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Towards Analyzing Recombination Operators in Evolutionary Search

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Parallel Problem Solving from Nature, PPSN XI (PPSN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6238))

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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.

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References

  1. Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies. In: Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)

    Google Scholar 

  2. Beyer, H.G., Schwefel, H.P., Wegener, I.: How to analyse evolutionary algorithms. Theoretical Computer Science 287(1), 101–130 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. Doerr, B., Theile, M.: Improved analysis methods for crossover-based algorithms. In: Proceedings of GECCO 2009, Montreal, Canada, pp. 247–254 (2009)

    Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276(1-2), 51–81 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Freǐdlin, M.I.: Markov Processes and Differential Equations: Asymptotic Problems. Birkhäuser Verlag, Basel (1996)

    Google Scholar 

  9. He, J., Yao, X.: Drift analysis and average time complexity of evolutionary algorithms. Artifical Intelligence 127(1), 57–85 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. He, J., Yao, X.: Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artificial Intelligence 145(1-2), 59–97 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jansen, T., Wegener, I.: The analysis of evolutionary algorithms - a proof that crossover really can help. Algorithmica 34(1), 47–66 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jansen, T., Wegener, I.: Real royal road functions - where crossover provably is essential. Discrete Applied Mathematics 149, 111–125 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. Lin, G., Yao, X.: Analysing crossover operators by search step size. In: Proceedings of CEC 1997, Indianapolis, IN, pp. 107–110 (1997)

    Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovač, Hamburg (1997)

    Google Scholar 

  17. Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Pearson Education, Englewood Cliffs (2003)

    Google Scholar 

  18. Spears, W.: Evolutionary Algorithms: The Role of Mutation and Recombination. Springer, Berlin (2000)

    MATH  Google Scholar 

  19. Storch, T., Wegener, I.: Real royal road functions for constant population size. Theoretical Computer Science 320(1), 123–134 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. 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)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210093, China

    Yang Yu, Chao Qian & Zhi-Hua Zhou

Authors
  1. Yang Yu
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  2. Chao Qian
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  3. Zhi-Hua Zhou
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Editor information

Editors and Affiliations

  1. Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, Department of ComputerScience, AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Robert Schaefer

  2. Departamento de Lenguajes y Ciencias de la Computación, ETSI Informática, Universidad de Málaga, Campus Teatinos, 29071, Málaga, Spain

    Carlos Cotta

  3. Department of Mathematics and Computer Science, University of Bielsko-Biala, Willowa 2, 43-309, Bielsko-Biala, Poland

    Joanna Kołodziej

  4. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Günter Rudolph

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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

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  • 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)

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