Self-Adaptation in Evolutionary Algorithms

Jim Smith, University of the West of England

Self-Adaptation in Self-Adaptation in Evolutionary AlgorithmsEvolutionary Algorithms

The Seventh EU/MEeting on The Seventh EU/MEeting on Adaptive, Self-Adaptive, and Adaptive, Self-Adaptive, and Multi-Level MetaheuristicsMulti-Level Metaheuristics


OverviewOverview

• What is Self-Adaptation?What is Self-Adaptation?• The origins … The origins … • Interbreeding …Interbreeding …• Self-adapting crossoverSelf-adapting crossover• Self-Adapting multiple operatorsSelf-Adapting multiple operators• Extensions to MAsExtensions to MAs• SummarySummary


What is Self-Adaptation?What is Self-Adaptation?

Informally, and rather vaguely, Informally, and rather vaguely, • A property of Natural and Artificial A property of Natural and Artificial

Systems that allows them to control Systems that allows them to control the way in which they adapt to the way in which they adapt to changing environmentschanging environments

Lets start with another question,Lets start with another question,

Why should we be interested?Why should we be interested?


MotivationMotivation

An EA has many strategy parameters, e.g.An EA has many strategy parameters, e.g.• mutation operator and mutation ratemutation operator and mutation rate• crossover operator and crossover ratecrossover operator and crossover rate• selection mechanism and selective selection mechanism and selective

pressure (e.g. tournament size)pressure (e.g. tournament size)• population sizepopulation size

Good parameter values facilitate good Good parameter values facilitate good performanceperformance

Q1: How can we find good parameter values ?Q1: How can we find good parameter values ?


Motivation 2Motivation 2

• EA parameters are static (constant EA parameters are static (constant during a run)during a run)

BUTBUT• an EA is a dynamic, adaptive processan EA is a dynamic, adaptive process

THUSTHUS• optimal parameter values may vary optimal parameter values may vary

during a runduring a run

Q2: How to vary parameter values?Q2: How to vary parameter values?


An example – Magic SquaresAn example – Magic Squares

Software by M. Herdy, TU BerlinSoftware by M. Herdy, TU BerlinObject is to arrange [1-100] for Object is to arrange [1-100] for equal row and column sumsequal row and column sumsRepresentation: permutationRepresentation: permutationFitness: sum of squared errorsFitness: sum of squared errorsMutation:Mutation:• picks value at random, picks value at random, • then another in a window,then another in a window,• and swaps their positionand swaps their position• window size controls mutationwindow size controls mutation

• Exit: click on TUBerlin logoExit: click on TUBerlin logo

magicsquares.exe

C:\Documents and Settings\jsmith.JIMSMITH\My Documents\eume-talk\magicsquares.exe


Parameter controlParameter control

Parameter control: setting values on-Parameter control: setting values on-line, line, during the actual runduring the actual run, e.g., e.g.

• predetermined time-varying schedule p = p(t)predetermined time-varying schedule p = p(t)• using feedback from the search processusing feedback from the search process• encoding parameters in chromosomes and encoding parameters in chromosomes and

rely on natural selectionrely on natural selection

Problems:Problems:• finding optimal p is hard, finding optimal p(t) finding optimal p is hard, finding optimal p(t)

is harderis harder• still user-defined feedback mechanism, how still user-defined feedback mechanism, how

to ``optimize"?to ``optimize"?• when would natural selection work for when would natural selection work for

strategy parameters?strategy parameters?


