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Genetic Algorithms Chapter 3
GA Quick Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Genetic algorithms ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
SGA technical summary tableau Emphasis on crossover Speciality All children replace parents Survivor selection Fitness-Proportionate Parent selection Bitwise bit-flipping with fixed probability Mutation N-point or uniform Recombination Binary strings Representation
Representation Genotype space = {0,1} L Phenotype space Encoding (representation) Decoding (inverse representation) 011101001 010001001 10010010 10010001
SGA reproduction cycle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
SGA operators: 1-point crossover ,[object Object],[object Object],[object Object],[object Object]
SGA operators: mutation ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],SGA operators: Selection fitness(A) = 3 fitness(B) = 1 fitness(C) = 2 A C 1/6 = 17% 3/6 = 50% B 2/6 = 33%
An example after Goldberg ‘89 (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
x 2 example: selection
X 2 example: crossover
X 2 example: mutation
The simple GA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Alternative Crossover Operators ,[object Object],[object Object],[object Object],[object Object],[object Object]
n-point crossover ,[object Object],[object Object],[object Object],[object Object]
Uniform crossover ,[object Object],[object Object],[object Object],[object Object]
Crossover OR mutation? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],Crossover OR mutation? (cont’d)
[object Object],[object Object],[object Object],[object Object],Crossover OR mutation? (cont’d)
Other representations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Integer representations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Real valued problems ,[object Object],[object Object]
Mapping real values on bit strings ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Floating point mutations 1 ,[object Object],[object Object],[object Object]
Floating point mutations 2 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Crossover operators for real valued GAs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Single arithmetic crossover ,[object Object],[object Object],[object Object],[object Object]
Simple arithmetic crossover ,[object Object],[object Object],[object Object],[object Object]
Whole arithmetic crossover ,[object Object],[object Object],[object Object],[object Object]
Permutation Representations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Permutation representation: TSP example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Mutation operators for permutations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Insert Mutation for permutations ,[object Object],[object Object],[object Object]
Swap mutation for permutations ,[object Object],[object Object]
Inversion mutation for permutations ,[object Object],[object Object]
Scramble mutation for permutations ,[object Object],[object Object],[object Object]
[object Object],[object Object],Crossover operators for permutations 1 2 3 4 5 5 4 3 2 1 1 2 3 2 1 5 4 3 4 5
Order 1 crossover ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Order 1 crossover example ,[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Partially Mapped Crossover (PMX)
PMX example ,[object Object],[object Object],[object Object]
Cycle crossover ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Cycle crossover example ,[object Object],[object Object]
Edge Recombination ,[object Object],[object Object]
Edge Recombination 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Edge Recombination example
Multiparent recombination ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Population Models ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Fitness Based Competition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Implementation example: SGA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Fitness-Proportionate Selection
Function transposition for FPS
Rank – Based Selection ,[object Object],[object Object],[object Object]
Linear Ranking ,[object Object],[object Object],[object Object],[object Object]
Exponential Ranking ,[object Object],[object Object],[object Object]
Tournament Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Tournament Selection 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Survivor Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Two Special Cases ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example application of order based GAs: JSSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Precedence constrained job shop scheduling GA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
JSSP example: operator comparison

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Genetic algorithms

  • 1. Genetic Algorithms Chapter 3
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  • 4. SGA technical summary tableau Emphasis on crossover Speciality All children replace parents Survivor selection Fitness-Proportionate Parent selection Bitwise bit-flipping with fixed probability Mutation N-point or uniform Recombination Binary strings Representation
  • 5. Representation Genotype space = {0,1} L Phenotype space Encoding (representation) Decoding (inverse representation) 011101001 010001001 10010010 10010001
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  • 11. x 2 example: selection
  • 12. X 2 example: crossover
  • 13. X 2 example: mutation
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  • 55.
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62.