Search Performance Quantification on Evolutionary Algorithm -Derivation and Application of Times of Improved Solutions

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 actual simulations in most of the studies. The parameters of genetic operations have also been decided experientially or by trial and error. This study tries to mathematically quantify the search performance of EAs using the parameters of the operations for the purpose of theoretical investigation of them. This paper defines "Number of Searchable Solutions (NSS)" and "Times of Improved Solutions (TIS)" to indicate search performance of EAs and attempts to formulate them. This paper employs hill climbing method to an unimodal increasing function as a basic study for this purpose, and it derives the formulas for NSS and TIS that consist of the parameters of the genetic operation. This paper shows that appropriate formulas are derived and it enables us to compare the performance and optimize the parameters of the operations without actual trials.