Scope/levelScope/level

The parameter may take effect on different levels: The parameter may take effect on different levels: • environment (fitness function)environment (fitness function)• population population • individualindividual• sub-individualsub-individual

Note 1: given component (parameter) determines Note 1: given component (parameter) determines possibilitiespossibilities

Note 2: Self-Adaptation relies on the implicit action Note 2: Self-Adaptation relies on the implicit action of selection acting on different strategies in the of selection acting on different strategies in the same population -> can’t have population level same population -> can’t have population level SASA


Global taxonomyGlobal taxonomy

P A R A M E T E R T U N ING(b e fo re th e ru n)

D E T E R M IN IS T IC(t im e de p en de n t)

A D A P T IVE(fe e db a ck fro m sea rch)

S E L F -A D A P T IVE(co d ed in ch ro m o som e s)

P A R A M E T ER C O N T R O L(d u ring th e ru n)

P A R A M E T E R S E T T ING


Features of Self-AdaptationFeatures of Self-Adaptation

Automatic control of operators or their Automatic control of operators or their parametersparameters

• Each individual encodes for its own Each individual encodes for its own parametersparameters

The range of values present will depend The range of values present will depend on:on:

• the action of selection on the the action of selection on the combined genotypescombined genotypes

• the action of genetic operators (e.g. the action of genetic operators (e.g. mutation) on those encoded valuesmutation) on those encoded values


Some implicit AssumptionsSome implicit Assumptions

There need to be links between:There need to be links between:• encoded parameter (might be encoded parameter (might be

stochastic e.g. step sizes) and change in stochastic e.g. step sizes) and change in problem encodingproblem encoding– Hence CMA interest in derandomised Hence CMA interest in derandomised

mutationsmutations

• Action of operator and change in fitnessAction of operator and change in fitness

• Individual fitness and action of selectionIndividual fitness and action of selection


The OriginsThe Origins

Various historical papersVarious historical papers

First major implementation was Self-First major implementation was Self-

adaptation of mutation step sizes in ES’sadaptation of mutation step sizes in ES’s

• Continuous variables mutated by adding noise Continuous variables mutated by adding noise

from a N(0from a N(0,C,C)) distribution distribution

• Step-size should ideally be correlated with Step-size should ideally be correlated with

distance to optimumdistance to optimum

• (1+1) ES used Rechenberg’s 1:5 success rule, (1+1) ES used Rechenberg’s 1:5 success rule,

but move to but move to λλ>1 offspring enabled other >1 offspring enabled other

methodsmethods


ES typical representationES typical representation

Chromosomes consist of three parts:Chromosomes consist of three parts:

• Object variables: xObject variables: x11,…,x,…,xnn

• Strategy parameters:Strategy parameters:

– Mutation step sizes: Mutation step sizes: 11,…,,…,nn

– Rotation angles: Rotation angles: 11,…, ,…, nn

• Not every component is always presentNot every component is always present

• Full size: Full size: x x11,…,x,…,xnn,, 11,…,,…,nn ,,11,…, ,…, kk

where k = n(n-1)/2 (no. of i,j pairs)where k = n(n-1)/2 (no. of i,j pairs)


MutationMutation

Main mechanism: Main mechanism: • changing value by adding random changing value by adding random

noise drawn from normal distributionnoise drawn from normal distribution• x’x’ii = x = xii + N(0, + N(0,))

Key idea: Key idea: is part of the chromosome is part of the chromosome x x11,…,x,…,xnn, , is also mutated into is also mutated into ’ ’

Thus: mutation step size Thus: mutation step size coevolves coevolves with the solution xwith the solution x


Mutate Mutate first first

Net mutation effect: Net mutation effect: x, x, x’, x’, ’ ’

Order is important: Order is important: • first first ’ then x ’ then x x’ = x + N(0, x’ = x + N(0,’)’)

Fitness of Fitness of x’ , x’ ,’ ’ provides two lots of provides two lots of informationinformation

• Primary: x’ is good if f(x’) is good Primary: x’ is good if f(x’) is good • Secondary: Secondary: ’ is good if x’ is’ is good if x’ is

Reversing mutation order would not workReversing mutation order would not work


Uncorrelated mutation: one Uncorrelated mutation: one

• Chromosomes: Chromosomes: x x11,…,x,…,xnn, , ’ ’ = = •• exp( exp( •• N(0,1)) N(0,1))

