Genetic Algorithms

• Elements:
  • Population
  • Fitness function
  • Mutation operator
  • Crossover operator
  • Selection
• Population
  • Each individual encodes a solution to the problem to be solved
  • Individuals are typically fixed-length strings ("genomes" or "chromosomes")
    • Bit strings: encode problems in binary
    • Lists of integers or floating-point values
    • Programming language instructions ("genetic programming"; not always fixed-length)
  • The genotype is the encoding of a particular solution as a genome.
  • The phenotype is the behavior exhibited when the genome is used to construct the solution.
• Fitness function
  • Measures the quality of the phenotype relative to the problem domain
• Mutation operator
  • When an individual is introduced into a new generation, it may mutate
  • Mutation rate is the probability of an individual mutating
  • Serves as a hill-climbing "subroutine" of the genetic search
  • Bit-string encoding: flip a random bit
• Crossover operator
  • Creation of two new individuals from two "parents"
  • One-point crossover:
    • A string index is selected at random
    • Each parental genome is "split" at this point
    • Two children are created by "splicing" the genomes
  • Two-point crossover:
    • Two string indices are selected at random
    • The segments in-between these indices are swapped to create the children
  • Uniform crossover:
    • For each index, there is a 50% chance of swapping the bits
• Selection
  • Fitness-proportionate selection
    • Fitness values are used to define a probability distribution
    • Individuals are selected with probability proportionate to fitness
  • Tournament selection
    • Individuals "compete" for selection
    • All tournament "winners" get selected
  • Important issue:
    • Some number of "weak" individuals should get selected
    • Helps to maintain diversity in the gene pool

Steady-state Genetic Algorithm

• Generate initial population
  • Each individual is randomly generated
  • Provides a "statistical sample" of the search space
• Select two individuals for crossover
• Generate two children
• Mutate two children
• Replace the two lowest-fitness individuals in the population with the children
• Repeat until the best individual has satisfactory fitness

Generational Genetic Algorithm

• Generate initial population (size P)
• Select N members of the population to be preserved in the next generation
• Use crossover to create P - N new individuals to replace the non-selected
• Mutate each individual
• Repeat until the best individual has satisfactory fitness