the standard genetic algorithm dr. chrisantha fernando systems biology centre university of...

The Standard Genetic AlgorithmThe Standard Genetic Algorithm

Dr. Chrisantha Fernando

Systems Biology Centre

University of Birmingham

Dr. Chrisantha Fernando

Systems Biology Centre

University of Birmingham

DIY Evolution. DIY Evolution.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

GenotypeGenotype

Binary String Real numbered String

Binary String Real numbered String

1101000101110101

1101011111110101 0.2, 0.5, 0.2, 0.83, 0.01, 0.3

0.6, 0.1, 0.5, 0.8, 0.9, 1.0

Representslength of left leg.

Size of head, etc…

Evaluation Evaluation

Interpret the genotype to produce the phenotype. In the simplest case they are the same thing. E.g. Imagine we desire the string

000000000 We can define fitness of any string as the number of

places where it is the same as the above string, e.g. 000000000 010101010 -------------

101010101 = 5 = Fitness

Interpret the genotype to produce the phenotype. In the simplest case they are the same thing. E.g. Imagine we desire the string

000000000 We can define fitness of any string as the number of

places where it is the same as the above string, e.g. 000000000 010101010 -------------

101010101 = 5 = Fitness

A Trivial ExampleA Trivial Example

int evaluate(int *g) { int i, r=0; for (i=0;i<10;i++)

r += (g(i) == 0); return(r);

}

int evaluate(int *g) { int i, r=0; for (i=0;i<10;i++)

r += (g(i) == 0); return(r);

}

I. Harvey

So first initialize a populationSo first initialize a population

int popn[30][10]; void initialise_popn() { int i,j; for (i=0;i<30;i++)

for (j=0;j<10;j++) popn[i][j]= flip_a_bit();

}

int popn[30][10]; void initialise_popn() { int i,j; for (i=0;i<30;i++)

for (j=0;j<10;j++) popn[i][j]= flip_a_bit();

}

I. Harvey

Main LoopMain Loop

For n times round generation loop evaluate all the population (of 30) select preferentially the fitter ones as parents for 30 times round repro loop pick 2 from parental pool recombine to make 1 offspring mutate the offspring end repro loop throw away parental generation and replace with

offspring End generation loop

For n times round generation loop evaluate all the population (of 30) select preferentially the fitter ones as parents for 30 times round repro loop pick 2 from parental pool recombine to make 1 offspring mutate the offspring end repro loop throw away parental generation and replace with

offspring End generation loop

I. Harvey

More complicated EvaluationsMore complicated Evaluations

Genotype encodes a neural network. Genotype encodes a neural network.







Dario Floreano’s Lab

Even More Complicated Evaluations

Even More Complicated Evaluations



Problems in PracticeProblems in Practice

An evaluation may take a long time, in which case the genetic algorithm will be slow.

An evaluation may be noisy, so the same agent may have different fitness each time you make an evaluation. If it is too noisy, then good agents may be lost from the population.

An evaluation may take a long time, in which case the genetic algorithm will be slow.

An evaluation may be noisy, so the same agent may have different fitness each time you make an evaluation. If it is too noisy, then good agents may be lost from the population.

Selection MethodsSelection Methods

Truncation Selection All parents come from top 50% or top 20% etc..

Fitness Proportionate Selection E.g. if all fitnesses are 2, 4, 6, 8, 9, then select parent

using roulette wheel selection with probability 2/29, 4/29, 6/29, 8/29, 9/29

Problems with this are If early on one agent dominates there is too much selective

pressure. If later agents have very similar fitnesses there is too little

selective pressure. Scaling methods can be used to get around these problems.

Truncation Selection All parents come from top 50% or top 20% etc..

Fitness Proportionate Selection E.g. if all fitnesses are 2, 4, 6, 8, 9, then select parent

using roulette wheel selection with probability 2/29, 4/29, 6/29, 8/29, 9/29

Problems with this are If early on one agent dominates there is too much selective

pressure. If later agents have very similar fitnesses there is too little

selective pressure. Scaling methods can be used to get around these problems.

Rank Selection: Ignore absolute fitness, can use other slopes, but here the best is selected 2x more than the average.

