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Introduction to Genetic Algorithms and Evolutionary Computation

Introduction to Genetic Algorithms and Evolutionary Computation. Andrew L. Nelson Visiting Research Faculty University of South Florida. Overview. References Introduction Sample Application Formulation Genome Population Fitness Function Selection Propagation Worked Example

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Introduction to Genetic Algorithms and Evolutionary Computation

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  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

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