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Global Convergence Analysis of Cuckoo Search Using Markov Theory

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Nature-Inspired Algorithms and Applied Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 744))

Abstract

The cuckoo search (CS) algorithm is a powerful metaheuristic algorithm for solving nonlinear global optimization problems. In this book chapter, we prove the global convergence of this algorithm using a Markov chain framework. By analyzing the state transition process of a population of cuckoos and the homogeneity of the constructed Markov chains, we can show that the constructed stochastic sequences can converge to the optimal state set. We also show that the algorithm structure of cuckoo search satisfies two convergence conditions and thus its global convergence is guaranteed. We then use numerical experiments to demonstrate that cuckoo search can indeed achieve global optimality efficiently.

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Acknowledgements

The authors would like to thank the financial support by Shaanxi Provincial Education Grant (12JK0744) and Shaanxi Provincial Soft Science Foundation (2012KRM58).

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Authors and Affiliations

  1. College of Science, Xi’an Polytechnic University, Xi’an, People’s Republic of China

    Xing-Shi He, Fan Wang & Yan Wang

  2. School of Science and Technology, Middlesex University, London, NW4 4BT, UK

    Xin-She Yang

Authors
  1. Xing-Shi He
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  2. Fan Wang
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  3. Yan Wang
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  4. Xin-She Yang
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Corresponding author

Correspondence to Xin-She Yang .

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Editors and Affiliations

  1. School of Science and Technology, Middlesex University, London, United Kingdom

    Xin-She Yang

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He, XS., Wang, F., Wang, Y., Yang, XS. (2018). Global Convergence Analysis of Cuckoo Search Using Markov Theory. In: Yang, XS. (eds) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, vol 744. Springer, Cham. https://doi.org/10.1007/978-3-319-67669-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-67669-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67668-5

  • Online ISBN: 978-3-319-67669-2

  • eBook Packages: EngineeringEngineering (R0)

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