evolutionary computation ( 진 화 연 산 ) 장 병 탁 서울대 컴퓨터공학부 e-mail:...

Evolutionary ComputationEvolutionary Computation(( 진 화 연 산진 화 연 산 ))

장 병 탁서울대 컴퓨터공학부

E-mail: [email protected]://scai.snu.ac.kr./~btzhang/

Byoung-Tak ZhangSchool of Computer Science and Engineering

Seoul National University

This material is also available online at http://scai.snu.ac.kr/

2

OutlineOutline

1. Basic Concepts

2. Theoretical Backgrounds

3. Applications

4. Current Issues

5. References and URLs

3

1. Basic Concepts1. Basic Concepts

4

Charles Darwin (1859)

“Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring.”

5

Evolutionary AlgorithmsEvolutionary Algorithms

A Computational Model Inspired by Natural Evolution and Genetics

Proved Useful for Search, Machine Learning and Optimization

Population-Based Search (vs. Point-Based Search) Probabilistic Search (vs. Deterministic Search) Collective Learning (vs. Individual Learning) Balance of Exploration (Global Search) and Exploitation

(Local Search)

6

Biological TerminologyBiological Terminology

Gene Functional entity that codes for a specific feature e.g. eye color Set of possible alleles

Allele Value of a gene e.g. blue, green, brown Codes for a specific variation of the gene/feature

Locus Position of a gene on the chromosome

Genome Set of all genes that define a species The genome of a specific individual is called genotype The genome of a living organism is composed of several Chromosomes

Population Set of competing genomes/individuals

7

Analogy to Analogy to Evolutionary BiologyEvolutionary Biology Individual (Chromosome) = Possible Solution Population = A Collection of Possible Solutions Fitness = Goodness of Solutions Selection (Reproduction) = Survival of the Fittest Crossover = Recombination of Partial Solutions Mutation = Alteration of an Existing Solution

8

The Evolution LoopThe Evolution Loop

select mating partners

recombine

mutate

evaluate

select

(terminate)

evaluate

initialize population

9

Basic Evolutionary AlgorithmBasic Evolutionary Algorithm

Generation of initial solutions (A priori knowledge, results of earlier run, random)

Evaluation

Selection

SolutionSufficiently

good?

END

Generation of variants by mutation

and crossover

YES

NO

10

ProcedureProcedure

begin

t <- 0;

initialize P(t);

evaluate P(t);

while (not termination condition) do

recombine P(t) to yield C(t);

evaluate C(t);

select P(t+1) from P(t) and C(t);

t <- t+1;

end

end

11

General Structure of EAsGeneral Structure of EAs

solutions

1100101010101110111000110110011100110001

1100101110

10111011101100101010

crossover

mutation

00110

1011101010

10011

00110 10010

evaluation

110010111010111010100011001001

solutions

fitnesscomputation

roulettewheel

selectionnew

population

encoding

chromosomes

12

Population and FitnessPopulation and Fitness

2

4

6 4

668

6

13

Selection, Crossover, and MutationSelection, Crossover, and Mutation

Reproduction

Distinction Mutation

Crossover2

4

6 4

8

66

10

8

8

6

14

Simulated EvolutionSimulated Evolution

Population (chromosomes)

Geneticoperators

Selection(mating pool)

Evaluation (fitness)

Decodedstrings

Newgeneration

Offspring

Mating

Manipulation

Reproduction

Parents

15

Selection StrategiesSelection Strategies

Proportionate Selection Reproduce offspring in proportion to fitness fi.

Ranking Selection Select individuals according to rank(fi).

Tournament Selection Choose q individuals at random, the best of which survives.

Other Ways

1j

tj

tit

isaf

afap

i

iap t

is

,0

1,1

qq

qtis iiap

1

1

16

Roulette Wheel SelectionRoulette Wheel Selection

10001

11010

01011

00101

10001

11010

01011

00101

1000

1

1101

0

0101

100

101

10001

11010 0101100101

1000111010

0101100101

intermediate parent population:

01011 11010 10001 10001

Probability of reproduction pi = fi / Sk fk

Selection is a stochastic process

17

Genetic Operators for BitstringsGenetic Operators for Bitstrings

• Reproduction: make copies of chromosome (the fitter the chromosome, the more copies)

