monte carlo methods and the genetic algorithm definitions and considerations john e. nawn mat 5900...
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Monte Carlo Methods and the Genetic Algorithm
Definitions and Considerations
John E. NawnMAT 5900March 17th, 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:◦Economics◦Number Theory◦Rankings◦Path Length Determination (TSP, etc.)
Based in Neo-Darwinian theory
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)
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…
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
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
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?
TerminologySelection
◦Criterion◦Fitness functions◦Reeves and Rowe:
Tournament selection Ranking
Termination◦Diversity thresholds◦Generation limits◦Computational limits
MutationsSimplicity of methodBinary
◦Reversal of allelesNon-binary
◦Stochastic selection of new alleles◦Differing mutation rates◦Selecting complete mutations and
error repair
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
Fitness FunctionsMethod comparing gene successRoulette wheel model of selectionSelection pressure =
individual fitness/ total fitnessBenefit of larger selection
pressureNiches
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?
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)
What to Expect NextCrossover possibilitiesHolland’s method - schemata
approachesThree applications:
◦General Path Problems or the Traveling Salesman Problem (TSP)
◦Ranking Styles◦Stock Selection
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