• x’x’ii = x = xii + + ’ ’ •• N(0,1) N(0,1)

• Typically the “learning rate” Typically the “learning rate” 1/ n 1/ n½½

• And we have a boundary rule And we have a boundary rule ’ < ’ < 00 ’ = ’ = 00


Mutants with equal likelihoodMutants with equal likelihood

Circle: mutants having the same chance to be createdCircle: mutants having the same chance to be created


Uncorrelated mutation: n Uncorrelated mutation: n ’s’s

• Chromosomes: Chromosomes: x x11,…,x,…,xnn, , 11,…, ,…, nn ’’ii = = ii •• exp( exp(’ ’ •• N(0,1) + N(0,1) + •• N Nii (0,1)) (0,1))

• x’x’ii = x = xii + + ’’ii •• N Nii (0,1) (0,1)

• Two learning rate parameters:Two learning rate parameters: ’ ’ overall learning rateoverall learning rate coordinate wise learning ratecoordinate wise learning rate

1/(2 n)1/(2 n)½ ½ and and 1/(2 n 1/(2 n½½) ) ½½

• And And ii’ < ’ < 00 ii’ = ’ = 00



Ellipse: mutants having the same chance to be createdEllipse: mutants having the same chance to be created


Correlated mutations Correlated mutations

• Chromosomes: Chromosomes: x x11,…,x,…,xnn, , 11,…, ,…, nn , ,11,…, ,…, kk where k = n where k = n • • (n-1)/2 (n-1)/2

• Covariance matrix C is defined as:Covariance matrix C is defined as:– cciiii = = ii

22

– ccijij = 0 if i and j are not correlated = 0 if i and j are not correlated

– ccijij = ½ = ½ •• (( ii2 2 - - jj

2 2 ) ) •• tan(2 tan(2 ijij) if i and j are ) if i and j are correlatedcorrelated

• Note the numbering / indices of the Note the numbering / indices of the ‘s ‘s


Correlated mutations cont’dCorrelated mutations cont’d

The mutation mechanism is then:The mutation mechanism is then: ’’ii = = ii •• exp( exp(’ ’ •• N(0,1) + N(0,1) + •• N Nii (0,1)) (0,1)) ’’jj = = jj + + •• N (0,1) N (0,1)

• x x ’ = ’ = xx + + NN((0,C’0,C’))– x x stands for the vector stands for the vector x x11,…,x,…,xnn – C’C’ is the covariance matrix is the covariance matrix CC after mutation of after mutation of

the the s s

1/(2 n)1/(2 n)½ ½ and and 1/(2 n 1/(2 n½½) ) ½ ½ and and 5° 5°

ii’ < ’ < 00 ii’ = ’ = 0 0 and and

• | | ’’j j | > | > ’’j j == ’’j j - 2 - 2 sign( sign(’’jj))



Ellipse: mutants having the same chance to be createdEllipse: mutants having the same chance to be created


Self-adaptation illustratedSelf-adaptation illustrated

• Given a dynamically changing fitness Given a dynamically changing fitness landscape (optimum location shifted landscape (optimum location shifted every 200 generations)every 200 generations)

• Self-adaptive ES is able to Self-adaptive ES is able to – follow the optimum and follow the optimum and – adjust the mutation step size after every adjust the mutation step size after every

shift !shift !


Self-adaptation illustratedSelf-adaptation illustrated

Changes in the fitness values (left) and the mutation step sizes (right)


Prerequisites for self-adaptation Prerequisites for self-adaptation

> 1 to carry different strategies> 1 to carry different strategies

> > to generate offspring surplus to generate offspring surplus

• Not “too” strong selection, e.g., Not “too” strong selection, e.g., 7 7 ••

• ((,,)-selection to get rid of misadapted )-selection to get rid of misadapted

‘s‘s

• Mixing strategy parameters by Mixing strategy parameters by

(intermediary) recombination on them(intermediary) recombination on them


Similar SchemesSimilar Schemes

• Fogel introduced similar methods into Fogel introduced similar methods into “Meta-EP”“Meta-EP”