1 0 0 0 0 1 0 0

• Crossover: exchange subparts of two chromosomes

• Mutation: randomly flip some bits

1 0 0 | 0 0 1 0 0 1 1 1 | 1 1 1 1 1 0 0 0 0 0 1 0 0

1 0 0 0 0 1 0 0

1 0 0 0 0 1 0 0

1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0

0 0 0 0 0 0 0 0

18

MutationMutation

For a binary string, just randomly “flip” a bit For a more complex structure, randomly select a

site, delete the structure associated with this site, and randomly create a new sub-structure

Some EAs just use mutation (no crossover) Normally, however, mutation is used to search in

the “local search space”, by allowing small changes in the genotype (and therefore hopefully in the phenotype)

19

Recombination (Crossover)Recombination (Crossover)

Crossover is used to swap (fit) parts of individuals, in a similar way to sexual reproduction

Parents are selected based on fitness Crossover sites selected (randomly, although other

mechanisms exist), with some prob. Parts of the parents are exchanged to produce

children

20

CrossoverCrossover

One-point crossover

parent Aparent B

1 1 0 1 0

1 0 0 0 1

offspring Aoffspring B

1 1 0 1 1

1 0 0 0 0

Two-point crossover

parent Aparent B

1 1 0 1 0

1 0 0 0 1

offspring Aoffspring B

1 1 0 0

1 0 0 1

0

1

21

2. Theoretical Backgrounds2. Theoretical Backgrounds

22

Major Evolutionary AlgorithmsMajor Evolutionary Algorithms

Genetic Programming

Evolution Strategies

Genetic Algorithms Evolutionary

ProgrammingClassifier Systems

• Genetic representation of candidate solutions• Genetic operators• Selection scheme• Problem domain

Hybrids: BGA

23

Variants of Evolutionary AlgorithmsVariants of Evolutionary Algorithms

Genetic Algorithm (Holland et al., 1960’s) Bitstrings, mainly crossover, proportionate selection

Evolution Strategy (Rechenberg et al., 1960’s) Real values, mainly mutation, truncation selection

Evolutionary Programming (Fogel et al., 1960’s) FSMs, mutation only, tournament selection

Genetic Programming (Koza, 1990) Trees, mainly crossover, proportionate selection

Hybrids: BGA (Muehlenbein et al., 1993) BGP (Zhang et al., 1995) and others.

24

Evolution Strategy (ES)Evolution Strategy (ES)

Problem of real-valued optimizationFind extremum (minimum) of function F(X): Rn ->R

Operate directly on real-valued vector X Generate new solutions through Gaussian

mutation of all components Selection mechanism for determining new parents

25

ES: RepresentationES: Representation

One individual:

The three parts of an individual:

Ixxa nnn

,,,,,,,, 111

x

: Object variables

: Standard deviations

: Rotation angles

Fitness

Variances

Covariances

)(xf

x

26

, where rx, r , r {-, d, D, i, I, g, G}, e.g. rdII rrr xr

GiSiTiiS

giSiTiS

IiSiTiS

iiSiTiS

DiTiS

diTiS

iS

i

rxxx

rxxx

rxxx

rxxx

rxx

rxx

rx

x

i

i

i

teintermedia dgeneralize panmictic)(

teintermedia dgeneralize)(

teintermedia panmictic2/)(

teintermedia2/)(

discrete panmicticor

discreteor

ionrecombinat no

,,,

,,,

,,,

,,,

,,

,,

,

ES: Operator - RecombinationES: Operator - Recombination

27

m{,’,} : I I is an asexual operator. n = n, n = n(n-1)/2

1 < n < n, n = 0

n = 1, n = 0

)),(,0(

)1,0(

))1,0()1,0(exp(

CNxx

N

NN

jjj

iii

0873.0

2

2

1

1

n

n

)1,0(

))1,0()1,0(exp(

iiii

iii

Nxx

NN

)1,0(

))1,0(exp( 0

iii Nxx

N

n/10

ES: Operator - MutationES: Operator - Mutation

28

ES: Illustration of Mutation ES: Illustration of Mutation HyperellipsoidsHyperellipsoids

Line of equal probability density to place an offspring

29

ES: Evolution Strategy vs. ES: Evolution Strategy vs. Genetic AlgorithmGenetic Algorithm

Create random initial population

Evaluate population

Select individuals for variation

Vary

Insert intopopulation

Create random initial population

Evaluate population

Vary

Selection

Insert intopopulation

30

Evolutionary Programming (EP) Evolutionary Programming (EP)

Original form (L. J. Fogel) Uniform random mutations Discrete alphabets selection

Extended Evolutionary Programming (D. B. Fogel) Continuous parameter optimization Similarities with ES

• Normally distributed mutation

• Self-adaptation of mutation parameters

)(

31

EP: RepresentationEP: Representation

Constraints for domain and variances Initialization only-operators does not survey

• Search space is principally unconstrained.

