5.1 in GWO in which the grey wolves

 

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

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.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

 

 

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