Mathematical Analysis of Genetic Algorithms Genetic Algorithms are - - PowerPoint PPT Presentation

mathematical analysis of genetic algorithms
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Mathematical Analysis of Genetic Algorithms Genetic Algorithms are - - PowerPoint PPT Presentation

Mathematical Analysis of Genetic Algorithms Genetic Algorithms are not appropriate for certain problems where finding the exact global optimum is required. Genetic Algorithms are non-deterministic. However, there are theories about


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SLIDE 1

Mathematical Analysis of Genetic Algorithms

  • Genetic Algorithms are not appropriate for certain

problems where finding the exact global optimum is required.

  • Genetic Algorithms are non-deterministic.

However, there are theories about how and why they work in idealized settings.

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SLIDE 2

Mathematical Analysis of Genetic Algorithms

The analysis of Genetic Algorithms requires us to understand the following concepts:

  • Search Space
  • Schema
  • Implicit parallelism
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SLIDE 3

The Schema Theorem

The observed best schemas are expected to receive an exponentially increasing number of samples in successive generations.

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SLIDE 4

The building blocks hypothesis

  • The genetic algorithm converges on high fitness

regions in some low-order schemas.

  • The algorithm detects biases on higher order

schemas by combining information from low-order schemas through cross-over and mutation

  • The algorithm converges on a small region of the

search space that has high fitness

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SLIDE 5

Deception

Low-order schemas lead the genetic algorithm away from good higher-order schemas.