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Exploring Genetic Algorithms: Concepts and Applications

Understand the Genetic Algorithm and its evolution through history, from Darwin to Mendel. Learn terminology, mutation and crossover processes, fitness functions, critiques, and future possibilities. Explore selected bibliography for further reading.

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Exploring Genetic Algorithms: Concepts and Applications

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  1. Monte Carlo Methods and the Genetic AlgorithmDefinitions and Considerations John E. Nawn MAT 5900 March 17th, 2011

  2. What is the Genetic Algorithm? • Heuristic search method employing randomness in order to determine the optimal solution to a wide range of problems • Applications include: • Economics • Number Theory • Rankings • Path Length Determination (TSP, etc.) • Based in Neo-Darwinian theory

  3. History of Genetic Algorithms • Operational Research (1940s and 1950s) – birth of heuristics • Evolutionsstrategie – Rechenberg and Schwefel (1960s) • Adaptation in Natural and Artificial Systems – John Holland (1975) • Increased computational complexity (1990s – 2000s)

  4. Evolution: A Survey • On the Origin of Species – Charles Darwin (1859) • Proposed natural selection – environment creates selection pressure for individuals in a species • Selected advantages may be heritable: provides method for determining fitness of offspring • What Darwin (and biologists) didn’t know…

  5. Genetics: A Survey • Gregor Mendel (1863) • Individuals within a species carry directions for their promulgation • Segregation (First Law) • Independent Assortment (Second Law) • Increasing technology and the discovery of mutations and crossovers • Genotype and phenotype

  6. Terminology • Population • Set of possible solutions in any given generation • Chromosomes • Basic units that undergo reproduction in the algorithm • Two types: binary and non-binary • Minimum size requirements • Genes and alleles • Reproduction

  7. Terminology • Mutation • Process of changing allele values in a chromosome • Inversions • How often? • What type? • Crossover • Process of combining parental chromosomes to yield new chromosomes • What type?

  8. Terminology • Selection • Criterion • Fitness functions • Reeves and Rowe: • Tournament selection • Ranking • Termination • Diversity thresholds • Generation limits • Computational limits

  9. Minimum String Length Requirements Reeves, Colin R.; p. 28

  10. Mutations • Simplicity of method • Binary • Reversal of alleles • Non-binary • Stochastic selection of new alleles • Differing mutation rates • Selecting complete mutations and error repair

  11. Crossovers (X) • Binary • NX – N-point crossovers • UX – Uniform crossover, or linear operator “masks” • Non-Binary • Difficulty in applying n-point crossovers • PMX – Partially matched crossover • UX – “in/out” order crossovers • Further possibilities – Fox/ McMahon and Poon/ Carter

  12. Fitness Functions • Method comparing gene success • Roulette wheel model of selection • Selection pressure = individual fitness/ total fitness • Benefit of larger selection pressure • Niches

  13. Critiques of the Genetic Algorithm:Biological and Philosophical Arguments • What is natural selection selecting for? • Evolution as a theory or fact: Lisa Gatlin • Individual genes and group interactions • Lamarckian or Darwinian evolution?

  14. Critiques of the Genetic Algorithm:Mathematical Arguments • Lack of theory in heuristic applications • Newton’s Method problem • Best possible solution or best solution? • Pseudo-randomness • Similarities to Markov chains and processes (a.k.a. t – 1 dependency)

  15. What to Expect Next • Crossover possibilities • Holland’s method - schemata approaches • Three applications: • General Path Problems or the Traveling Salesman Problem (TSP) • Ranking Styles • Stock Selection

  16. Selected Bibliography • Craig, Nancy L. et. al. Molecular Biology: Principles of Genome Function. New York: Oxford University Press, 2010. Print. • Krzanowski, Roman and Jonathan Raper. Spatial Evolutionary Modeling. New York: Oxford University, Inc., 2001. Print. • Reeves, Colin R. and Johathan E. Rowe. Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory. Boston: Kluwer Academic Publishers, 2003. Print. • Russell, Peter J. iGenetics: A Mendelian Approach. San Francisco: Pearson Education, Inc., 2005. Print

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