Genetic Algorithms Talk

8/6/2019 Genetic Algorithms Talk

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IntroductionAlgorithmExamples

Conclusions

Genetic algorithms and evolutionary programming

Fabian J. Theis

Institute of BiophysicsUniversity of Regensburg, Germany

[email protected]

Regensburg 11-Jan-05

Theis Genetic algorithms and evolutionary programming
http://goforward/http://find/http://goback/


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Conclusions

Outline

Introduction

Reinforcement learningImitate natureGenetic algorithms

AlgorithmBasic algorithm

Data representation

Selection

ReproductionExamples2d-function optimizationGenetic MastermindHyerplane detection

Conclusions



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Conclusions


Algorithm

Introduction



Data representation

Selection

ReproductionExamples2d-function optimizationGenetic MastermindHyerplane detection

Conclusions



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Conclusions


Introduction

idea of genetic algorithms (GAs) extract optimization strategies nature uses successfully

Darwinian Evolution transform them for application in mathematical optimization

theory

abstract goal: find the global optimum of a problem/function

in a defined phase space


I d i


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Conclusions


Introduction

idea of genetic algorithms (GAs) extract optimization strategies nature uses successfully

Darwinian Evolution transform them for application in mathematical optimization

theory

abstract goal: find the global optimum of a problem/function

in a defined phase space


I t d ti


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Conclusions


Optimization

GA as special kind of reinforcement learning

no access to the full problem/function but: rewards are given for a given action/search space position goal: use rewards to find optimum this contrasts to learning by (given) examples as in supervised

learning e.g. using neural networks traverse search space manually


Introduction


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Conclusions


Optimization

simple algorithm: random sampling pick a single location in the search space store it if reward is higher than at previous locations, discard it

otherwise repeat

other such algorithms Markov-Chain-Monte-Carlo search (MCMC) simulated annealing if derivative of reward is available: (conjugated) gradient

ascent/descent etc.


Introduction


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Conclusions


Optimization

simple algorithm: random sampling pick a single location in the search space store it if reward is higher than at previous locations, discard it

otherwise repeat

other such algorithms Markov-Chain-Monte-Carlo search (MCMC) simulated annealing if derivative of reward is available: (conjugated) gradient

ascent/descent etc.


Introduction


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Conclusions


Genetic algorithms

here: imitate natures robust way of evolving successfulorganisms organisms ill-suited to an environment die off, whereas fit ones

reproduce offspring is similar to the parents, so population fitness

increases with generations mutation can randomly generate new species The Origin of Species by Means of Natural Selection, C.R.

Darwin, D. Appleton and Company, NY, 1897

history: introduced by J. Holland 1975 further invesigated by his students e.g. K. DeJong 1975 more recently theoretical advances e.g. by M. Vose 1993


IntroductionR i f l i


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Conclusions


Genetic algorithms

whats good for nature is good for artificial systems imagine population of individual explorers sent into the

optimization phase-space

explorer is defined by its genes, encoding his phase-spaceposition optimization problem is given by a fitness function

the struggle of life begins selection

crossover mutation

according to these rules populations tend to increase overallfitness


IntroductionR i f t l i


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AlgorithmExamples

Conclusions


Genetic algorithms





crossover mutation



IntroductionReinforcement learning


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AlgorithmExamples

Conclusions


Genetic algorithms





crossover mutation





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AlgorithmExamples

Conclusions


Genetic algorithms





crossover mutation





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AlgorithmExamples

Conclusions


Genetic algorithms

advantages global not only local optimization

simple and hence easy to implement easy parallelization possible

disadvantages how to encode phase-space position rather low speed and high computational cost

parameter dependencies (population size, selection andreproduction parameters)


IntroductionAl ith

Reinforcement learning


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AlgorithmExamples

Conclusions


Genetic algorithms

advantages global not only local optimization

simple and hence easy to implement easy parallelization possible

disadvantages how to encode phase-space position rather low speed and high computational cost

parameter dependencies (population size, selection andreproduction parameters)


IntroductionAlgorithm

Basic algorithmData re resentation


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AlgorithmExamples

Conclusions

Data representationSelectionReproduction

Algorithm

Introduction



Data representation

SelectionReproduction

Examples2d-function optimizationGenetic MastermindHyerplane detection

Conclusions



Basic algorithmData representation


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AlgorithmExamples

Conclusions


Basic genetic algorithm

Data : population, a set of individualsfitness-function Fitness, a function measuring fitnessof an individual

Result: an individual

repeat

1 parents Selection (population, Fitness)2 population Reproduction (parents)

until some individual is fit enough;

3 return the best individual in population according to Fitness





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AlgorithmExamples

Conclusions


Individual

an individual encodes the data space position classic GA approach: representation by word (chromosome)

over a finite alphabet each letter is called gene real DNA: alphabet is {A, G, T, C} here: usually binary alphabet {0, 1} some authors speak more general of evolutionary programming

if alphabet is larger finite alphabet implies discrete search space

continuous search space use continuous alphabet i.e. genes R or bounded genes [a, b]

so individual Rn respectively [a1, b1] . . . [an, bn]





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AlgorithmExamples

Conclusions


Individual










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AlgorithmExamples

Conclusions


Individual










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gExamples

Conclusions

pSelectionReproduction

Selection

goal: select individuals that produce the next generation probabilistic selection

based on fitness function f better individuals have increased chance of reproduction usually selection with replacement very fit individuals

reproduce several times selection probabilities roulette wheel (Holland 1975)