Individual

EP) (metaor EP) (std and

,),(n

ssn

x

sx

RAARA

AAIxa

32

EP: Operator - RecombinationEP: Operator - Recombination

No recombination Gaussian mutation does better (Fogel and Atmar).

• Not all situations

Evolutionary biology• The role of crossover is often overemphasized.

Mutation-enhancing evolutionary optimization Crossover-segregating defects The main point of view from researchers in the field of Genetic

Algorithms

33

EP: Operator - MutationEP: Operator - Mutation

General form (std. EP)

Exogenous parameters must be tuned for a particular task

Usually Problem

• If global minimum’s fitness value is not zero, exact approachment is not possible

• If fitness values are very large, the search is almost random walk

• If user does not know about approximate position of global minimum, parameter tuning is not possible

)1,0()( iiiii Nxxx

ii ,

)1,0()( iii Nxxx

34

EP: Differences from ESEP: Differences from ES

Procedures for self-adaptation Deterministic vs. Probabilistic selection -ES vs. -EP Level of abstraction: Individual vs. Species

),( )(

35

Genetic ProgrammingGenetic Programming

Applies principles of natural selection to computer search and optimization problems - has advantages over other procedures for “badly behaved” solution spaces [Koza, 1992]

Genetic programming uses variable-size tree-representations rather than fixed-length strings of binary values.

Program tree

= S-expression

= LISP parse tree Tree = Functions (Nonterminals) + Terminals

36

GP: RepresentationGP: Representation

S-expression: (+ 1 2 (IF (> TIME 10) 3 4))Terminals = {1, 2, 3, 4, 10, TIME}Functions = {+, >, IF}

+

2

4> 3

1 IF

TIME 10

37

GP: Operator - CrossoverGP: Operator - Crossover

+

b

a b

+

b

+

a a b

+

a b

a b

+

b

+

a

b

38

GP: Operator - MutationGP: Operator - Mutation

a b

+

b

/

a

+

b

+

b

/

a

-

b a

39

Breeder GP (BGP) Breeder GP (BGP) [Zhang and Muehlenbein, 1993, 1995][Zhang and Muehlenbein, 1993, 1995]

ES (real-vector) GA (bitstring)

Breeder GA (BGA)(real-vector + bitstring)

GP (tree)

Breeder GP (BGP)(tree + real-vector + bitstring)

Muehlenbein et al. (1993)

Zhang et al. (1993)

40

GAs: Theory of Simple GAGAs: Theory of Simple GA

Assumptions Bitstrings of fixed size Proportionate selection

Definitions Schema H: A set of substrings (e.g., H = 1**0) Order o: number of fixed positions (FP) (e.g., o(H) = 2) Defining length d: distance between leftmost FP and

rightmost FP (e.g., d(H) = 3)

41

GAs: Schema Theorem (Holland GAs: Schema Theorem (Holland et al. 1975)et al. 1975)

)(11

)(1

)(

),(),()1,( Ho

mc pn

Hdp

tf

tHftHmtHm

),( tHm

cp mp ,

Number of members of H

Probability of crossover and mutation, respectively

Interpretation: Fit, short, low-order schemata (or building blocks) exponentially grow.

42

Convergence velocity of (+, )-ES

ES-),( afor and ES-)( afor 0 where

)1(11

minmin

1

1),(

min

kk

kdpppv

k vkk

vkkkkkk

vjjj

8erf1

82exp

821

2exp11

~

12

exp22

~erf

2

~exp

2

~1

2

2

2

2

22

2

22

1

11

1

1

1

2

1

1

1

11

ES: TheoryES: Theory

43

EP: Theory (1)EP: Theory (1)

Analysis of std. EP(Fogel) Aims at giving a proof of convergence for resulting

algorithm

• Mutation:

Analysis of a special case EP(1,0,q,1)• Identical to a (1+1)-ES having

Objective function• Simplified sphere model

)1,0()( iii Nxxx

),,0,1( qEP

n

iii rxxf

1

222 )(

~

)(xf

44

EP: Theory (2)EP: Theory (2)

Combination with the optimal SD

When dimension is increased, the performance is worse than an algorithm that is able to retain the opt. SD

The convergence rate of a (1+1)-EP by

224.1)(

~ *2

2

nrxf i

nr /224.1*2

8erf1

48

1exp

22

22

2

222

r

n

r

n

r

n

)(~222 r

rnnn

8erf1

48exp

2

1~2

2

45

Breeder GP: Motivation for GP Breeder GP: Motivation for GP TheoryTheory

In GP, parse trees of Lisp-like programs are used as chromosomes.

