Impacts of Linnik Flight Usage Patterns on Cuckoo Search for Real-Parameter Global Optimization Problems

Patchara Nasa-Ngium,Khamron Sunat,Sirapat Chiewchanwattana

doi:10.1109/access.2019.2923557

Patchara Nasa-Ngium, Khamron Sunat + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2923557

Copy DOI

Abstract

Several contemporary algorithms, including cuckoo search (CS), were applied to the CEC 2017 problem set, which includes a wide variety of 120 very difficult subproblems. We found that the algorithms were ineffective, especially when the number of dimensions was high. We configured several usage patterns of Linnik flight with the inverse of the golden ratio (1/ $\Phi $ ) to replace Levy flight in CS, resulting in a new search mechanism that increased the efficiency of the CS algorithm. The impacts of each Linnik flight usage pattern were evaluated using the CEC 2017. The experimental results showed that: 1) CS variants that used Linnik flight were more capable than CS variants that used Levy flight and 2) CS variants that used a mixture of Linnik flight and quantum-behaved mechanisms were even more capable. The primary effect of Linnik flight is the strengthening of the ranking, while that of the quantum-behaved mechanisms is a decreased error. A chaotic-initialized quantum-Linnik flight CS (CQLCS) algorithm is proposed. Among the 66 competitive methods applied to the CEC 2017, CQLCS ranked first and won the contemporary competitive algorithms section, which also included several advanced variants of differential evolution (DE) and particle swarm optimization (PSO) algorithms. The CQLCS could potentially be improved further by adjusting the probability of the occurrence of Linnik flight. The processes for building improved variants were analyzed to discover how, or if, this improvement could be achieved. Finally, the CQLCS algorithm required fewer lines of code to run than did the DE and PSO variants.

Highlights

A challenging aspect of science and engineering problems is that most are naturally highly nonlinear, multimodal, non-differentiable, or constrained design problems
The proposed chaotic-initialized quantum-Linnik flight CS (CQLCS) does not significantly increase the overall complexity compared with the original CS
We test CS with several usage patterns of Lévy flight: a nest learned from every dimension of the host nest, a nest learned from only partial dimensions of the host nest, and a nest learned from every dimension of the host nest using either Lévy flight or one of two quantumbehaved mechanisms

Summary

Introduction

A challenging aspect of science and engineering problems is that most are naturally highly nonlinear, multimodal, non-differentiable, or constrained design problems. Local search methods, such as gradient-based optimization techniques, can rarely solve these problems; several meta-heuristic algorithms have been created [1]–[4] because of the ‘‘no free lunch (NFL)’’ theorem of optimization. The NFL theorem [5] states that even if an algorithm can effectively solve a problem, it is not necessarily true that the algorithm can solve other problems effectively. Among the meta-heuristic algorithms, evolutionary algorithms (EAs) have been shown to be highly effective and have excellent global search capabilities [6], [7]. In recent years, algorithms based on swarm intelligence have become competitive alternatives to EAs [8]

Objectives

Findings

Discussion

Conclusion