Rank Selection: Ignore absolute fitness, can use other slopes, but here the best is selected 2x more than the average.



0

2

ElitismElitism

Force a direct un-mutated copy of the best of the last generation.

Never loose the best. Useful if there is a lot of noise in fitness

assessments, or if mutation is very likely to produce a low fitness offspring.

Force a direct un-mutated copy of the best of the last generation.

Never loose the best. Useful if there is a lot of noise in fitness

assessments, or if mutation is very likely to produce a low fitness offspring.

Mutation (Asexual Reproduction)Mutation (Asexual Reproduction)

Mutate at randomly chosen loci with a small probability.

Mutate all loci by a very small amount (vector mutation).

With binary you do bit flips, with real valued mutation you might multiply the value by a Gaussian distributed random number.

Mutate at randomly chosen loci with a small probability.

Mutate all loci by a very small amount (vector mutation).

With binary you do bit flips, with real valued mutation you might multiply the value by a Gaussian distributed random number.

Recombination (Sexual Reproduction)

Recombination (Sexual Reproduction)

10100010000111

00000011101111

Parent A

Parent B

10100010101111

00000011000111

1-point random equal crossover

00100010100111

Uniform crossover

The Competing Conventions Problem

The Competing Conventions Problem

Head, Eye, Face, Leg

Face, Eye, Leg, Head

Head, Eye, Face, Leg

Face, Eye, Leg, Head

Head, Eye, Face, Head

Face, Eye, Leg, Leg OK, so two heads, and two legs. Sometimes competingconventions can help, some-times it can hinder.

Schema TheoremSchema Theorem

John Holland. A theory of how GAs work. Not everyone

agrees with this, but it is worth reading his book if you are interested.

John Holland. A theory of how GAs work. Not everyone

agrees with this, but it is worth reading his book if you are interested.

A Black ArtA Black Art

No universal algorithm suitable for all cases.

Need to get a feeling for it by doing it.

No universal algorithm suitable for all cases.

Need to get a feeling for it by doing it.

Relationship to Real GenomesRelationship to Real Genomes

Usually GAs use haploid genomes, not diploid ones, i.e. there is only one copy of each ‘gene’.

Usually GAs use haploid genomes, not diploid ones, i.e. there is only one copy of each ‘gene’.

Homework. I’m happy to help if you need. [email protected]

Homework. I’m happy to help if you need. [email protected]

The Card Problem You have 10 cards numbered from 1 to 10. You have to choose a way of dividing them into 2 piles,

so that the cards in Pile_0 SUM to a number as close as possible to 36, and the remaining cards in Pile_1 MULTIPLY to a number as close as possible to 360.

Genotype encoding Each card can be in Pile_0 or Pile_1, there are 1024 possible ways of sorting them into 2 piles, and

you have to find the best. Think of a sensible way of encoding any possible solution-attempt as a genotype.

Fitness Some of these solution-attempts will be closer to the target than others. Think of a sensible way of

evaluating any solution-attempt and scoring it with a fitness-measure.

The GA Write a program, in any sensible programming language, to run a GA with your genotype encoding

and Fitness function. Run it 100 times and see what results you get.

Who can write the GA that solves the problem in the least number of generations?

The Card Problem You have 10 cards numbered from 1 to 10. You have to choose a way of dividing them into 2 piles,

so that the cards in Pile_0 SUM to a number as close as possible to 36, and the remaining cards in Pile_1 MULTIPLY to a number as close as possible to 360.

Genotype encoding Each card can be in Pile_0 or Pile_1, there are 1024 possible ways of sorting them into 2 piles, and

you have to find the best. Think of a sensible way of encoding any possible solution-attempt as a genotype.

Fitness Some of these solution-attempts will be closer to the target than others. Think of a sensible way of

evaluating any solution-attempt and scoring it with a fitness-measure.

The GA Write a program, in any sensible programming language, to run a GA with your genotype encoding

and Fitness function. Run it 100 times and see what results you get.

Who can write the GA that solves the problem in the least number of generations?

the standard genetic algorithm dr. chrisantha fernando systems biology centre university of...

Documents