5.1 INTRODUCTION

Grey wolf optimization

is a swarm intelligent technique developed by Mirjalil et al., 2014, which

mimics the leadership hierarchy of wolves are well known for group hunting.

Grey wolf belongs to canidae family and mostly prefer to live in a pack. They

have a strict social dominant hierarchy; the leader is a male or female, called

Alpha

.The alpha is mostly responsible for

decision making. The orders of the dominant wolf should be followed by the pack.

The Beta (

are subordinate wolves which help the alpha in

decision making. The beta is an advisor to alpha and discipliner for the pack.

The lower ranking grey wolf is omega (

which has to submit all other dominant wolves’

.If a wolf is neither an alpha or beta nor omega, is called delta. Delta (

wolves dominate omega and reports to

alpha and beta. The hunting techniques and the social hierarchy of wolves are

mathematically modelled in order to develop GWO and perform optimization. The

GWO algorithm is tested with the standard test functions that indicate that it

has superior exploration and exploitation characteristics than other swarm

intelligence techniques. Further, the GWO has been successfully applied for

solving various engineering optimization problems. Moreover, most of the swarm

intelligent techniques that are used to solve the optimization problems cannot

have the leader to control over the entire period. This drawback is rectified

in GWO in which the grey wolves have natural leadership mechanism. Further this

algorithm has a few parameters only and easy to implement which makes it

superior than earlier ones. Due to the versatile properties of the GWO to solve

the optimization problems.

5.2 OVERVIEW OF GREY WOLF

OPTIMIZATION ALGORITHM

The GWO mimics the hunting behaviour and the social

hierarchy of grey wolves. In addition to the social hierarchy of grey wolves,

pack hunting is another appealing societal action of grey wolves. The main

segments of GWO are encircling, hunting and attacking the prey. The algorithmic

steps of GWO are presented below.

5.2.1 ALGORITHMIC STEPS AND PSEUDO CODE

The

GWO algorithm is described briefly with the following steps:

Step 1: Initialize the

GWO parameters such as search agents (Gs) , design variable size (Gd). Vectors

a, A, C and maximum number of iterations (itermax).

(5.1)

(5.2)

The values of

are linearly decreased from 2 to 0 over the

course of iterations.

Step 2: Generate wolves randomly based on the size of the pack.

Mathematically, these wolves can be expressed as,

(5.3)

Where,

is the initial value

of the jth pack of the ith wolves.

Step 3:Estimate the fitness

value of each hunt agent using equations (5.4)-(5.5)

(5.4)

(5.5)

Step 4: Identify the best hunt agent (

),

the second best hunt agent (

and the third best hunt (

)

using equations (5.6)-(5.11).

(5.6)

(5.7)

(5.8)

(5.9)

(5.10)

(5.11)

Step 5: Renew the location of the current

hunt agent using equation (5.12)

(5.12)

Step 6: Estimate the fitness value of all

hunts.

Step 7: Update the value of

,

and

.

Step 8: Check for stopping conditions

i.e., whether the Iter reaches Itermax,if yes, print the best

value of solution otherwise go to step 5.

The Pseudo code for GWO

algorithm is as follows

1:Generate initial search algorithm Gi(i=1,2,…,n)

2:Initialize

the vector’s a,A and C.

3:Estimate the

fitness value of each hunt agent

= the best hunt agent

= the second best hunt agent

= the third best hunt agent

4:Iter=1

5:repeat

6:for i=1:Gs(grey

wolf pack size)

Renew the location

of the current hunt agent using equation(5.12).

End for

7:Estimate the fitness value of all hunt agents.

8:Update the

vectors a,A and C.

9:Update the

values of

.

10:Iter=Iter+1

11:until

Iter>=maximum number of iterations {Stopping criteria}

12:output

End