Grey Wolf Optimizer

Seyedali Mirjalili

a,

⇑

, Seyed Mohammad Mirjalili

b

, Andrew Lewis

a

a

School of Information and Communication Technology, Grifﬁth University, Nathan Campus, Brisbane QLD 4111, Australia

b

Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University, G.C. 1983963113, Tehran, Iran

article info

Article history:

Received 27 June 2013

Received in revised form 18 October 2013

Accepted 11 December 2013

Available online 21 January 2014

Keywords:

Optimization

Optimization

techniques

Heuristic algorithm

Metaheuristics

Constrained optimization

GWO

abstract

This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) inspired by grey wolves

(Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey

wolves in nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for sim-

ulating the leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encir-

cling prey, and attacking prey, are implemented. The algorithm is then benchmarked on 29 well-known

test functions, and the results are veriﬁed by a comparative study with Particle Swarm Optimization

(PSO), Gravitational Search Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming

(EP), and Evolution Strategy (ES). The results show that the GWO algorithm is able to provide very com-

petitive results compared to these well-known meta-heuristics. The paper also considers solving three

classical engineering design problems (tension/compression spring, welded beam, and pressure vessel

designs) and presents a real application of the proposed method in the ﬁeld of optical engineering. The

results of the classical engineering design problems and real application prove that the proposed algo-

rithm is applicable to challenging problems with unknown search spaces.

Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Meta-heuristic optimization techniques have become very pop-

ular

over the last two decades. Surprisingly, some of them such as

Genetic Algorithm (GA) [1], Ant Colony Optimization (ACO) [2],

and Particle Swarm Optimization (PSO) [3] are fairly well-known

among not only computer scientists but also scientists from differ-

ent ﬁelds. In addition to the huge number of theoretical works,

such optimization techniques have been applied in various ﬁelds

of study. There is a question here as to why meta-heuristics have

become remarkably common. The answer to this question can be

summarized into four main reasons: simplicity, ﬂexibility, deriva-

tion-free mechanism, and local optima avoidance.

First, meta-heuristics are fairly simple. They have been mostly

inspired

by very simple concepts. The inspirations are typically re-

lated to physical phenomena, animals’ behaviors, or evolutionary

concepts. The simplicity allows computer scientists to simulate dif-

ferent natural concepts, propose new meta-heuristics, hybridize

two or more meta-heuristics, or improve the current meta-heuris-

tics. Moreover, the simplicity assists other scientists to learn meta-

heuristics quickly and apply them to their problems.

Second, ﬂexibility refers to the applicability of meta-heuristics

to

different problems without any special changes in the structure

of the algorithm. Meta-heuristics are readily applicable to different

problems since they mostly assume problems as black boxes. In

other words, only the input(s) and output(s) of a system are impor-

tant

for a meta-heuristic. So, all a designer needs is to know how to

represent his/her problem for meta-heuristics.

Third, the majority of meta-heuristics have derivation-free

mechanis

ms. In contrast to gradient-based optimization ap-

proaches, meta-heuristics optimize problems stochastically. The

optimization process starts with random solution(s), and there is

no need to calculate the derivative of search spaces to ﬁnd the opti-

mum. This makes meta-heuristics highly suitable for real problems

with expensive or unknown derivative information.

Finally, meta-heuristics have superior abilities to avoid local op-

tima

compared to conventional optimization techniques. This is

due to the stochastic nature of meta-heuristics which allow them

to avoid stagnation in local solutions and search the entire search

space extensively. The search space of real problems is usually un-

known and very complex with a massive number of local optima,

so meta-heuristics are good options for optimizing these challeng-

ing real problems.

The No Free Lunch (NFL) theorem [4] is

worth mentioning here.

This theorem has logically proved that there is no meta-heuristic

best suited for solving all optimization problems. In other words,

a particular meta-heuristic may show very promising results on a

set of problems, but the same algorithm may show poor perfor-

mance on a different set of problems. Obviously, NFL makes this

ﬁeld of study highly active which results in enhancing current ap-

proaches and proposing new meta-heuristics every year. This also

0965-9978/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

⇑

Corresponding author. Tel.: +61 434555738.

E-mail addresses: seyedali.mirjalili@grifﬁthuni.edu.au (S. Mirjalili),

mohammad.smm@gmail.com (S.M. Mirjalili), a.lewis@grifﬁth.edu.au (A. Lewis).

Advances in Engineering Software 69 (2014) 46–61

Contents lists available at ScienceDirect

Advances in Engineering Software

journal homepage: www.elsevier.com/locate/advengsoft