Random walks, Lévy flights, Markov chains and metaheuristic optimization

Yang, Xin-She ORCID: https://orcid.org/0000-0001-8231-5556, Ting, T. O. and Karamanoglu, Mehmet ORCID: https://orcid.org/0000-0002-5049-2993 (2013) Random walks, Lévy flights, Markov chains and metaheuristic optimization. In: Future information communication technology and applications: ICFICE 2013. Lecture Notes in Electrical Engineering, 235 (235) . Springer Netherlands, pp. 1055-1064. ISBN 9789400765153. [Book Section]

Abstract

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.

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