Genetic Algorithms Siddhartha K. Shakya School of Computing. The Robert Gordon University Aberdeen, UK

What are GAs?  Class of Evolutionary algorithm  Based on Darwinian Evolution  First proposed by John Holland 1960s. 1970s  Used to solve wide verity of Optimization problems occurring in engineering Science and Business.

What is an Optimization Problem?  Is to find optimum or near optimum solution from the possible set of candidate solution  Search through big solution space to find best solution  There is some scoring criteria for evaluating goodness of solution also called fitness of solution

Example: Graph colouring problem (GCP) Given a set of colours, GCP is to try and assign Colour to each nodes in such the way that neighbouring nodes will not have same colour a b d e f c

What is a solution and a fitness?  Solution is a set of colours assigned to the nodes of graph.  Fitness is the number of correctly coloured nodes.

What is a solution and a fitness? Given 2 colour Black = 0 White = 1 a b d e f c a b d e f c a b d e f c a b d e f c a b d e f c Fitness = 1 Fitness = 2 Fitness = 6 Fitness = 0

Graph Colouring Problem (GCP)  Looks very simple  But as the size of the graph grows, it becomes increasingly difficult.  Lots of different problems can be see as a GCP  One of the approach to solve GCP is GA

Representation of Problem in GA  Solution is usually represented as a bit string called chromosome a b d e f c abcdef 1 fitness a b d e f c

Work flow of GA 1. Initialization of parent population 2. Evaluation 3. Selection 4. Crossover/recombination 5. Mutation 6. Evaluate child and Go to step 3 until termination criteria satisfies

Initialization of parent population  Generate the M number of solution string known as parent population  Mostly random

Evaluation  Give fitness to each of the solution a b d e f c Parent population fitness

Selection  Fit solution are likely to survive and bad solution are likely to die off  Select some of the best fit chromosomes from parent population according some selection criteria (eg. Roulette wheel selection) Parent population fitness selectionfitness

Crossover/Recombination  Exchange partial solution between pair of selected solution with some probability value eg 70% Selected Solution Child Population After Crossover

Mutation  Change the value of an allele of solution with some small probability value eg 1%  Motivation is to explore new point in the solution space Child Population After Crossover Child Population After mutation

Replace with parent population and repeat process  Evaluate child population and replace parent population  Go to selection step and repeat the process until termination criteria satisfies  Eg. Exit after given number of iteration finishes Replaced Parent Population fitness a b d e f c

Putting Everything together Parent population fitness Selected Solution After Crossover After mutation fitness InitializationEvaluation Selection Crossover Mutation Repeat iteration a b d e f c Given 2 colours (0,1)

Conclusion  Different selection, crossover and mutation operators exists.  Different GAs designed for different problems  Hybridise GA with other search algorithms  Probabilistic Model Building Genetic Algorithms (PMBGAs)

Links  Introductory tutorial on GA By D.E Goldberg  GA Archive Introductory Books  David E. Goldberg Genetic Algorithms in search, optimization and machine learning. Addison-Wesley  Mitchell, M. (1998). An Introduction to genetic Algorithm. MIT Press (HB)