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

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 1

Contents Introduction � Genetic algorithm concepts � The Recessive Trait Properties � GA as a computation work � Numerical Example � Conclusion � Questions and Discussion � 2

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 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 3

Genetic algorithm concepts (1) � 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 . 4

Genetic algorithm concepts (2) � 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. 5

Properties of human inheritance 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. A A A A A A A A a A a A a a M F A A A a A A a 6 Recessive Sex linked Dominant

blue eyes 100% 7 The Recessive Trait Propertie blue eyes 50% blue eyes 25% brown eyes 100%

GA as a computation technique The GA method works using following steps: � 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 genetic operators demonstrate how to generate the new population from the old ones. 8

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. 9

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. 10

Generating the new population If the Parents are Gene 1 2 3 4 5 6 7 8 NO Parent 1 0 1 1 1 0 1 0 1 Parent 2 0 0 1 0 0 1 1 0 Then the reproducing using the RCGA will be Gene NO 1 2 3 4 5 6 7 8 Child 1 0 1 1 1 0 1 0 o Child 2 0 1 1 0 0 1 1 0 Child 3 0 0 1 0 0 1 0 1 Child 4 0 0 1 1 0 1 1 1 11

Numerical Examples- PEAKS function � The first example: D etermine 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 3 2 0 1 12 0 -1 -2 -2 -3 y x

PEAKS function: Effect of GA parameters Population size set [ 20 60 100 200 300 500 ] Mutation rate set [ 0% 5% 10% 15% 20% 50%] -6.55 -6.5 0 -6.45 0.05 0.1 0.15 -6.4 0.2 0.5 -6.35 0.5 -6.3 0.2 20R 0.15 20T 60 R 0.1 60 T 100 R 100 T 0.05 200 R 200 T 300 R 0 300 T 500 R 500 T 13 The minimum of the PEAKS function

PEAKS function: GA performances -5.2 RCGA -5.4 TUCGA -5.6 -5.8 F(z) -6 -6.2 -6.4 -6.6 0 2 4 6 8 10 12 14 16 18 20 No. of generations Population size = 60 & Mutation rate = 10% Algorithm z X Y TCGA -6.3259 0.2579 -1.5000 14 RCGA -6.5511 0.2283 -1.6255

Numerical Examples- AVC � The second example : Development of an Active Vibration Control (AVC) of a flexible beam system. � A flexible beam is subjected to a force ‘F’. F 15

AVC – platform features � The force causes vibration of the beam . Y F beam mass 0.037 kg beam length 0.635 m beam constant 1.351 beam segments 19 � The vibration can be modelled using the finite difference (FD) method 1 = − − λ + Δ 2 2 Y Y SY ( t ) F ( X , t ) + − 16 J 1 J 1 J m

AVC – controller � The vibration of the flexible beam system can be compensated using a controller with GA Secondary source Detector Observed Signal C Primary source 17

AVC controller using GAs ˆ r ∑ F = − ˆ GAs fitness function min y ( k ) y ( k ) = k 1 F y U − ˆ 1 B ( z ) = ˆ y ( z ) U ( z ) − ˆ 1 ( ) A z GAs 18

AVC – Beam fluctuation along its length before cancellation controller Without controller Beam fluctuation at the end point after cancellation in implementing the AVC system using TUCGA With TCGA controller With RCGA Beam fluctuation at the end point after cancellation in controller implementing the AVC system using RCGA 19

Comparative performance in time domain -3 x 10 1 No Cancellation TCGA RCGA 0.8 0.6 0.4 0.2 Deflection (m) 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (sec) 2_D Beam fluctuation at the end point 20

Comparative performance in frequency domain MGA -10 No Cancellation -20 TCGA RCGA -30 -40 Spectral density (db) -50 -60 -70 -80 -90 -100 -110 -120 0 10 20 30 40 50 60 70 80 90 100 Frequency (Hz) Performance of the TUCGA and RCGA in auto-power spectral density 21

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. 22

Thank YOU 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 23