Evolutionary Computing Slides

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Introduction To Evolutionary Computing

Book i n Natural Computing Series · January 2003

DOI: 10.1007/978-3-662-05094-1

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2 authors:

A. E. Eiben

VU University Amsterdam

303 PUBLICATIONS 9,328 CITATIONS

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Jim Smith

University of the West of England, Bristol

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Available from: A. E. Eiben

Retrieved on: 04 May 2016

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Introduction to

Evolutionary Computing II

A.E. EibenFree University Amsterdam

http://www.cs.vu.nl/~gusz/

with thanks to the EvoNet Training Committee and its “Flying Circus”


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A.E. Eiben, Introduction to EC II 2 EvoNet Summer School 2002

Contents

The evolutionary mechanism and its

components

Examples: the 8-queens problem Working of an evolutionary algorithm

EC dialects and beyond

Advantages & disadvantages of EC

Summary


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The main evolutionary cycle

Population

ParentsParent selection

Survivor selectionOffspring

Recombination

(crossover)

Mutation

Intialization

Termination


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The two pillars of evolution

Increasing population

diversity by geneticoperators

mutation

recombination

Push towards novelty

Decreasing population

diversity by selection of parents

of survivors

Push towards quality

There are two competing forces active


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Components:

representation / individuals (1)

Individuals have two levels of existence• phenotype: object in original problem context, the outside

• genotype: code to denote that object, the inside

(a.k.a. chromosome, “digital DNA”):

a d c a a c b

genotype:phenotype:

The link between these levels is called representation


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Genotype spacePhenotype space

Encoding

(representation)

Decoding

(inverse representation)

B 0 c 0 1 c d

G 0 c 0 1 c d

R 0 c 0 1 c d

Components:

representation / individiuals (2)


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Sometimes producing

the phenotype from the

genotype is a simple

and obvious process. Other times the

genotype might be a set

of parameters to some

algorithm, which workson the problem data to

produce the phenotype

Problem

DataGenotype

Phenotype

Growth

Function

Components:



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Components:


• Search takes place in the genotype space

• Evaluation takes place in the phenotype space

• Repr: Phenotypes Genotypes

• Fitness(g) = Value(repr -1(g))

• Repr must be invertible, in other words decoding must be

injective (Q: surjective?)

• Role of representation: defines objects that can be

manipulated by (genetic) operators

• Note back on Darwinism: no mutations on phenotypic

level! (right term: small random variations)


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Components: evaluation, fitness

measure

Role:• represents the task to solve, the requirements to adapt to

• enables selection (provides basis for comparison)

Some phenotypic traits are advantageous, desirable,e.g. big ears cool better,

These traits are rewarded by more offspring that willexpectedly carry the same trait


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Components: population

Role: holds the candidate solutions of the problem asindividuals (genotypes)

Formally, a population is a multiset of individuals,

i.e. repetitions are possible

Population is the basic unit of evolution,

i.e., the population is evolving, not the individuals

Selection operators act on population level

Variation operators act on individual level


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Components: selection

Role:

Gives better individuals a higher chance of becoming parents

surviving

Pushes population towards higher fitness

E.g. roulette wheel selection

fitness(A) = 3

fitness(B) = 1

fitness(C) = 2

A C

1/6 = 17%

3/6 = 50%

B

2/6 = 33%


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Components: Mutation

Role: causes small (random) variance

before

1 1 1 0 1 1 1after

1 1 1 1 1 1 1


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Components: Recombination

1 1 1 1 1 1 1 0 0 0 0 0 0 0parents

cut cut

1 1 1 0 0 0 0 0 0 0 1 1 1 1offspring

Role: combines features from different sources


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Place 8 queens on an 8x8 chessboard in

such a way that they cannot check each other

Example: the 8 queens problem


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The 8 queens problem

Representation

1 23 45 6 7 8

Genotype:a permutation of

the numbers 1 - 8

Phenotype:

a board configuration

Obvious mapping


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Penalty of one queen:

the number of queens she can check.

Penalty of a configuration:the sum of the penalties of all queens.

