About the Computation Time of Adaptive Evolutionary Algorithms

The computation time of general adaptive evolutionary algorithms based on finite search space is investigated in this paper. An adaptive evolutionary algorithm can be formalized as an inhomogeneous Markov chain. By using Markov property, some exact analytic expressions of the mean first hitting time corresponding to the adaptive evolutionary algorithm are obtained. The upper and lower bounds are also estimated by introducing drift analysis and Dynkin's formula. Furthermore, the convergence of a constructive adaptive (1 + 1) ***EA is studied and its time complexity for a well-known toy problem is given.

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

[2]  Xin Yao,et al.  A Note on Problem Difficulty Measures in Black-Box Optimization: Classification, Realizations and Predictability , 2007, Evolutionary Computation.

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

[4]  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).

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

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

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

[8]  Xin Yao,et al.  A study of drift analysis for estimating computation time of evolutionary algorithms , 2004, Natural Computing.

[9]  Marc Schoenauer,et al.  Rigorous Hitting Times for Binary Mutations , 1999, Evolutionary Computation.

[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]  Xin Yao,et al.  Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results , 2007, Int. J. Autom. Comput..

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

[13]  Günter Rudolph,et al.  How Mutation and Selection Solve Long-Path Problems in Polynomial Expected Time , 1996, Evolutionary Computation.

[14]  Josselin Garnier,et al.  Statistical distribution of the convergence time of evolutionary algorithms for long-path problems , 2000, IEEE Trans. Evol. Comput..