Performance of programs are evaluated by training error and the program size tends to grow as training error decreases.

Eventual goal of learning is to get small generalization error and the generalization error tends to increase as program size grows.

How to control the program growth?

46

Breeder GP: Breeder GP: MDL-Based MDL-Based Fitness FunctionFitness Function

)()|()|()( gi

giii ACADEDAFgF

)|( giADE

)( giAC

,

Training error of neural trees A for data set D

Structural complexity of neural trees A

Relative importance of each term

47

Breeder GP: Adaptive Occam Breeder GP: Adaptive Occam Method (Zhang et al., 1995)Method (Zhang et al., 1995)

otherwisetCtE

N

tEiftC

tEN

t

tCttEtF

bestbest

bestbest

best

iii

)()1(

1

)1()(

)1(

)(

)()()()(

2

2

Desired performance level in error

Training error of best progr. at gen t-1

Complexity of best progr. at gen. t

)1( tEbest

)(tCbest

48

Bayesian Evolutionary Computation (1/2)Bayesian Evolutionary Computation (1/2)

The best individual is defined as the most probable model of data D given the priori knowledge

The objective of evolutionary computation is defined to find the model A* that maximizes the posterior probability

Bayesian theorem is used to estimate P(A|D) from a population A(g) of individuals at each generation.

)(

)()|(

)()|(

)()|(

)()|(

)(

)()|()|(

gA

APADP

APADP

dAAPADP

APADP

DP

APADPDAP

A

)|(maxarg* DAPAA

49

Bayesian process: The BEAs attempt to explicitly estimate the posterior distribution of the individuals from their prior probability and likelihood, and then sample offspring from the distribution.

Bayesian Evolutionary Computation (2/2)Bayesian Evolutionary Computation (2/2)

[Zhang, 99]

50

Canonical BEACanonical BEA

(Initialize) Generate from the prior distribution P0(A). Set generation count t 0.

(P-step) Estimate posterior distribution Pt(A|D) of the individuals in At.

(V-step) Generate L variations by sampling from Pt(A|D).

(S-step) Select M individuals from A´ into based on Pt(A´i |D). Set the best individual .

(Loop) If the termination condition is met, then stop. Otherwise, set t t+1 and go to (P-step).

},,{ 001

0MAA A

},,{A 1 LAA

},,{A 111

tM

tt AA

51

Basic Idea behind BEABasic Idea behind BEA

52

Evolving Neural Trees with BEAEvolving Neural Trees with BEA

Posterior probability of a neural tree A

)!3(

)exp(

2exp

2

1

2

))((exp

2

1

)()|(),|(

),(),|()()|()|(

3

1

1

21

21

2),(

k

w

fy

kPkPkDP

kpkDPAPADPDAP

k

k

jjk

N

cckcN

x

ww

ww

w

53

Features of EAsFeatures of EAs

Evolutionary techniques are good for problems that are ill-defined or difficult

Many different forms of representation Many different types of EA Leads to many different types of crossover,

mutation, etc. Some problems with convergence, efficiency However, they are able to solve a diverse range of

problems

54

Advantages of EAsAdvantages of EAs

Efficient investigation of large search spaces Quickly investigate a problem with a large number of

possible solutions

Problem independence Can be applied to many different problems

Best suited to difficult combinatorial problems

55

Disadvantages of EAsDisadvantages of EAs

No guarantee for finding optimal solutions with a finite amount of time: True for all global optimization methods.

No complete theoretical basis (yes). But much process is being made.

Parameter tuning is largely based on trial and error (genetic algorithms); solution: Self-adaptation (evolution strategies).

Often computationally expensive: Parallelism.

