Genetic Algorithms

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Genetic Algorithms

• Jan Prokaj

2
Genetic Algorithms

• Background
• What they are
• Genetic algorithm step by step
• Genetic algorithm applet
• Summary
• Bibliography

3
Background

• Pioneered by John H. Holland in 1960s at the
  University of Michigan
• Solve optimization problems
• Based on evolution in nature
• Reproduction
• Variation
• Heritable characteristics
• Natural selection

4
Definitions

• Population
• A set of chromosomessolutionsat one period of
  time
• Chromosome
• An individual in a population
• One point in the search space
• Search space
• All potential solutions to a problem

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Search Space
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Genetic Algorithm (GA)
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Genetic Algorithm

• f(chromosome) //define fitness function
• Create the initial population
• do
• Compute a fitness value for each chromosome
• Discard unfit chromosomes
• while lt population size
• Select mates
• Reproduce
• Mutate
• while gt convergence threshold // lt N iterations
• output

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Genetic Algorithm

• Each iteration is a generation
• Each individual in a population is a possible
  solution
• Often encoded in a string of bits
• Objective is to maximize the fitness value for
  each individual
• The fitness function is defined by a particular
  problem

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Fitness function

• Input chromosome p1,p2,,pN
• Output f(p1,p2,,pN)
• Can be quite complicated
• Example
• Finding the peak in Rocky Mountains
• f(longitude, latitude) elevation
• Maximizing gas mileage
• f(engine size, car weight, ??) mpg ( )

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Initial Population

• Chromosomes are randomly generated
• Large size provides a good sampling of the search
  space
• Usually trimmed before starting iterations
• Different sampling methods (next slide)

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Initial Population sampling
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Natural Selection

• Occurs each generation of the algorithm
• The least fit chromosomes are discarded (Nbad)
• Nbad replaced by offspring from the most fit
  chromosomes (Ngood)
• Number of fittest chromosomes can be thresholded
  or fixed

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Pairing

• Takes place between Ngood until enough offspring
  is produced to replace Nbad
• Different methods
• Top to bottom
• Random pairing
• Weighted random pairing (roulette wheel
  weighting)
• Tournament selection

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Mating / Crossover

• Select a crossover point between the first and
  the last bit of the parents chromosomes
• Simple crossover (more complicated exist)

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Mutations

• Random mutations alter a small percentage of the
  bits in chromosomes
• Typically 1-5 of bits mutate per iteration
• Generally not done on good solutions
• Types
• Single point
• Insertion, deletion
• Allow to explore the search space

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Convergence

• After a while, all the chromosomes stabilize
• Population statistics can be used to test for
  convergence
• Rate of convergence depends on various factors
  (mutation rate, crossover rate,)

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Genetic Algorithm applets

• http//cs.felk.cvut.cz/xobitko/ga/

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Applications

• Nonlinear dynamical systems - predicting, data
  analysis
• Designing neural networks, both architecture and
  weights
• Robot trajectory
• Evolving LISP programs (genetic programming)
• Strategy planning
• Finding shape of protein molecules
• TSP and sequence scheduling
• Functions for creating images, music

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Summary

• Optimization algorithm
• Principles from nature
• Complex problems need a lot of iterations
• long computational time
• Wide applications
• Implementation may be difficult for some problems

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Bibliography

• Dewdney, A.K. The New Turing Omnibus. Owl Books,
  New York. 1993
• Ghanea-Hercock, R. Applied Evolutionary
  Algorithms in Java. Springer, New York. 2003.
• Haupt, R. L. and Haupt S.E. Practical Genetic
  Algorithms. Wiley, New York. 1998
• Obitko, M. An introduction to genetic algorithms
  with Java applets. http//cs.felk.cvut.cz/xobitko
  /ga/. 1998.
• Reeves, C.R. and Rowe, J.E. Genetic
  AlgorithmsPrinciples and Perspectives. Kluwer,
  Norwell, MA. 2003