An Experimental Method to Estimate Running Time of Evolutionary Algorithms for Continuous Optimization

Abstract

Running time analysis is a fundamental problem of critical importance in evolutionary computation. However, the analysis results have rarely been applied to advanced evolutionary algorithms (EAs) in practice, let alone their variants for continuous optimization. In this paper, an experimental method is proposed for analyzing the running time of EAs that are widely used for solving continuous optimization problems. Based on Glivenko–Cantelli theorem, the proposed method simulates the distribution of gain, which is introduced by average gain model to characterize progress during the optimization process. Data fitting techniques are subsequently adopted to obtain a desired function for further analyses. To verify the validity of the proposed method, experiments were conducted to estimate the upper bounds on expected first hitting time of various evolutionary strategies, such as (1, $\lambda $ ) evolution strategy, standard evolution strategy, covariance matrix adaptation evolution strategy, and its improved variants. The results suggest that all estimated upper bounds are correct. Backed up by the proposed method, state-of-the-art EAs for continuous optimization will have identical results about the running time as simplified schemes, which will bridge the gap between theoretical foundation and applications of evolutionary computation.