• Some authors use Cauchy rather than Some authors use Cauchy rather than Gaussian distributionsGaussian distributions– Fast EP creates off spring using bothFast EP creates off spring using both

• Closely related is Hansen and Ostermaier’s Closely related is Hansen and Ostermaier’s Covariance Matrix Adaptation ESCovariance Matrix Adaptation ES– seeks to remove some of the stochasticity seeks to remove some of the stochasticity

between step sizes and actual moves madebetween step sizes and actual moves made– Uses cumulation of steps rather than single Uses cumulation of steps rather than single

stepstep


Do we understand what is Do we understand what is happening?happening?

• Continuous search spaces relatively Continuous search spaces relatively

amenable to theoretical analysisamenable to theoretical analysis

• Most search spaces can be locally Most search spaces can be locally

modelled by simple functions (sphere, modelled by simple functions (sphere,

ridge etc.)ridge etc.)

• Lots of theoretical results focussing on Lots of theoretical results focussing on

the progress rate the progress rate

• Ongoing research esp. by Schwefel and Ongoing research esp. by Schwefel and

Beyer’s group at Dortmund/VoralbergBeyer’s group at Dortmund/Voralberg


Interbreeding: ES meets GAsInterbreeding: ES meets GAs BBäck (1991)äck (1991)

Mutation rate eMutation rate encoded as binary stringncoded as binary string• Decode to [0,1] to give mutation rate P(m)Decode to [0,1] to give mutation rate P(m)• Bits encoding for mutation changed at P(m)Bits encoding for mutation changed at P(m)• Decode again: P(m)’ for problem encodingDecode again: P(m)’ for problem encoding

1 mutation rate vs. 1 per problem variable1 mutation rate vs. 1 per problem variable

Fitness-proportionate vs. truncation selectionFitness-proportionate vs. truncation selection

Results were promisingResults were promising• Needed high selection pressureNeeded high selection pressure• Multiple rates better for complex problemsMultiple rates better for complex problems


Extensions of evolving P(m)Extensions of evolving P(m)

Smith (1996) – Steady State GAsSmith (1996) – Steady State GAs• Significantly outperformed fixed mutation Significantly outperformed fixed mutation

ratesrates• Also needed high selection pressure:Also needed high selection pressure:

– Create Create λλ copies of offspring copies of offspring – Select best for inclusion Select best for inclusion if betterif better than member being than member being

replacedreplaced

• Gray coding of mutation rates preferableGray coding of mutation rates preferable

Hinterding et al 1996 – used continuous variable Hinterding et al 1996 – used continuous variable with log-normal adaptationwith log-normal adaptation

Glickman and Sycara (2001) found problem with Glickman and Sycara (2001) found problem with premature convergence on some problemspremature convergence on some problems


Some theoretical ResultsSome theoretical Results

BBäck (1993)äck (1993)• showed self-adapted mutation rates were close showed self-adapted mutation rates were close

to theoretical optimum for OneMaxto theoretical optimum for OneMax

Stephens, Olmedo, Vargas, and Waelbroeck Stephens, Olmedo, Vargas, and Waelbroeck (1998)(1998)

• Expanded on concept of Expanded on concept of neutralityneutrality in mapping in mapping• showed optimal mutation rate is not only showed optimal mutation rate is not only

problem but population dependantproblem but population dependant• adaptation of mutation rates can arise from adaptation of mutation rates can arise from

asymmetry in the genotype to phenotype asymmetry in the genotype to phenotype redundancyredundancy


A simpler model: Smith (2001)A simpler model: Smith (2001)

