Towards an analytic framework for analysing the computation time of evolutionary algorithms

In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise. This paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms. The framework is built on the absorbing Markov chain model of evolutionary algorithms. The first step towards a systematic comparative study among different EAs and their first hitting times has been made in the paper.

[1]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[2]  Thomas Bäck,et al.  Evolutionary Algorithms: The Role of Mutation and Recombination , 2000 .

[3]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[4]  Joe Suzuki,et al.  A Markov chain analysis on simple genetic algorithms , 1995, IEEE Trans. Syst. Man Cybern..

[5]  Xin Yao,et al.  A new evolutionary approach to cutting stock problems with and without contiguity , 2002, Comput. Oper. Res..

[6]  Raúl Hector Gallard,et al.  Genetic algorithms + Data structure = Evolution programs , Zbigniew Michalewicz , 1999 .

[7]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[8]  J. Davenport.  Editor , 1960 .

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

[10]  Erick Cantú-Paz,et al.  Markov chain models of parallel genetic algorithms , 2000, IEEE Trans. Evol. Comput..

[11]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

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

[13]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..

[14]  Thomas Jansen,et al.  On the Analysis of Evolutionary Algorithms - A Proof That Crossover Really Can Help , 1999 .

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

[16]  A. Wright,et al.  Markov chain models of genetic algorithms , 1999 .

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

[18]  Thomas Bäck,et al.  The Interaction of Mutation Rate, Selection, and Self-Adaptation Within a Genetic Algorithm , 1992, PPSN.

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

[20]  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..

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

[22]  Michael D. Vose,et al.  Modeling genetic algorithms with Markov chains , 1992, Annals of Mathematics and Artificial Intelligence.

[23]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[24]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[25]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[26]  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).

[27]  Schloss Birlinghoven,et al.  How Genetic Algorithms Really Work I.mutation and Hillclimbing , 2022 .

[28]  Ingo Wegener,et al.  Methods for the Analysis of Evolutionary Algorithms on Pseudo-Boolean Functions , 2003 .

[29]  Xin Yao,et al.  An evolutionary approach to materialized views selection in a data warehouse environment , 2001, IEEE Trans. Syst. Man Cybern. Part C.

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

[31]  Lishan Kang,et al.  On the Convergence Rates of Genetic Algorithms , 1999, Theor. Comput. Sci..

[32]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

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

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

[35]  Xin Yao,et al.  Evolutionary computation : theory and applications , 1999 .

[36]  Günter Rudolph,et al.  Finite Markov Chain Results in Evolutionary Computation: A Tour d'Horizon , 1998, Fundam. Informaticae.

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

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

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

[40]  P. Lancaster,et al.  The theory of matrices : with applications , 1985 .

[41]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[42]  D. Cooke,et al.  Finite Markov Processes and Their Applications , 1981 .

[43]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.