Abstract
Recombination (also called crossover) operators are widely used in EAs to generate offspring solutions. Although the usefulness of recombination has been well recognized, theoretical analysis on recombination operators remains a hard problem due to the irregularity of the operators and their complicated interactions to mutation operators. In this paper, as a step towards analyzing recombination operators theoretically, we present a general approach which allows to compare the runtime of an EA turning the recombination on and off, and thus helps to understand when a recombination operator works. The key of our approach is the Markov Chain Switching Theorem which compares two Markov chains for the first hit of the target. As an illustration, we analyze some recombination operators in evolutionary search on the LeadingOnes problem using the proposed approach. The analysis identifies some insight on the choice of recombination operators, which is then verified in experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies. In: Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)
Beyer, H.G., Schwefel, H.P., Wegener, I.: How to analyse evolutionary algorithms. Theoretical Computer Science 287(1), 101–130 (2002)
Chen, T., Tang, K., Chen, G., Yao, X.: On the analysis of average time complexity of estimation of distribution algorithms. In: Proceedings of CEC 2007, Singapore, pp. 25–28 (2007)
Doerr, B., Happ, E., Klein, C.: Crossover can provably be useful in evolutionary computation. In: Proceedings of GECCO 2008, Atlanta, GA, pp. 539–546 (2008)
Doerr, B., Theile, M.: Improved analysis methods for crossover-based algorithms. In: Proceedings of GECCO 2009, Montreal, Canada, pp. 247–254 (2009)
Droste, S., Jansen, T., Wegener, I.: A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for linear functions with boolean inputs. Evolutionary Computation 6(2), 185–196 (1998)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276(1-2), 51–81 (2002)
Freǐdlin, M.I.: Markov Processes and Differential Equations: Asymptotic Problems. Birkhäuser Verlag, Basel (1996)
He, J., Yao, X.: Drift analysis and average time complexity of evolutionary algorithms. Artifical Intelligence 127(1), 57–85 (2001)
He, J., Yao, X.: Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artificial Intelligence 145(1-2), 59–97 (2003)
Jansen, T., Wegener, I.: The analysis of evolutionary algorithms - a proof that crossover really can help. Algorithmica 34(1), 47–66 (2002)
Jansen, T., Wegener, I.: Real royal road functions - where crossover provably is essential. Discrete Applied Mathematics 149, 111–125 (2005)
Lehre, P.K., Yao, X.: Crossover can be constructive when computing unique input output sequences. In: Li, X., Kirley, M., Zhang, M., Green, D., Ciesielski, V., Abbass, H.A., Michalewicz, Z., Hendtlass, T., Deb, K., Tan, K.C., Branke, J., Shi, Y. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 595–604. Springer, Heidelberg (2008)
Lin, G., Yao, X.: Analysing crossover operators by search step size. In: Proceedings of CEC 1997, Indianapolis, IN, pp. 107–110 (1997)
Richter, J.N., Wright, A., Paxton, J.: Ignoble trails - where crossover is provably harmful. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 92–101. Springer, Heidelberg (2008)
Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovač, Hamburg (1997)
Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Pearson Education, Englewood Cliffs (2003)
Spears, W.: Evolutionary Algorithms: The Role of Mutation and Recombination. Springer, Berlin (2000)
Storch, T., Wegener, I.: Real royal road functions for constant population size. Theoretical Computer Science 320(1), 123–134 (2004)
Yu, Y., Zhou, Z.-H.: A new approach to estimating the expected first hitting time of evolutionary algorithms. Artificial Intelligence 172(15), 1809–1832 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yu, Y., Qian, C., Zhou, ZH. (2010). Towards Analyzing Recombination Operators in Evolutionary Search. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-15844-5_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15843-8
Online ISBN: 978-3-642-15844-5
eBook Packages: Computer ScienceComputer Science (R0)