A study of drift analysis for estimating computation time of evolutionary algorithms

This paper introduces drift analysis and its applications in estimating average computation time of evolutionary algorithms. Firstly, drift conditions for estimating upper and lower bounds of the mean first hitting times of evolutionary algorithms are presented. Then drift analysis is applied to two specific evolutionary algorithms and problems. Finally, a general classification of easy and hard problems for evolutionary algorithmsis given based on the analysis.

[1]  H. Teicher,et al.  Probability theory: Independence, interchangeability, martingales , 1978 .

[2]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[3]  Hans-Paul Schwefel,et al.  How to analyse evolutionary algorithms , 2002, Theor. Comput. Sci..

[4]  Ingo Wegener,et al.  A Rigorous Complexity Analysis of the (1 + 1) Evolutionary Algorithm for Separable Functions with Boolean Inputs , 1998, Evolutionary Computation.

[5]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[6]  Günter Rudolph,et al.  Convergence of non-elitist strategies , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[7]  XI FachbereichInformatik Finite Markov Chain Results in Evolutionary Computation: a Tour D'horizon , 1998 .

[8]  Xin Yao,et al.  Towards an analytic framework for analysing the computation time of evolutionary algorithms , 2003, Artif. Intell..

[9]  Xin Yao,et al.  Drift analysis and average time complexity of evolutionary algorithms , 2001, Artif. Intell..

[10]  Xin Yao,et al.  From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms , 2002, IEEE Trans. Evol. Comput..

[11]  RudolphGünter Finite Markov chain results in evolutionary computation , 1998 .

[12]  Bruce E. Hajek,et al.  The time complexity of maximum matching by simulated annealing , 1988, JACM.

[13]  R. Syski Passage Times for Markov Chains , 1992 .

[14]  B. Hajek Hitting-time and occupation-time bounds implied by drift analysis with applications , 1982, Advances in Applied Probability.

[15]  Xin Yao,et al.  Erratum to: Drift analysis and average time complexity of evolutionary algorithms [Artificial Intelligence 127 (2001) 57-85] , 2002, Artif. Intell..

[16]  I. Wegener,et al.  A rigorous complexity analysis of the (1+1) evolutionary algorithm for linear functions with Boolean inputs , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[17]  Günter Rudolph,et al.  Theory of Evolutionary Algorithms: A Bird's Eye View , 1999, Theor. Comput. Sci..

[18]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.