Introduction to Genetic Algorithms and Evolutionary Computation

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

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

3. References • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • 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, 2nd Ed., IEEE Press, Piscataway, NJ, 2000. • M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, Cambridge, Massachusetts, 1998. Genetic Algorithms

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

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

6. Sample Application Domain • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • 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

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

8. Genome • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • 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

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

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

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

12. Selection • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • 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

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

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

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

16. Worked Example • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • World size: • 4X4 • Population size: • N = 4 • Genome: • 16 bits • Fitness: • F(p) = (8-Steps before reaching goal) – (squares from goal) • Propagation: Greedy, Elitist Genetic Algorithms

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

18. Ex: Fitness Calculation • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • Fitness calculations: • F(p1) = (8-8) – 4 = -4 • F(p2) = -5 • F(p3) = -6 • F(p4) = -4 Genetic Algorithms

19. Ex: Selection and Propagation • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • Select p1 and p4 as parents of the next generation, P(1) • Produce offspring using crossover and mutation Genetic Algorithms

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

21. Ex: Repeat for next Generation • References • Introduction • Sample Application • Formulation • Genome • Population • Fitness Function • Selection • Propagation • Worked Example • Case Study: Evolving Neural Controllers • Repeat: • F(p1) = -4 • F(p2) = -4 • F(p3) = 0 • F(p4) = -4 Genetic Algorithms

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