# Optimal Randomness in Swarm-Based Search

## TL;DR

This paper investigates the impact of different heavy-tailed probability distributions on the effectiveness of swarm-based search algorithms, proposing four novel algorithms and testing them on benchmark functions and system identification tasks.

## Contribution

It introduces four new Cuckoo Search algorithms using various heavy-tailed distributions, expanding understanding of optimal randomness in swarm-based optimization.

## Key findings

- Heavy-tailed distributions improve search performance.
- Proposed algorithms outperform standard Cuckoo Search.
- Effective in system identification tasks.

## Abstract

L\'{e}vy flights is a random walk where the step-lengths have a probability distribution that is heavy-tailed. It has been shown that L\'{e}vy flights can maximize the efficiency of resource searching in uncertain environments, and also movements of many foragers and wandering animals have been shown to follow a L\'{e}vy distribution. The reason mainly comes from that the L\'{e}vy 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's necessary to discuss the optimal randomness in swarm-based search algorithms. In this study, 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.