56

3. Applications3. Applications

57

Application Fields (1)Application Fields (1)

Experimental optimization & optimization with subjective evaluation Coffee recipes; general food recipes Biochemical fermentation processes Wind tunnel experiments Two-phase nozzle optimization experiments

Technical optimization Design & Production Logistics Control of dynamic processes

58


Structure optimization Structure & parameters of plants Connection structure & weights of neural nets Number of thicknesses of layers in multilayer

structures

Data Mining Clustering (number & centers of clusters) Fitting models to data Time series prediction

59


Path Planning Traveling Salesman Problem

Robot Control Evolutionary Robotics Evolvable Hardware

60

Hot Water Flashing Nozzle (1)Hot Water Flashing Nozzle (1)

Start

Hot water entering Steam and droplet at exit

At throat: Mach 1 and onset of flashing

Application Example 1Application Example 1

Hans-Paul Schwefel performed the original experiments

61

Hot Water Flashing Nozzle (2)Hot Water Flashing Nozzle (2)Application Example 1Application Example 1

62

Minimal Weight Trust Layout Minimal Weight Trust Layout

LoadStart

922 kp

(LP minimum)

Optimum

738 kp


63

Concrete Shell RoofConcrete Shell Roof

under own and outer load (snow and wind)

Height 1.34m

Spherical shapeOptimal shape

Half span 5.00m

Savings : 36% shell thickness 27% armation

max minOrthogonal bending strength

m


64

Dipole Magnet Structure (1)Dipole Magnet Structure (1)

Mag

ne

tNS

yx

Mag

ne

tNS

yx

Mag

ne

tNS

yx

P1n

Fie

ld re

gio

n

of

inte

rest

y-

Ran

ge


65

Dipole Magnet Structure (2)Dipole Magnet Structure (2)

Analysis of the magnetic field by Finite Element Analysis (FEM)

Minimize sum of squared deviations from the ideal

Individuals: Vectors of positions (y1, …, yn)

Middle: 9.8% better than upper graphic; bottom: 2.7% better


66

Optical Multilayers (1)Optical Multilayers (1)

Goal: Find a filter structure such that the real reflection behavior matches the desired one as close as possible.

Filter layers; - Thicknesses - Materials

……..

Substrate (Glass)

Reflection

Wavele

ng

th

Desired

Current


67


Problem parameters; Thickness of layers Layer materials (integer values) Number of layers n.

Mixed-integer, variable-dimensional problem.

nddd ,,1

n ,,1


68


Objective function:

: Reflection of the actual filter for wavelength

Calculation according to matrix method.

: Desired reflection value

,,

dR

R~

dRdRdf

d

2~,,,


69


Example topology: Only layer thicknesses vary; n=2


70


Example structure:


71


Parallel evolutionary algorithm Per node: EA for mixed-integer representation Isolation and migration of best individuals Mutation of discrete variables: Fixed pm per population


72

Circuit Design (1)Circuit Design (1)

Difficulty of automated circuit design: A vary hard problem

Exponential in the number of components More than 10300 circuits with a mere 20 components

An important problem Too few analog designers There is an “Egg-shell” of analog circuitry around almost all

digital circuits Analog circuits must be redesigned with each new generation of

process technology No existing automated techniques

In contrast with digital Existing analog techniques do only sizing of components, but do

not create the topology


73

Circuit Design (2)Circuit Design (2)Application Example 6Application Example 6

OutIn

Developing Circuit

Development of a circuit with Genetic Programming

74


Each function in the circuit-constructing tree acts on a part of the circuit and changes it in some way (e.g. creates a capacitor, creates a parallel structure, adds a connection to ground, etc)

A “writing head” points from each function to the part of the circuit that the function will act on.

Each function inherits writing heads from its parent in the tree


75


Example of circuit – constructing program tree

(LIST (C (-0.963 (- (- -0.875 – 0.113) 0.880)) (series (flip end) (series (flip end) (L –0.277 end) end) (L (- -0.640 0.749) (L –0.123 end)))) (flip (nop (L –0.657 end)))))


LIST

C FLIP

NOP

-0.658 END

SERIES

SERIES

FLIP END

L

L

-0.277 ENDEND

L

- L

-0.658 -0.749 -0.658 END

-

-0.963 -

- -0.880

-0.875 -0.113

FLIP

END

76

Neural Network Design (1)Neural Network Design (1)

Introduction: EC for NNs Preprocessing of Training Data

Feature selection Training set optimization

Training of Network Weights Non-gradient search

Optimization of Network Architecture Topology adaptation Pruning unnecessary connections/units


77


Encoding Schemes for NNs

Bit-strings Properties of network structure are encoded as bit-

strings.

Rules Network configuration is specified by a graph-

generation grammar.

Trees Network is represented as “neural trees”.


78


Neural Tree ModelsNeural Tree Models Neural trees

Tree-structured neural networks Nonterminal nodes: Neural units Terminal nodes: Inputs Links: connection weights wij from j to i

Layer of node i: path length of the longest path to a terminal node of the substrees of i.

