Introduction to Genetic Algorithms and Evolutionary Computation Andrew

Introduction to Genetic Algorithms and Evolutionary Computation Andrew L. Nelson Visiting Research Faculty University of South Florida 1

Overview • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Outline to the left • Current topic in red • • Introduction Algorithm Formulation Example Case Study Genetic Algorithms 2

References • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Holland, J. J. , Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor Michigan, 1975. • D. B. Fogel, Evolutionary Computation, Toward a New Philosophy of Machine Intelligence, 2 nd Ed. , IEEE Press, Piscataway, NJ, 2000. • M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, Massachusetts, 1998. Genetic Algorithms 3

Introduction • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Genetic Algorithms • Base on Natural Evolution • Stochastic Optimization • Stochastic Numerical Techniques • Evolutionary Computation • Artificial Life • Machine Learning • Artificial Evolution Genetic Algorithms 4

Introduction • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Population of candidate solutions • Evaluate the quality of each solution • Survival (and reproduction) of the fittest • Crossover and Mutation Genetic Algorithms 5

Sample Application Domain • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Finding the best path between two points in "Grid World" • Creatures in world: • Occupy a single cell • Can move to neighboring cells • Goal: Travel from the gray cell to the green cell in the shortest number of steps Genetic Algorithms 6

Algorithm Formulation • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Components of a Genetic Algorithm: • • Genome Fitness metric Stochastic modification Cycles of generations • Many variations Genetic Algorithms 7

Genome • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • The genome is used represent candidate solutions • Fixed length Bitstrings • Holland • Traditional • Convergence theorems exist • Real-valued genomes • Artificial evolution • Difficult to prove convergence Genetic Algorithms 8

Genome • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Example: Representation of a path through a square maze: • Representation: N=00, E=10, S=11, W=01 Genetic Algorithms 9

Population • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Population, P is made up of individuals pn where N is the population size Genetic Algorithms 10

Fitness Function • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • F(p) called Objective Function • Example: Shortest legal path to goal • F(pn) = S(steps) Genetic Algorithms 11

Selection • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Selection Methods of selection of the parents of the next generation of candidate solutions • Diverse methods • Probabilistic: • Chance of be selected is proportional to fitness • Greedy: • the fittest solutions are selected Genetic Algorithms 12

Propagation • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • The next generation is generated from the fittest members of the current population • Genetic operators: • Crossover (recombination) • Mutation Genetic Algorithms 13

Propagation: Crossover • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Example: 1 point crossover • Two parents generate 1 offspring Genetic Algorithms 14

Propagation: Mutation • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Example: Bitstring point mutation • Replace randomly selected bits with their complements • One parent generates one offspring Genetic Algorithms 15

Worked Example • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • World size: • 4 X 4 • Population size: • N=4 • Genome: • 16 bits • Fitness: • F(p) = (8 -Steps before reaching goal) (squares from goal) – • Propagation: Greedy, Elitist Genetic Algorithms 16

Ex: Initial Population • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Initial Population P(0): 4 random 16 -bit strings Genetic Algorithms 17

Ex: Fitness Calculation • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Fitness calculations: • F(p 1) = (8 -8) – 4 = -4 • F(p 2) = -5 • F(p 3) = -6 • F(p 4) = -4 Genetic Algorithms 18

Ex: Selection and Propagation • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Select p 1 and p 4 as parents of the next generation, P(1) • Produce offspring using crossover and mutation Genetic Algorithms 19

Ex: Book Keeping. . . • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • The next generation is. . . Genetic Algorithms 20

Ex: Repeat for next Generation • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Repeat: • • F(p 1) = -4 F(p 2) = -4 F(p 3) = 0 F(p 4) = -4 Genetic Algorithms 21

Case Study • • • References Introduction Sample Application Formulation • Genome • Population • Fitness Function • Selection • Propagation Worked Example Case Study: Evolving Neural Controllers 2/9/2004 • Evolution of neural networks for autonomous robot control using competitive relative fitness evaluation Genetic Algorithms 22