Optimal Randomness in Swarm-Based Search

Jiamin Wei, YangQuan Chen, Yongguang Yu and Yuquan Chen
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Jiamin Wei: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
YangQuan Chen: School of Engineering, University of California, Merced, 5200 Lake Road, Merced, CA 95343, USA
Yongguang Yu: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
Yuquan Chen: School of Engineering, University of California, Merced, 5200 Lake Road, Merced, CA 95343, USA

Mathematics, 2019, vol. 7, issue 9, 1-19

Abstract: Lévy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that Lévy flights can maximize the efficiency of resource searching in uncertain environments and also the movements of many foragers and wandering animals have been shown to follow a Lévy distribution. The reason mainly comes from the fact that the Lévy distribution has an infinite second moment and hence is more likely to generate an offspring that is farther away from its parent. However, the investigation into the efficiency of other different heavy-tailed probability distributions in swarm-based searches is still insufficient up to now. For swarm-based search algorithms, randomness plays a significant role in both exploration and exploitation or diversification and intensification. Therefore, it is necessary to discuss the optimal randomness in swarm-based search algorithms. In this study, cuckoo search (CS) is taken as a representative method of swarm-based optimization algorithms, and the results can be generalized to other swarm-based search algorithms. In this paper, four different types of commonly used heavy-tailed distributions, including Mittag-Leffler distribution, Pareto distribution, Cauchy distribution, and Weibull distribution, are considered to enhance the searching ability of CS. Then four novel CS algorithms are proposed and experiments are carried out on 20 benchmark functions to compare their searching performances. Finally, the proposed methods are used to system identification to demonstrate the effectiveness.

Keywords: optimal randomness; swarm-based search; cuckoo search; heavy-tailed distribution; global optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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