Modified Crossover Operator Approach
for Evolutionary Optimization
A A Madkour, M A Hossain and K P Dahal.
Department of Computing, School of Informatics
University of Bradford, Bradford, UK
11/04/2020
1
Contents
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
Introduction

Genetic algorithm concepts

The Recessive Trait Properties

GA as a computation work

Numerical Example

Conclusion

Questions and Discussion
2
Introduction
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
Over the last decade, Genetic Algorithms (GAs)
have been extensively used as search and
optimization tools.

The concept of the GAs was first conceived by
John Holland of the University of Michigan 1975

This investigation provides a modified approach
for population inheritance using a concept taken
from the Recessive Trait idea for evolutionary
optimization to reduce the randomization "lucky"
of the traditional GAs crossover operator
3
Genetic algorithm concepts


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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 those chromosomes.
4
Genetic algorithm concepts
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
When a baby is conceived, it is supplied with two
copies of every chromosome: one copy from the
mother and the other one from the father.

The information from all of those genes takes
together to makes up the plan for the human
body, its functions and its properties.
5
Genetic algorithm concepts

There are three methods of human inheritance, dominant,
recessive and sex linked.
1.
The sex linked properties: expressing depend on the
person sex.
2.
The dominant properties: only one genetic trait is needed
for this property to be expressed.
3.
The recessive properties : a person needs to inherit two
copies of the gene for the trait to be expressed.
A
A
A
A
A
A
A
A
a
a
A
a
A
a
M
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A A
aF
Sex linked
A A
Dominant
A a
Recessive
6
The Recessive Trait Propertie
100%
brown
eyes
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25%
blue
eyes
50%
blue
eyes
100% blue
eyes
7
GA as a computation work
The method of GAs evolutionary computation works as:


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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.
8
Genetic operators

The genetic operators demonstrate how to
generate the new population from the old ones.
Modified genetic
The Traditional
geneticalgorithm
algorithm
1.
2.
2.
3.
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Ranking
Sort the population
the old population
according
according
to its fitness.
to its
fitness
Choose the best N population to Generate
Send
the new
the2N
good
population
solutions to the mating pool
and
Generate
eliminate
the new
the bad
population
ones using
by marring
a selection
method
the nearest
(roulette
fitness
wheel
parents,
selection,…).
keeping the
3. Do
common
a crossover
genes randomly
and randomly
between
swapping
the mating
pool
the different
population
genes,
using
to one
create
of the
a 2N
crossover
method.
population.
4. Do random mutation to the created
9
population.
Generating of the new population
Gene
NO
1
2
3
4
5
6
7
8
Parent 1
0
1
1
0
0
1
0
0
Parent 2
1
1
0
0
1
1
0
1
The Traditional genetic algorithm (Uniform crossover)
Gene NO
1
2
3
4
5
6
7
8
Child 1
0
1
0
0
0
1
0
0
Child 2
1
1
1
0
1
1
0
1
The Modified genetic algorithm
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Gene NO
1
2
3
4
5
6
7
8
Child 1
0
1
1
0
1
1
0
1
Child 2
1
1
0
0
0
1
0
0
Child 3
1
1
0
0
1
1
0
1
Child 4
0
1
1
0
0
1
0
10
0
Numerical Examples


The first example: Determine the minimum value
of the Matlab PEAKS function.
PEAKS is a function of two variables, obtained
by translating and scaling Gaussian distributions
evaluated as.
z = 3 * (1 - x).^2. * exp(-(x.^2 ) - (y + 1).^2)
- 10 * (x/5 - x.^3 - y.^5). * exp(-x.^2 - y.^2)
- 1/3 * exp(-(x + 1).^2 - y.^2)
Peaks
6
4
2
0
-2
-4
-6
2
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0
-2
y
-3
-2
0
-1
x
1
2
3
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Numerical Example
Population size set
[ 20 60 100
-5.2
200 300 500 ]
MGAs
TGAs
-5.4
Mutation rate set
[ 0% 5% 10% 15% 20% 50%]
-5.6
F(z)
-5.8
-4.8
-6
TGAs
MGAs
-5
-6.2
-5.2
-6.4
-5.4
-6.6
10
20
30
40
50
No. of generations
60
70
80
90
100
f(Z)
0
-5.6
-5.8
The minimum value evaluation of the peaks function
-6
-6.2
Population size = 60 & Mutation rate = 10%
-6.4
Algorithm
-6.6
0
TGA
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20
60
z
100
No. of Population
-6.3259
X
200
0.2579
300
Y
500
-1.5000
The minimum
of the PEAKS
MGA
-6.5511
0.2283 function
-1.6255
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Numerical Examples

The second example : Development of an active
vibration control (AVC) of a flexible beam system
Y
Secondary
source
U
U Detector
beam mass
beam constant
0.037 kg
C
beam length
Observed
Signal
0.635 m
1.351Primary beam segments
19
source
1
YJ1  YJ1   SYJ  (t ) U(X, t )
m
2
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2
13
Numerical Example
MGA
-3
x 10
-10
1
No Cancellation
No Cancellation
TCGA
TCGA RCGA
RCGA
-20
0.8
-30
0.6
-40
-50
0.2
Deflection (m)
Spectral density (db)
0.4
-60
0
-70
-0.2
-80
-0.4
-90
-100
-0.6
-110
-0.8
-120
-1
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0
0
0.2
10
0.4
20
0.6
30
0.8
1
40 Time 50
60
(sec)
Frequency (Hz)
1.2
70
1.4
80
1.6
90
1.8
100
Beam
fluctuation
along
its
length
before
cancellation
Beam
fluctuation
at
the
end
point
after
cancellation
in
Performance
ofBeam
the MGA
and TGA inatauto-power
spectral density
2_D
fluctuation
the
end
point
14
implementing
implementing the
the AVC
AVC system
system using
using MGA
TGA
Conclusion
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
This research has presented the investigation
into a MGA population inheritance using a
concept taken from the recessive trait idea.

The MGA offered better convergence, higher
accuracy and faster solution for each problem
as compared to the TGA (using same initial
populations, bit representation, and mutation
rate).

The MGA is very sample and easy to implement
for any numerical optimization problem for any
fitness function.
15
Modified Crossover Operator Approach
for Evolutionary Optimization
Questions & Discussion
A A Madkour, M A Hossain and K P Dahal.
11/04/2020
MOSAIC Group, Department of Computing,
School of Informatics, University of Bradford,
Bradford, UK
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