Grey Wolf Optimization Algorithm Numerical Example

 Grey Wolf Optimization Algorithm Numerical Example

Grey Wolf Optimization Algorithm Steps

1.) Initialize Grey Wolf Population.

2.) Initialize a, A, and C.

3.) Calculate the fitness of each search agent.

4.) 𝑿_𝜶 = best search agent

5.) 𝑿_𝜷 = second-best search agent

6.) 𝑿_𝜹 = third best search agent.

7.) while (t<Max number of iteration)

8.) For each search agent 

     update the position of the current search agent by the above equations

end for

9.) update a, A, and C

10.) Calculate the fitness of all search agents.

11.) update 𝑿_𝜶, 𝑿_𝜷, 𝑿_𝜹

12.) t = t+1

end while

13.) return 𝑿_𝜶

Grey Wolf Optimization Algorithm Numerical Example

STEP 1.  Initialize the Grey wolf Population [Initial Position for each Search Agent] 𝒙_(𝒊  )  (i = 1,2,3,…n) 

  n = 6 // Number of Search Agents

 [ -100, 100] // Range

Initial Wolf Position 

    3.2228

    4.1553

   -3.8197

    4.2330

    1.3554

   -4.1212

STEP 2. Calculate Fitness for Each Search Agent. 

  Objective Function: F6(x)  = sum(abs((𝒙_𝒊  + 0.5)).^2);

Initial Fitness Value

13.8592

21.6718

11.0204

22.4013

3.4425

13.1131  

STEP 3. Compare the gray wolves fitness value, and determine the current first three best wolves.

  Select: 𝑿_𝑨𝒍𝒑𝒉𝒂,𝑿_𝑩𝒆𝒕𝒂, 𝑿_𝑫𝒆𝒍𝒕𝒂

X(Alpha) = 3.4425

X(Beta) = 11.0204

X(Delta) = 13.1131

STEP 4. Check  ( t < Maxt )

  t = 0

0 < 50 [True]

STEP 5. Update position of Current search agent

a = 2- t*((2)/Maxt);                  [where a is decreases linearly from 2 to 0]

A1= 2*a*r1-a;

C1= 2*r2;

(𝐷_𝛼lpha ) =|𝐶_1. (𝑋_𝛼lpha )  − 𝑋 (𝑡)|  

(𝑋_1 ) =| (𝑋_𝛼lpha )  − 𝐴_1  .(𝐷_𝛼lpha )  |

X1= AlphaPosition  - A1 * Dalpha;

(𝐷_𝛼lpha )  =  0.6154

𝑋_1 =  0.6361

(𝐷_𝛽eta )   = 1.8659

𝑋_2 =  5.9968

(𝐷_Delta )   =  1.6909

𝑋_3 = -3.7867

𝑋_1 = 0.6361

𝑋_2 = 5.9968        

𝑋_3 = -3.7867

Updated position for Current Search Agent.

𝑿  (𝒕+𝟏) = ((𝑋_1 ) + (𝑋_2 ) + (𝑋_3 ) )/3

𝑿 (𝟎+𝟏) = ((0.6361+5.9968−3.7867))/3

𝑿 (𝟏) = 3.4732

𝑋_1 = 0.6361        NewFitness = 1.2910                     //AlphaScore

𝑋_2 = 5.9968        NewFitness = 5.5976                     //BetaScore

𝑋_3 = -3.7867       NewFitness =  10.8023                  //DeltaScore

STEP 6. Update Alpha, Beta and Delta Position. 

  Compare the Fitness Value and Wolf Score. 

If ( AlphaOldFitnessValue > AlphaNewFitness )

THEN 

          Update Alpha: Replace AlphaOldPosition with AlphaNewPosition and          AlphaNewFitnessValue; 

Else

       Use Old Position and Fitness Value. 

 Compare the Fitness Value and Wolf Score. 

1.) UPDATE Alpha

If ( AlphaOldFitnessValue > AlphaNewFitness )

If ( 3.4425 > 1.2910 )

THEN 

          Update Alpha: Replace AlphaOldPosition with AlphaNewPosition and          AlphaNewFitnessValue; 

2.) UPDATE Beta Wolf

If ( BetaOldFitnessValue > BetaNewFitness )

If ( 11.0204 > 5.5976 )

THEN 

  Update Alpha: Replace BetaOldPosition with BetaNewPosition and  BetaNewFitnessValue; 

3.) UPDATE Delta Wolf

If ( DeltaOldFitnessValue > DeltaNewFitness )

If ( 13.1131 > 10.8023 )

THEN 

 Update Alpha: Replace DeltaOldPosition with DeltaNewPosition and DeltaNewFitnessValue; 

REPEAT LOOP until stopping criteria met.

STEP 5. Update Alpha, Beta, and Delta Position. 

REPEAT LOOP 

Estimate the position of Prey by Alpha, Beta and Delta

Grade the Wolf: Best Solution is Alpha.

REPEAT LOOP until Condition Met.

a = 2-t*((2)/Maxt);                  % a decreases linearly from 2 to 0

A1= 2*a*r1-a;

C1= 2*r2;

(𝐷_𝛼lpha ) =  2.2059

𝑋_1 =  0.3045

(𝐷_𝛽eta )   = 6.9456

𝑋_2 =  -2.6423

(𝐷_Delta )   =  4.5037

𝑋_3 = 2.4711

𝑋_1 = 0.3045

𝑋_2 = -2.6423        

𝑋_3 = 2.4711

Updated position for Current Search Agent.

𝑿 ⃗  (𝒕+𝟏) = ((𝑋_1 ) ⃗+ (𝑋_2 ) ⃗+ (𝑋_3 ) ⃗)/3

𝑿 ⃗  (𝟏+𝟏) = ((0.3045−2.623+2.4711))/3

𝑿 ⃗  (𝟐) = 0.1526

Calculate Fitness for Update position of Current search agent

𝑋_1 = 0.3045        NewFitness = 0.6473                     //AlphaScore

𝑋_2 = -2.6423        NewFitness = 4.5895                     //BetaScore

𝑋_3 = 2.4711          NewFitness =  8.8276                  //DeltaScore

STEP 7.Return 𝑋_𝐴𝑙𝑝ℎ𝑎 

𝑋_𝐴𝑙𝑝ℎ𝑎 = 0.3045        AlphaFitnessValue = 0.6473

Software Testing using Metaheuristic Optimization

Test Suite Prioritization Problem Solved using Grey Wolf Optimization Algorithm.

Topics Covered in this Video:

INTRODUCTION TO SOFTWARE ENGINEERING

SOFTWARE DEVELOPMENT LIFE CYCLE

SOFTWARE TESTING

SOFTWARE TESTING OBJECTIVE

SOFTWARE TESTING LEVELS

SOFTWARE TESTING TOOLS

SOFTWARE TESTING USING METAHEURISTIC OPTIMIZATION ALGORITHMS

TEST SUITE PRIORITIZATION PROBLEM

TEST SUITE PRIORITIZATION USING OPTIMIZATION ALGORITHMS

SOFTWARE TESTING CHALLANGES

SOFTWARE TESTING DESIGN STTATIES

SEARCH BASED SOFTWARE TESTING

WHITE BOX TESTING

BLACK BOX TESTING

TEST SUITE DESIGN EXAMPLE

TEST SUITE

TEST SUITE PRIORITIZATION

#Metaheuristic #Algorithms

Meta-heuristic Algorithms

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