Optimal Randomness in Swarm-Based Search

Four different randomness-enhanced CS algorithms using different heavy-tailed distributions (namely CSML, CSP, CSC and CSW)

Swarm-based search has been a hot topic for a long time. Among the proposed swarm-based search algorithms, cuckoo search (CS) famous for utilizing Levy flights has been proved to be an efficient approach for global optimum searching. It has been shown that Levy flights can maximize the efficiency of resource searches in uncertain environments, and also movements of many foragers and wandering animals have been shown to follow a Levy distribution. The reason mainly comes from that the Levy distribution, a heavy-tailed distributions has an infinite second moment, and hence is more likely to generate an offspring that is farther away from its parent.

However, investigation into the efficiency of other different heavy-tailed probability distributions is still insufficient up to now. Therefore, it's necessary to discuss the optimal randomness especially in 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. Accordingly, four different randomness-enhanced CS algorithms (namely CSML, CSP, CSC and CSW) are presented by applying Mittag-Leffler, Pareto, Cauchy and Weibull distributions.

It is noted that our research is on purpose to study the optimal randomness, and by experiments on cuckoo search, the conclusions might be generalized to other swarm-based search algorithms.

The details of the original algorithm can be found in
https://arxiv.org/abs/1905.02776