P(choice of individual i) =f(i)

jf(j)

problem: negative f? minimization? ranking methods, i.e. choose individuals according to fitness

rank e.g. normalized geometric ranking (Joines and Houck1994)

tournament selection, i.e. select best among a randomly

selected subsetTheis Genetic algorithms and evolutionary programming




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gExamples

ConclusionsSelectionReproduction

Selection



reproduce several times selection probabilities

roulette wheel (Holland 1975)


jf(j)








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ExamplesConclusions


Selection



reproduce several times selection probabilities

roulette wheel (Holland 1975)


jf(j)





IntroductionAlgorithmE l

Basic algorithmData representationS l i


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ExamplesConclusions


Reproduction

typically consists of two stages crossover (or mating): selected individuals are randomly paired

and (usually two) children are produced mutation: genes can be altered by random mutation to a

different value according to a small probability

use genetic operators to produce and alter new offspring

basic search mechanism in GAs


IntroductionAlgorithmE l

Basic algorithmData representationS l ti


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ExamplesConclusions


Reproduction

typically consists of two stages crossover (or mating): selected individuals are randomly paired

and (usually two) children are produced mutation: genes can be altered by random mutation to a

different value according to a small probability

use genetic operators to produce and alter new offspring

basic search mechanism in GAs



Basic algorithmData representationSelection


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ExamplesConclusions


Crossover

let x, y An

be the genes of the two parents simple crossover

choose r randomly in {1, . . . , n} generate children x, y An by

x

i := xi if i < r

yi otherwise

yi :=

yi if i < rxi otherwise

in the case of continuous genes: arithmetic crossover choose r randomly in [0, 1] generate children x, y An by

x := rx + (1 r)y

y := (1 r)x + ry





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ExamplesConclusions


Crossover

let x, y An



x

i := xi if i < r

yi otherwise

yi :=



x := rx + (1 r)y

y := (1 r)x + ry





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ExamplesConclusions


Crossover

let x, y An



x

i := xi if i < r

yi otherwise

yi :=



x := rx + (1 r)y

y := (1 r)x + ry





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ExamplesConclusions


Mutation

let xi A be the gene of an individual that is to be mutated binary gene: binary mutation

xi := 1 xi discrete or continuous bounded A: uniform mutation

set xi to be a uniformly randomly chosen element ofA

also possible: non-uniform mutation

needs fixed distribution for element choice



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Conclusions Reproduction

Mutation

let xi A be the gene of an individual that is to be mutated binary gene: binary mutation

xi := 1 xi discrete or continuous bounded A: uniform mutation

set xi to be a uniformly randomly chosen element ofA

also possible: non-uniform mutation

needs fixed distribution for element choice



C l i

Basic algorithmData representationSelectionR d i


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Conclusions Reproduction

One generation example



C l i

2d-function optimizationGenetic MastermindHyerplane detection


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ConclusionsHyerplane detection

Algorithm

IntroductionReinforcement learningImitate natureGenetic algorithms


Data representation



Conclusions



Conclusions



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Conclusionsy p

Examples

continuous example global optimization of continuous function f : [a, b] R

binary example genetic Mastermind select optimal guess using GA

example from our research perform overcomplete blind source separation by sparse

component analysis key problem: hyperplane detection solution: optimize cost function using GAs



Conclusions



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Conclusionsy

Examples







Conclusions



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Conclusions

Examples







Conclusions



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Conclusions

2d-function optimization

10 8 6 4 2 0 2 4 6 8 10

5

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40

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x

multipeak

0 10 20 30 40 50 60 70 80 90 10020

25

30

35

40

45

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f performance (optimal individual and mean)



Conclusions



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Co c us o s

Genetic Mastermind



Conclusions



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Hyerplane detection

1

0.5

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perform overcomplete blind source separation by sparse

component analysis Georgiev et al. [2004], Theis et al. [2004] key problem: hyperplane detection

solution: optimize cost function using GAs



Conclusions


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Algorithm

IntroductionReinforcement learningImitate natureGenetic algorithms


Data representation



Conclusions



Conclusions


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Conclusions

genetic algorithms perform global optimization

they mimic nature by letting a population evolve according to

their fitness algorithm

selection reproduction: by crossover and mutation

simple applicability in real-world situations



Conclusions


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Resources

books: Goldberg [1989],Schoneburg et al. [1994]

Matlab GA optimization

toolbox:http://www.ie.ncsu.edu/

mirage/GAToolBox/gaot

Details and papers on mywebsite

http://fabian.theis.name This research was supported

by the DFG1 and BMBF2.

ReferencesP. Georgiev, F. Theis, and A. Cichocki. Sparse

component analysis and blind sourceseparation of underdetermined mixtures.IEEE Trans. on Neural Networks in print,2004.

D. Goldberg. Genetic Algorithms in SearchOptimization and Machine Learning.Addison Wesley Publishing, 1989.

E. Schoneburg, F. Heinzmann, andS. Feddersen. Genetische Algorithmen undEvolutionsstrategien. Addison WesleyPublishing, 1994.

F. Theis, P. Georgiev, and A. Cichocki. Robust

overcomplete matrix recovery for sparsesources using a generalized houghtransform. In Proc. ESANN 2004, pages343348, Bruges, Belgium, 2004. d-side,Evere, Belgium.

1graduate college: Nonlinearity and Nonequilibrium in Condensed Matter2project ModKog


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Genetic Algorithms Talk