A Novel Hybrid Firefly Algorithm for Global Optimization

Lina Zhang,Liqiang Liu,Yuntao Dai,Xin-She Yang,Wen-Bo Du

doi:10.1371/journal.pone.0163230

Lina Zhang, Liqiang Liu + Show 3 more

Open Access

https://doi.org/10.1371/journal.pone.0163230

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Journal: PLOS ONE	Publication Date: Sep 29, 2016
Citations: 116	License type: CC BY 4.0

Affiliation: Harbin Engineering University, Middlesex University

Abstract

Global optimization is challenging to solve due to its nonlinearity and multimodality. Traditional algorithms such as the gradient-based methods often struggle to deal with such problems and one of the current trends is to use metaheuristic algorithms. In this paper, a novel hybrid population-based global optimization algorithm, called hybrid firefly algorithm (HFA), is proposed by combining the advantages of both the firefly algorithm (FA) and differential evolution (DE). FA and DE are executed in parallel to promote information sharing among the population and thus enhance searching efficiency. In order to evaluate the performance and efficiency of the proposed algorithm, a diverse set of selected benchmark functions are employed and these functions fall into two groups: unimodal and multimodal. The experimental results show better performance of the proposed algorithm compared to the original version of the firefly algorithm (FA), differential evolution (DE) and particle swarm optimization (PSO) in the sense of avoiding local minima and increasing the convergence rate.

Highlights

Global optimization is crucially important in many applications, such as image processing [1], antenna design [2], chemistry [3], wireless sensor network [4], and so on
It is can be seen that hybrid firefly algorithm (HFA) performs significantly better than firefly algorithm (FA), differential evolution (DE), and particle swarm optimization (PSO)
We have proposed a novel hybrid firefly algorithm (HFA) by combining some of the advantages of both firefly algorithm and differential evolution

Summary

Introduction

Global optimization is crucially important in many applications, such as image processing [1], antenna design [2], chemistry [3], wireless sensor network [4], and so on. Algorithm 1 Pseudo-code for the standard FA algorithm Objective function f(x), x = (x1,Á Á Á,xD)T Initialize a population of fireflies xi (i = 1,2,Á Á Án) Calculate the light intensity Ii at xi by f(xi) Define light absorption coefficient γ While (t < MaxGeneration) for i = 1:n all n fireflies for j = 1:n all n fireflies Calculate the distance r between xi and xj using Cartesian distance equation if (Ij > Ii) Attractiveness varies with distance r via b0eÀ gr Move firefly i towards j in all d dimensions end if Evaluate new solutions and update light intensity end for j end for i Rank the fireflies and find the current best end while Post-process results and visualization. The earlier observations and studies in the literature indicated that the firefly algorithm can subdivide the whole population into subgroups automatically in terms of the attraction mechanism via the variation of light intensity and one of the FA variants can escape from the local minima owing to long-distance mobility by Lévy flight [34] Such advantages mean that FA is good at exploration as well as diversification.

DÀ 1 10sin2ð3pyiÞ þ ðyi À

Experimental Results and Analysis

Conclusions