Search Performance Quantification on Evolutionary Computation -Derivation of Times of Improved Solutions (Ver.3)-

Abstract

Recently, Evolutionary Algorithms (EAs), which are based on the biological evolutionary process, are widely studied in a lot of fields. However, their probabilistic behavior makes the theoretical investigation difficult. As a result, the search performances of EAs have been tested through simulations in most of the studies. The parameters of genetic operations have also been decided experientially or by trial and error. This paper tries to mathematically analyze the search performance of EAs using the parameters of the operations for theoretical investigation of them. This paper defines the number of searchable solutions (NSS) and the times of improved solutions (TIS) to indicate search performance of EAs and attempts to formulate them. This paper employs hill climbing method to a monotone increasing function as a basic study of this research, and it derives the formulas for these indicators, NSS and TIS, that consist of the parameters of the genetic operation. This paper shows that appropriate formulas were derived and they enable us to compare and optimize the performance of the parameters for the operations in EAs without actual trials.