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Genetic Algorithms

Genetic Algorithms - ERE284 GeneticAlgorithms...

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Genetic Algorithms Genetic Algorithms Applications to Reservoir Engineering Applications to Reservoir Engineering ERE 284 ERE 284 Barı ş  G ű yag ű ler Burak Yeten
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G ü yag ü ler Genetic Algorithm Aspects Developed by John Holland, 1975 - SGA Many developments since then Applications to real world problems Hybridization with other algorithms  Mimics mechanics of natural selection and  natural genetics
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G ü yag ü ler Genetic Algorithm (GA) Create initial population N Return best Y Select individuals Apply GA operators: crossover, mutation Stop  criteria  met?
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G ü yag ü ler GA Vocabulary Individual    011...0010     x     Fitness = f(x ) Chromosome Problem parameters Evaluation Function Generation 1 Generation 2 Generation  N Individual 1 Individual 2 Individual  n Individual 1 Individual 2 Individual  n Individual 1 Individual 2 Individual  n
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G ü yag ü ler GA Data Structures Binary Variables decoded into  0 ’s and  1 ’s Arranged linearly 0011010011000111 x 1 x 2 x 3 x 4 Integer/Float Combination
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G ü yag ü ler Operators Crossover  010111 ,100101 One point  0101 11 ,1001 01 0101 01,1001 11 Two point 0 101 11 ,1 001 01 0 001 11 ,1 101 01 Uniform 010111 ,100101 1 10 1 1 1, 0 00 1 0 1 Mutation Bit inversion 1 0 0 1 Bit reinitialization  1,0 ⇒?
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G ü yag ü ler GAs, Why Do They Work? Some terms: Schema introduced by ‘ * ’ (wildcard) 0**10 - 0 00 10,0 01 10,0 10 10,0 11 10 Order of a schema, o( binary string ) o( 0**10 ) = 3 Length of a schema,  δ ( binary string ) δ ( 0**10 ) = 5-1 = 4
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G ü yag ü ler GAs, Why Do They Work? The Schema Theorem:  Selection based  on  fitness  increases the sampling rate of  above-average building-blocks  exponentially Crossover  introduces new building-blocks  and enables information exchange Mutation  introduces new building-blocks
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