Analytic dynamic systemsAnalytic dynamic systems approach approach • Set of n fixed mutation ratesSet of n fixed mutation rates• When changing mutation rate, pick When changing mutation rate, pick

another one uniformly at randomanother one uniformly at random– Very different to log-normal, or even bit-Very different to log-normal, or even bit-

flippingflipping

• Accurately predicted behaviour of real Accurately predicted behaviour of real algorithm,algorithm,

• Especially around transitions on Especially around transitions on dynamic functiondynamic function


0 100 200 300 400 500Generations

25

30

35

40

45

50

Mea

n Fi

tnes

s

Self-Adaptive vs. Static mutationpredicted mean fitness vs. time

0.0005

0.001

0.0025

0.005

0.0075

0.01

0.025

0.050.0750.1

Adaptive


Evolution of Mutation ratesEvolution of Mutation ratesfollowing a transitionfollowing a transition

1000 1010 1020 1030 1040 1050

Generations

0

10

20

30

40

50

Prop

ortio

n of

pop

ulat

ion

in M

utat

ion

clas

s

P(m) = 0.0005

0.025

0.05

0.075

0.1

model 0.0005

model 0.025

model 0.05

model 0.075model 0.1


Markov Chain model: Smith (2002) Markov Chain model: Smith (2002)

Extended model to include binary coded ratesExtended model to include binary coded rates

Two types of control modelled:Two types of control modelled:

• External “Innovation Rate” External “Innovation Rate”

• Internal – mutation acts on its own encodingInternal – mutation acts on its own encoding

Results showed Results showed ““Internal” Control will often Internal” Control will often get stuck on local optimumget stuck on local optimum– Premature convergence of mutation rates Premature convergence of mutation rates

– observed by several othersobserved by several others

Refined Prerequisite: Need for Refined Prerequisite: Need for diversitydiversity of of strategiesstrategies


But does it work in practice?But does it work in practice?

• Experimental results: Smith & Stone Experimental results: Smith & Stone (2002)(2002)

• Simple model has higher success rates Simple model has higher success rates than log-normal adaptationthan log-normal adaptation

• Much better at escaping from local Much better at escaping from local optimaoptima

• Explanation in terms of greater Explanation in terms of greater diversity of mutation ratesdiversity of mutation rates


Self-adapting Recombination:Self-adapting Recombination: Schaffer and Morishima (1987) Schaffer and Morishima (1987)

Self-adapt the Self-adapt the formform of crossover by of crossover by encoding “punctuation marks” between encoding “punctuation marks” between lociloci

RecombinationRecombination: : • start copying from parent 1 until you get to a start copying from parent 1 until you get to a

punctuation mark,punctuation mark,• then switch to copying from parent 2 … then switch to copying from parent 2 …

Two ways of adapting punctuation marks:Two ways of adapting punctuation marks:• They are subject to mutationThey are subject to mutation• The way they are inherited during crossoverThe way they are inherited during crossover• Works ok, but it is possible for one child to Works ok, but it is possible for one child to

inherit all the crossover points inherit all the crossover points


Self-adapting RecombinationSelf-adapting Recombination Spears (1995) Spears (1995)

Self-adapt the Self-adapt the choicechoice of predefined crossover of predefined crossover• Extra bit on genome for uniform/1XExtra bit on genome for uniform/1X

• Individual level model:Individual level model:– Use crossover encoded by pairs of parentsUse crossover encoded by pairs of parents

• Population level modelPopulation level model– Measure proportion of parents encoding for 1XMeasure proportion of parents encoding for 1X– Use this as probability of using 1x Use this as probability of using 1x for any pairfor any pair– Statistically the same ( at a coarse level)Statistically the same ( at a coarse level)

Better results with individual level adaptationBetter results with individual level adaptation


LLinkage inkage EEvolving volving GGenetic enetic OOperator: Smith perator: Smith (1996,1998,2002)(1996,1998,2002)

Model gene linkage as boolean array: Model gene linkage as boolean array: A(A(i,ji,j)=1 => )=1 => ii and and jj inherited together inherited together

