monte carlo methods and the genetic algorithm definitions and considerations
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Monte Carlo Methods and the Genetic Algorithm Definitions and Considerations. John E. Nawn MAT 5900 March 17 th , 2011. 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: - PowerPoint PPT PresentationTRANSCRIPT
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Monte Carlo Methods and the Genetic Algorithm
Definitions and Considerations
John E. NawnMAT 5900March 17th, 2011
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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
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History of Genetic AlgorithmsOperational Research (1940s and
1950s) – birth of heuristicsEvolutionsstrategie – Rechenberg
and Schwefel (1960s)Adaptation in Natural and
Artificial Systems – John Holland (1975)
Increased computational complexity (1990s – 2000s)
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Evolution: A SurveyOn 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…
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Genetics: A SurveyGregor Mendel (1863)Individuals within a species carry
directions for their promulgationSegregation (First Law)Independent Assortment (Second
Law)Increasing technology and the
discovery of mutations and crossovers
Genotype and phenotype
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TerminologyPopulation
◦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
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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?
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TerminologySelection
◦Criterion◦Fitness functions◦Reeves and Rowe:
Tournament selection Ranking
Termination◦Diversity thresholds◦Generation limits◦Computational limits
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Minimum String Length Requirements
Reeves, Colin R.; p. 28
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MutationsSimplicity of methodBinary
◦Reversal of allelesNon-binary
◦Stochastic selection of new alleles◦Differing mutation rates◦Selecting complete mutations and
error repair
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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
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Fitness FunctionsMethod comparing gene successRoulette wheel model of selectionSelection pressure =
individual fitness/ total fitnessBenefit of larger selection
pressureNiches
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Critiques of the Genetic Algorithm:Biological and Philosophical ArgumentsWhat is natural selection
selecting for?Evolution as a theory or fact: Lisa
GatlinIndividual genes and group
interactions Lamarckian or Darwinian
evolution?
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Critiques of the Genetic Algorithm:Mathematical ArgumentsLack of theory in heuristic
applicationsNewton’s Method problemBest possible solution or best
solution?Pseudo-randomnessSimilarities to Markov chains and
processes (a.k.a. t – 1 dependency)
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What to Expect NextCrossover possibilitiesHolland’s method - schemata
approachesThree applications:
◦General Path Problems or the Traveling Salesman Problem (TSP)
◦Ranking Styles◦Stock Selection
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Selected BibliographyCraig, 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