Random Walks, Lévy Flights, Markov Chains and Metaheuristic Optimization

Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 235)


Stochastic components such as random walks have become an intrinsic part of modern metaheursitic algorithms. The efficiency of a metaheuristic algorithm may implicitly depend on the appropriate use of such randomization. In this paper, we provide some basic analysis and observations about random walks, Lévy flights, step sizes and efficiency using Markov theory. We show that the reason why Lévy flights are more efficient than Gaussian random walks, and the good performance of Eagle Strategy. Finally, we use bat algorithm to design a PID controller and have achieved equally good results as the classic Ziegler-Nichols tuning scheme.


Lévy flights Markov chains Metaheuristic and random walks 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Science and TechnologyMiddlesex UniversityLondonUK
  2. 2.Department of Electrical and Electronic EngineeringXi’an Jiaotong-Liverpool UniversitySuzhouPeople’s Republic of China

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