• Recombination R : Recombination R : R(A) ->A’,R(A) ->A’,• different operators specified by random different operators specified by random

vector vector xx

The LEGO algorithm :The LEGO algorithm :• generalisation of Schaffer and Morisihmageneralisation of Schaffer and Morisihma• encode encode AA in genome and self-adapt it in genome and self-adapt it• can create any common crossovercan create any common crossover• So far only done for adjacent linkageSo far only done for adjacent linkage


LEGO processLEGO process


Some results:Some results:

Series of experiments comparingSeries of experiments comparing• Fixed crossover strategiesFixed crossover strategies• Population level LEGO ( 3 variants)Population level LEGO ( 3 variants)• Component level LEGOComponent level LEGO

Results showResults show• LEGO outperforms 1X, UX on most LEGO outperforms 1X, UX on most

problemsproblems

Getting the scope right is vitalGetting the scope right is vital


Results on concatenated trapsResults on concatenated traps


Some counter examplesSome counter examples

Tuson and Ross compared adaptive vs. Tuson and Ross compared adaptive vs. self-adaptive P(c)self-adaptive P(c)

• Adaptive (using COBRA heuristic) was Adaptive (using COBRA heuristic) was betterbetter

One possible reason (several authors)One possible reason (several authors)• Self-adaptation rewards better strategies Self-adaptation rewards better strategies

– because they produce better offspringbecause they produce better offspring– BUT if parents are similar many different BUT if parents are similar many different

crossover masks will produce the same crossover masks will produce the same offspringoffspring

No selective pressure: no evolutionNo selective pressure: no evolution

no self-adaptationno self-adaptation


Crossover = Self-Adaptive mutation?Crossover = Self-Adaptive mutation?

Deb and Beyer (2001) ,followed by others, Deb and Beyer (2001) ,followed by others, proposed:proposed:

• Effects of operators Effects of operators transmission function transmission function• Selection takes care of changes in Selection takes care of changes in meanmean fitness fitness• Variation operators should increase diversityVariation operators should increase diversity

So Self-adaptation should have the properties So Self-adaptation should have the properties thatthat

• Children are more likely to be created close to Children are more likely to be created close to parentsparents

• Mean population fitness is unchangedMean population fitness is unchanged• Variance in population fitness should increase Variance in population fitness should increase

exponentially with time on flat landscapesexponentially with time on flat landscapes


Crossover in continuous spaces: Crossover in continuous spaces: Implicit Self-AdaptationImplicit Self-Adaptation

They (and others) showed that:They (and others) showed that:• for continuous variables, and other for continuous variables, and other

casescases– (Crossover can produce new values)(Crossover can produce new values)

• appropriately defined crossover appropriately defined crossover operators e.g. SBX, and others operators e.g. SBX, and others

• could demonstrate these propertiescould demonstrate these properties• ““implicit self-adaptation” implicit self-adaptation”


Combinations of operatorsCombinations of operators

Smith (1996, 1998)Smith (1996, 1998)• Self-Adaptive P(m) rate for each block in LEGOSelf-Adaptive P(m) rate for each block in LEGO• results better than either in their ownresults better than either in their own

Hinterding et al. (1996)Hinterding et al. (1996)• added population size adaptation heuristic and added population size adaptation heuristic and

self-adaptation of crossover to mutationself-adaptation of crossover to mutation

Eiben, Back et al. (1998, ongoing)Eiben, Back et al. (1998, ongoing)• Tested lots of combinations of adaptive Tested lots of combinations of adaptive

operatorsoperators• Concluded that population resizing mechanism Concluded that population resizing mechanism

from Arabas’ was most important factorfrom Arabas’ was most important factor


Population sizing: Arabas (1995)Population sizing: Arabas (1995)

• Each population member is given a Each population member is given a lifespanlifespan when it is created and has an when it is created and has an ageage

• LifespanLifespan is a function of fitness relative is a function of fitness relative to population mean and rangeto population mean and range

• Steady state modelSteady state model• Each time a member is created, all ages Each time a member is created, all ages

incrementedincremented• Member deleted if Member deleted if age >= lifespanage >= lifespan

is this really self-adaptation?is this really self-adaptation?


