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

Contents Introduction Genetic algorithm concepts The Recessive Trait Properties GA as a computation work Numerical Example Conclusion Questions and Discussion 16/11/2018

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 16/11/2018

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. 16/11/2018

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. 16/11/2018

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 16/11/2018

The Recessive Trait Propertie 100% brown eyes 25% blue eyes 50% blue eyes 100% blue eyes 16/11/2018

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. 16/11/2018

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. 16/11/2018

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 16/11/2018

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. 16/11/2018

Population size = 60 & Mutation rate = 10% Numerical Example The minimum value evaluation of the peaks function Population size set [ 20 60 100 200 300 500 ] 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 -6.3259 0.2579 -1.5000 MGA -6.5511 0.2283 -1.6255 16/11/2018

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 16/11/2018

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 16/11/2018

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. 16/11/2018

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