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Chaotic Evolution: fusion of chaotic ergodicity and evolutionary iteration for optimization

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Abstract

We propose a novel population-based optimization algorithm, Chaotic Evolution (CE), which uses ergodic property of chaos to implement exploration and exploitation functions of an evolutionary algorithm. CE introduces a mathematical mechanism into an iterative process of evolution and simulates ergodic motion in a search space with a simple principle. A control parameter, direction factor rate, is proposed to guide search direction in CE. It is easy to extend its search capability by using different chaotic system in CE algorithm framework. The scalability of CE is higher than that of some other evolutionary computation algorithms. A series of comparative evaluations and investigations is conducted to analyse characteristics of the proposal. Our proposal can obtain better optimization performance by comparing with differential evolution and some of its variants. We point out that the chaos theory is used not only to describe and explain a non-linear system, but also to implement a variety of optimization algorithms based on its ergodic property.

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Acknowledgments

The author would like to thank Yoshida Scholarship Foundation for its support of his doctoral research. He is also grateful to the editor and anonymous reviewers for their valuable comments and suggestions on this paper.

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  1. Graduate School of Design, Kyushu University, 4-9-1, Shiobaru, Minami-ku, Fukuoka, 815-8540, Japan

    Yan Pei

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Correspondence to Yan Pei.

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Pei, Y. Chaotic Evolution: fusion of chaotic ergodicity and evolutionary iteration for optimization. Nat Comput 13, 79–96 (2014). https://doi.org/10.1007/s11047-013-9409-2

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