But why stop there …..But why stop there …..

So far we have looked at the standard EA So far we have looked at the standard EA operators: operators:

• mutation rates / step sizes, mutation rates / step sizes,

• Recombination operator probabilities or Recombination operator probabilities or definitiondefinition

• survivor selection (debatable)survivor selection (debatable)

But we know that EA +Local Search often gives But we know that EA +Local Search often gives good results ( good results ( Memetic AlgorithmsMemetic Algorithms))

• How do we choose which one to use?How do we choose which one to use?• Is it best to choose from a fixed set?Is it best to choose from a fixed set?


Multi-memetic algorithms Krasnogor Multi-memetic algorithms Krasnogor and Smith (2001)and Smith (2001)

• Extra gene encodes choice of LS operatorExtra gene encodes choice of LS operator– different moves and depthsdifferent moves and depths

• With small probability changed choiceWith small probability changed choice• Compared with MAs using fixed strategyCompared with MAs using fixed strategy

• Results showed that:Results showed that:– ““Best” fixed memes changed as search Best” fixed memes changed as search

progressedprogressed– the multi-meme tracked performance of the multi-meme tracked performance of

current best fixed memecurrent best fixed meme– Final results better over range of TSPFinal results better over range of TSP


Grammar for memes:Grammar for memes:Krasnogor and Gustaffson (2004)Krasnogor and Gustaffson (2004)

Specified grammar for memes Specified grammar for memes describingdescribing– What local search method usedWhat local search method used– When in Ea cycle it is usedWhen in Ea cycle it is used– Etc.Etc.

Proposed that memes could be self-Proposed that memes could be self-adapted as words in this grammaradapted as words in this grammar

some promising initial results on bio-some promising initial results on bio-informatics problemsinformatics problems


Self-adapting MemesSelf-adapting MemesSmith (2002, 2003,2005, 2007)Smith (2002, 2003,2005, 2007)

CO-evolution of Memetic Algorithms (COMA)CO-evolution of Memetic Algorithms (COMA)• General framework for coevolutionGeneral framework for coevolution• populations of memes and genespopulations of memes and genes• Memes encoded as tuples Memes encoded as tuples

<depth, pivot, pairing, condition, action><depth, pivot, pairing, condition, action>• Condition/action : patterns to match Condition/action : patterns to match • If If pairing = linkedpairing = linked

– Memes are inherited, recombined, mutated Memes are inherited, recombined, mutated with geneswith genes

– System is effectively self-adapting local searchSystem is effectively self-adapting local search


ResultsResults

Self-Adapting COMA shows fast scalable Self-Adapting COMA shows fast scalable optimisation on a range of problemsoptimisation on a range of problems

If problem structure can be exploited:If problem structure can be exploited:• Adapts rule length to problems structureAdapts rule length to problems structure• Quickly finds and exploits building blocksQuickly finds and exploits building blocks

If there is no structure to exploitIf there is no structure to exploit• Keeps evolving local search neighbourhoodsKeeps evolving local search neighbourhoods• Can provide a means of escape from local Can provide a means of escape from local

optimumoptimum


Scalability: Trap FunctionsScalability: Trap Functions


Adaptation of BehaviourAdaptation of Behaviour


SummarySummary

Self-adaptation worksSelf-adaptation works• For a range of different For a range of different

representationsrepresentations• For a range of different operatorsFor a range of different operators• Needn’t be restricted to mutationNeedn’t be restricted to mutation

Promising Areas for future researchPromising Areas for future research• Self-adaptation in GP, LCS, … ?Self-adaptation in GP, LCS, … ?• Self-Adaptation for dynamic Self-Adaptation for dynamic

optimisationoptimisation


• Thank you for listening…Thank you for listening…