Recessive Trait Cross Over Approach of GAs Population Inheritance - - PowerPoint PPT Presentation

1

Recessive Trait Cross Over Approach of GAs Population Inheritance for Evolutionary Optimisation

Amr Madkour, Alamgir Hossain, and Keshav Dahal

Department of Computing, School of Informatics University of Bradford, Bradford, UK

{A.A.M.Madkour, m.a.hossain1, k.p.dahal}@bradford.ac.uk

2

Contents

• Introduction
• Genetic algorithm concepts
• The Recessive Trait Properties
• GA as a computation work
• Numerical Example
• Conclusion
• Questions and Discussion

3

Introduction

Over the last decade, Genetic Algorithms (GAs)

have been extensively used as search and

• ptimization tools.

The concept of the GAs was first conceived by

John Holland of the University of Michigan 1975

This investigation proposes a modified crossover

approach for population inheritance using a concept taken from the Recessive Trait idea

The proposed approach reduces the randomization

"lucky" of the traditional GA crossover operator

4 In the nucleus of each human cell there are a total of

23 pairs of chromosomes that are made up of long chemical chains called DNA .

Genetic information is stored on these chromosomes.

Genetic algorithm concepts (1)

5 When a baby is conceived it is supplied with two

copies of chromosome: one copy from the mother and the other one from the father.

The information from all of these genes together

makes the plan for the human body, its functions and its properties.

Genetic algorithm concepts (2)

6

Properties of human inheritance

A A A A a A Dominant A A A A a a Recessive A A A A a A A a a Sex linked

F M

• 1. Sex linked: expression of this property

depend on the person sex.

• 2. Dominant: only one genetic trait is needed

for this property to be expressed.

• 3. Recessive: a person needs to inherit two

copies of the gene for the trait to be expressed.

7

The Recessive Trait Propertie

25% blue eyes 50% blue eyes 100% blue eyes 100% brown eyes

8

GA as a computation technique

Create a population of individuals,

• Evaluate their fitness.

Generate a new population by applying the

genetic operators

Repeat this process for a number of times.

The GA method works using following steps: The genetic operators demonstrate how to generate the new population from the old ones.

9

The Traditional Crossover GA (TCGA)

• 1. ranks the old population according to its

fitness

• 2. sends the good solutions to the mating pool

and eliminate the bad ones using a selection method (roulette wheel selection,…).

• 3. performs crossover operation between

population in the mating pool using one of the crossover methods.

• 4. does a random mutation to the newly

created population.

10

The Recessive Trait Crossover GA (RCGA)

• 1. sorts the population according to its fitness.
• 2. chooses the best N individuals to generate

the new 2N individuals.

• 3. generates the new population by mating

the nearest fitness parents, keeping the common genes and randomly swapping the different genes, to create a 2N population.

• 4. does random mutation to the newly

created population.

11

Generating the new population

Gene NO 1 2 3 4 5 6 7 8 Parent 1 1 1 1 1 1 Parent 2 1 1 1 Gene NO 1 2 3 4 5 6 7 8 Child 1 1 1 1 1

• Child 2

1 1 1 1 Child 3 1 1 1 Child 4 1 1 1 1 1

Then the reproducing using the RCGA will be If the Parents are

12

Numerical Examples- PEAKS function

• 3
• 2
• 1

1 2 3

• 2

2

• 6
• 4
• 2

2 4 6 x Peaks y

y.^2)

• 1).^2

+ exp(-(x * 1/3

• y.^2)
• exp(-x.^2

* y.^5).

• x.^3
• (x/5

* 10

• 1).^2)

+ (y

• )

exp(-(x.^2 * x).^2.

• (1

* 3 = z

The first example: Determine

the minimum value of the Matlab PEAKS function.

PEAKS is a function of two variables,

• btained

by translating and scaling Gaussian distributions evaluated as.

13

PEAKS function: Effect of GA parameters

20R 20T 60 R 60 T 100 R 100 T 200 R 200 T 300 R 300 T 500 R 500 T 0.05 0.1 0.15 0.2 0.5

• 6.55
• 6.5
• 6.45
• 6.4
• 6.35
• 6.3

0.05 0.1 0.15 0.2 0.5

The minimum of the PEAKS function Population size set [ 20 60 100 200 300 500 ] Mutation rate set [ 0% 5% 10% 15% 20% 50%]

14

PEAKS function: GA performances

Population size = 60 & Mutation rate = 10% Algorithm z X Y TCGA

• 6.3259

0.2579

• 1.5000

RCGA

• 6.5511

0.2283

• 1.6255

2 4 6 8 10 12 14 16 18 20

• 6.6
• 6.4
• 6.2
• 6
• 5.8
• 5.6
• 5.4
• 5.2
• No. of generations

F(z) RCGA TUCGA

15

Numerical Examples- AVC

F

The second example : Development of an

Active Vibration Control (AVC) of a flexible beam system.

A flexible beam is subjected to a force ‘F’.

16

AVC – platform features

F Y

beam mass 0.037 kg beam length 0.635 m beam constant 1.351 beam segments 19

m t X F t SY Y Y

J J J

1 ) , ( ) (

2 2 1 1

Δ + − − =

− +

λ

The force causes vibration of the beam .

The vibration can be modelled using the

finite difference (FD) method

17

AVC – controller

The vibration of the flexible beam system can be

compensated using a controller with GA

C

Observed Signal

Detector Secondary source Primary source

18

GAs

) ( ) ( ˆ ) ( ˆ ) ( ˆ

1 1

z U z A z B z y

− −

=

F

F ˆ

y U

AVC controller using GAs

∑

=

− =

r k

k y k y

1

) ( ˆ ) ( min function fitness GAs

19

Beam fluctuation along its length before cancellation Beam fluctuation at the end point after cancellation in implementing the AVC system using TUCGA Beam fluctuation at the end point after cancellation in implementing the AVC system using RCGA

Without controller With TCGA controller With RCGA controller

AVC – controller

20

Comparative performance in time domain

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 x 10

• 3

Time (sec) Deflection (m) No Cancellation TCGA RCGA

2_D Beam fluctuation at the end point

21

Performance of the TUCGA and RCGA in auto-power spectral density

10 20 30 40 50 60 70 80 90 100

• 120
• 110
• 100
• 90
• 80
• 70
• 60
• 50
• 40
• 30
• 20
• 10

MGA Frequency (Hz) Spectral density (db) No Cancellation TCGA RCGA

Comparative performance in frequency domain

22

Conclusion

This research has presented the investigation

into a RCGA population inheritance using a concept taken from the recessive trait idea.

The RCGA offered better convergence, higher

accuracy and faster solution for each problem as compared to the TUCGA (using same initial populations, bit representation, and mutation rate).

The RCGA is very sample and easy to

implement for any numerical optimization problem for any fitness function.

23

Pleas feel free to contact us for further discussion

Amr Madkour, Alamgir Hossain, and Keshav Dahal

MOSAIC Group, Department of Computing, School of Informatics, University of Bradford, Bradford, UK

{A.A.M.Madkour, m.a.hossain1, k.p.dahal}@bradford.ac.uk

Thank YOU