm (GA) on the CPU architecture is close to the time for processing l individuals on the GPU architecture by the genetic algorithm. The initial information is data arrays containing information about the processing time of a given number of individuals by the genetic algorithm on the available hardware architectures. Fuzzy numbers are determined based on these arrays?~? and?~?, describing the processing time of a given number of individuals, respectively, on the CPU and GPU architectures. The peculiarities of the subject area do not allow considering the well-known methods of comparison based on the equalities of the membership functions and the nearest clear sets as adequate. Based on the known formula “close to Y (around Y)” the way to compare fuzzy numbers?~? and?~? was developed in order to determine the degree of closeness of the processing time of k and l individuals, respectively, on the hardware architectures of the CPU and GPU.