1. 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
16/11/2018

2. Contents Introduction Genetic algorithm concepts
The Recessive Trait Properties
GA as a computation work
Numerical Example
Conclusion
Questions and Discussion
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3. Introduction
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
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4. Genetic algorithm concepts
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.
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5. Genetic algorithm concepts
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.
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6. Genetic algorithm concepts
There are three methods of human inheritance, dominant, recessive and sex linked.
The sex linked properties: expressing depend on the person sex.
The dominant properties: only one genetic trait is needed for this property to be expressed.
The recessive properties : a person needs to inherit two copies of the gene for the trait to be expressed. A a
Sex linked F M A a
Dominant A a
Recessive
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7. The Recessive Trait Propertie
100% brown eyes
25% blue eyes
50% blue eyes
100% blue eyes
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8. GA as a computation work
The method of GAs evolutionary computation works as:
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.
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9. Genetic operators
The genetic operators demonstrate how to generate the new population from the old ones.
The Traditional genetic algorithm
The Modified genetic algorithm
Sort the population according to its fitness.
Choose the best N population to Generate the new 2N population
Generate the new population by marring the nearest fitness parents, keeping the common genes and randomly swapping the different genes, to create a 2N population.
Do random mutation to the created population.
Ranking the old population according to its fitness
Send the good solutions to the mating pool and eliminate the bad ones using a selection method (roulette wheel selection,…).
Do a crossover randomly between the mating pool population using one of the crossover method.
Do random mutation to the created population.
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10. Generating of the new population
Gene NO 1 2 3 4 5 6 7 8
Parent 1
Parent 2
The Traditional genetic algorithm (Uniform crossover)
Gene NO 1 2 3 4 5 6 7 8
Child 1
Child 2
The Modified genetic algorithm
Gene NO 1 2 3 4 5 6 7 8
Child 1
Child 2
Child 3
Child 4
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11. 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.
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12. Population size = 60 & Mutation rate = 10%
Numerical Example
The minimum value evaluation of the peaks function
Population size set
[ ]
Mutation rate set
[ 0% 5% 10% 15% 20% 50%]
The minimum of the PEAKS function
Population size = 60 & Mutation rate = 10%
Algorithm z X Y
TGA
0.2579
MGA
0.2283
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13. Numerical Examples
The second example : Development of an active vibration control (AVC) of a flexible beam system U Y U
beam mass
0.037 kg
beam length
0.635 m
beam constant
1.351
beam segments 19
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14. Numerical Example 2_D Beam fluctuation at the end point
Performance of the MGA and TGA in auto-power spectral density
Beam fluctuation along its length before cancellation
2_D Beam fluctuation at the end point
Beam fluctuation at the end point after cancellation in implementing the AVC system using MGA
Beam fluctuation at the end point after cancellation in implementing the AVC system using TGA
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15. Conclusion
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.
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16. Questions & Discussion
Modified Crossover Operator Approach for Evolutionary Optimization
Questions & Discussion
A A Madkour, M A Hossain and K P Dahal.
MOSAIC Group, Department of Computing,
School of Informatics, University of Bradford,
Bradford, UK
16/11/2018