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Global Convergence Analysis of Cuckoo Search Using Markov Theory

  • Xing-Shi He
  • Fan Wang
  • Yan Wang
  • Xin-She YangEmail author
Chapter
Part of the Studies in Computational Intelligence book series (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.

Keywords

Cuckoo search Convergence rate Global convergence Markov chain theory Optimization Swarm intelligence 

Notes

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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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.College of ScienceXi’an Polytechnic UniversityXi’anPeople’s Republic of China
  2. 2.School of Science and TechnologyMiddlesex UniversityLondonUK

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