Note: penalty is to be minimized

Fitness of a configuration:

inverse penalty to be maximized


Fitness evaluation


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Mutation

Small variation in one permutation, e.g.:• swapping values of two randomly chosen positions, or

• inverting a randomly chosen segment

1 23 45 6 7 8 1 23 4 567 8


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Recombination

Combining two permutations into two new permutations:

• choose random crossover point

• copy first parts into children

• create second part by inserting values from otherparent:

• in the order they appear there

• beginning after crossover point

• skipping values already in child

8 7 6 42 531

1 3 5 24 678

8 7 6 45 123

1 3 5 62 874


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Parent selection:

Roulette wheel selection, for instance

Survivor selection (replacement)

When inserting a new child into the population, choosean existing member to replace by:

sorting the whole population by decreasing fitness

enumerating this list from high to low

replacing the first with a fitness lower than the given child

Note: selection works on fitness values, no need to adjust it

to representation


Selection


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Working of an EA

Phases in optimizing on a 1-dimensional fitness landscape

Early phase:

quasi-random population distribution

Mid-phase:

population arranged around/on hills

Late phase:

population concentrated on high hills


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Typical run

Typical run of an EA shows so-called “anytime behavior”

B e s t f i t n e s s i n p o p u l a t i o n

Time (number of generations)


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B e s t f i t n e s s

i n p o p u l a t i o

n


Progress in 1st half

Progress in 2nd half

Long runs?


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B e

s t f i t n e s s i n

p o p u l a t i o n

T: time needed to reach level F after random initialisation

T

F: fitness after smart initialisationF

Smart initialisation?


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Scale of “all” problems

P e r f o

r m a n c e o f m e t h

o d s o n p r o b l e m s

Random search

Special, problem tailored method

Evolutionary algorithm

Goldberg’89 view


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EAs and domain knowledge

Trend in the 90ies: adding problem specific knowledge

to EAs (special variation operators, repair, etc)

Result: EA performance curve “deformation”:

better on problems of the given type

worse on problems different from given type

Amount of added knowledge is variable


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P e r f o

r m a n c e o f m e t h o d s o n p r o b l e m s

EA 1

EA 4

EA 3EA 2

Scale of “all” problems

P

Michalewicz’96 view


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General EA framework and dialects

There is a general, formal EA framework (omitted here)

In theory:

every EA is an instantiation of this framework, thus:

specifying a particular EA or a type of EAs (a “dialect”)needs only filling in the characteristic features

In practice

this would be too formalistic

there are many exceptions (EAs not fitting into thisframework)

why care about the taxonomy, or label?


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Genetic algorithms &

genetic programming

Genetic algorithms (USA, 70’s, Holland, DeJong): Typically applied to: discrete optimization

Attributed features:

not too fast

good solver for combinatorial problems

Special: many variants, e.g., reproduction models, operators

Genetic programming (USA, 90’s, Koza) Typically applied to: machine learning tasks


competes with neural nets and alike slow

needs huge populations (thousands)

Special: non-linear chromosomes: trees, graphs

&


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Evolution strategies &

evolutionary programming

Evolution strategies (Germany, 70’s, Rechenberg, Schwefel) Typically applied to:

numerical optimization


fast & good optimizer for real-valued optimization

relatively much theory

Special: self-adaptation of (mutation) parameters standard

Evolutionary programming (USA, 60’s, Fogel et al.) Typically applied to: machine learning (old EP), optimization


very open framework: any representation and mutation op’s OK

Special:

no recombination

self-adaptation of parameters standard (contemporary EP)


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Beyond dialects

Field merging from the early 1990’s

No hard barriers between dialects, manyhybrids, outliers

Choice for dialect should be motivated by givenproblem

Best practical approach: choose representation,operators, population model, etc. pragmatically(and end up with an “unclassifiable” EA)

There are general issues for EC as a whole


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Advantages of EC

No presumptions w.r.t. problem space

Widely applicable

Low development & application costs

Easy to incorporate other methods

Solutions are interpretable (unlike NN) Can be run interactively, accommodate user

proposed solutions

Provides many alternative solutions

Intrinsic parallelism,straightforward parallelimplementations


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Disadvantages of EC

No guarantee for optimal solution within

finite time

Weak theoretical basis May need parameter tuning

Often computationally expensive, i.e. slow


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The performance of EC

Acceptable performance at acceptable costs on a wide rangeof problems

EC niche (where supposedly superior to other techniques):

complex problems with one or more of the following features

many free parameters

complex relationships between parameters

mixed types of parameters (integer, real)

many local optima

multiple objectives noisy data

changing conditions (dynamic fitness landscape)


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A E Eiben Introduction to EC II 34 EvoNet Summer School 2002

Summary

Evolutionary Computation:

is a method, based on biological metaphors,

of breeding solutions to problems

has been shown to be useful in a number of

areas

could be useful for your problem

its easy to give it a try

is FUN

Documents

Evolutionary Computing Slides