Genetic Algorithms Seth Bacon 4/25/2005 Seth Bacon 1 What are - - PowerPoint PPT Presentation

4/25/2005 Seth Bacon 1

Genetic Algorithms

Seth Bacon

4/25/2005 Seth Bacon 2

What are Genetic Algorithms

Search algorithm based on

selection and genetics

Manipulate a population of

candidate solutions to find a good solution

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What are GAs used for

Approximate solutions for NP-

Complete and NP-Hard problems

Artificial Intelligence Business, engineering and

science.

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The Population

Each member of the population is

represented by a “chromosome”

Typically a binary string although

they can be more complex

Each chromosome is generated at

random (usually)

Each chromosome represents a

solution (although not necessarily a good one)

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Steps of a GA

Generate Initial Population Run Tournament Fitness evaluation Selection Crossover Mutation Reach conclusion

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Generation of Initial Pop

Must supply a large enough

population to create genetic diversity

The longer the chromosome the

greater the population

The more “noise” (poor solutions

not leading to the good solution) the greater the population

“A correctly-sized population is the first step toward competent and efficient genetic algorithms.” – Cantú-Paz

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Fitness Evaluation

Ranks a chromosome based on it’s

performance

Defined by the user Unique to each problem

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Selection

Technique for selecting parents of the

next generation

Based on rank from fitness Different selection schemes

Selection of top x-chromosomes Random selection of top x-chromosomes out of top

y-chromosomes (y > x)

Etc.

Try to keep population diverse to protect

from a premature poor solutions

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Crossover

Mating of two different chromosomes Methods

Randomly chosen crossover point. Everything to

the left of the point stays put. Everything to the right switches with the other chromosome.

n-point crossover Completely random crossover (n = length of

chromosome)

Used to “explore the solution space”. Controlled randomness?

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Mutation

Randomly changes a value in the

chromosome

Used to keep diversity up However its probability should be

kept low or else you are destroying too much information.

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Reaching a Conclusion

After x number of generations you

stop and take out the most robust chromosome.

When improvement of the

chromosomes per generation has reached a plateau

When the fittest chromosome has

bred all the others out of the

• population. (Only happens w/o

mutation)

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Parallel GAs

Single-population master-slave

GAs

Multiple-population GAs Fine-grained GAs Hierarchical hybrid (Not discussed)

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Master-Slave GAs

Very similar to serial GAs Slaves calculate the fitness

• Tp = Time to compute a generation
• Tc = is the communication time between processors
• P = the number of processors
• Tf = the time require for a fitness evaluation
• n = size of the population

Tp = PTc + nTf/P

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Master-Slave GAs

P* = sqrt(nTf/Tc)

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Master Slave GAs

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Multiple-Population GAs

Distributed panmictic population Panmictic - random mating within a

breeding population

Only occasional breeding between

processors

Each population converges on a

solution

Increases diversity

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Fine Grained GAs

Each processor has its own

subpopulation (preferably consisting of

• nly one chromosome)

Fitness and mutation per processor Selection and mating on a local

neighborhood (which overlap)

Diffuses population across all

subpopulation

“…well suited for massively parallel SIMD computers, but it is also possible to implement them very efficiently on coarse-grain MIMD computers.” – Cantú-Paz

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Examples

http://cs.felk.cvut.cz/~xobitko/ga/ex

ample_f.html

Highly recommend this site let’s you play with

a lot of the concepts

http://cs.felk.cvut.cz/~xobitko/ga/pa

rams.html

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Sources

Cantu-Paz, Erick. Efficient and Accurate

Parallel Genetic Algorithms. Kluwer Academic Publishers 2000

Antonette M. Logar, Edward M. Corwin,

ans Thomas M. English. Implementation

• f Massively Parallel Genetic Algorithms

On the MasPar MP-1. Department of Computer Science

http://cs.felk.cvut.cz/~xobitko/ga/