Type of Units Sigma unit: the sum of weighted inputs Pi unit: the product of weighted inputs Output of a neuron: sigmoid transfer function

},{ F},,,{ 21 nxxxT

j

jiji ywnet

j

jiji ywnet

inetii enetfy

1

1)(


79


S1

S2 P1 S4 S5

X2 X4 X1 S3 X3

X2 X1 X3 X2 X5

P2 X4 X4 S6

X1 X3

W11 W12 W13 W14

W21 W22 W31 W32 W33 W51 W52 W71 W72

W41 W42 W61 W62 W63 W81 W82


Tree-Structured ModelTree-Structured Model

80


Generate M Trees

Evaluate Fitness of Trees

Create L New Trees

Select Fitter Trees

Termination Condition? STOP

Posterior Distribution

Model Selection

Model Variation(Variation Operators)

Yes

No

Prior Distribution


Evolving Neural Networks by BEAsEvolving Neural Networks by BEAs

81


Structural Adaptation by Subtree Crossover Neuron type, topology, size and shape of networks are

adapted by crossover.

Neuron types and receptive fields are adapted by mutation. Connection weights are adapted by an EC-based stochastic

hill-climbing.


82

Fuzzy System Design (1)Fuzzy System Design (1)

Fuzzy system comprises Fuzzy membership functions (MF) Rules

Task is to tailor the MF and rules to get best performance

Every change to MF affects the rules Every change to the rules affects the MF


83


Solution is to design MF and rules simultaneously Encode in chromosomes

Aarameters of the MF Associations and Certainty Factors in rules

Fitness is measured by performance of the Fuzzy System


84


Evolutionary Computation and Fuzzy Systems

Fuzzy Sets (Zadeh): Points have Memberships

Evolutionary Computation can be Used to Optimize Fuzzy Control Systems

Evolve Membership Functions/Rules

FUZZY MEMBERSHIP FOR “COOL”

Membership

0.0

1.0

0o 2.5o

Temperature (C)


85


NM=Negative Medium, NS=Negative Small, ZE=Zero, PS=Positive Small, PM=Positive Medium, _=No Entry

Defuzzification is Just Weighed Centroid Mutation Up/Down by One. Two-Point Xover on String Representing the 5x5

Metrix

Cart Centering and Fuzzy PartitionsFuzzy Control Strategy after 100 Gen.

Fm

x(v=x)

NM NS ZE PS PM

PM PM PM

PM

PM

PM

PM

PM

PM

NM

PM

NM NM NM

NM

NMNM

NS

NM NS ZE PS PM

NM

NS

ZE

PS

PM

x

v


GA for Fuzzy Control of CartGA for Fuzzy Control of Cart

86

Data Mining (1)Data Mining (1)

Data Mining Task Types of problem to be solved: Classification Clustering Dependence Modeling etc., etc.


87


Basic Ideas of GAs in Data Mining Candidate rules are represented as individuals of a

population Rule quality is computed by a fitness function Using task-specific knowledge


88


Classification with Genetic Algorithms Each individual represents a rule set

• i.e. an independent candidate solution

Each individual represents a single rule A set of individuals (or entire population) represents a

candidate solution (rule set)


89


Individual Representation In GABIL, an individual is a rule set, encoded as a bit string

[DeJong et al. 93] It uses k bits for the k values of a categorical attribute If all k bits of an attribute are set to 1 the attribute is not used by

the rule Goal attribute: Buy furniture Marital_status: Single/Married/Divorced House:Own/Rented/University Marital_status House Buy? The string 011 100 1 Represents the rule IF(Marital_status=M or D) and (House = 0) THEN (Buy furniture=y)


90


An individual is a variable-length string representing a set of fixed-length rules

rule 1 rule 2

011 100 1 101 110 0

Mutation: traditional bit inversion Crossover: corresponding crossover points in the

two parents must semantically match


91

Information Retrieval (1)Information Retrieval (1)Text Data

Classification System

Information Filtering System

questionuser profile

feedback

answer

DB

LocationDate

DB Record

DB Template Filling& InformationExtraction System

Information FilteringInformation Extraction

filtered data

Text Classification

Preprocessing and Indexing


92

Information Retrieval (2)Information Retrieval (2)

[Kim & Zhang, 2000]

Link Information,HTML Tag Information

chromosomes

<TITLE> <H> <B> … <A>

Retrieval

Fitness

wn…w3w2w1

wn…w3w2w1 wn…w3w2w1 wn…w3w2w1

wn…w3w2w1 wn…w3w2w1


Evolutionary Learning:Evolutionary Learning: Applications in IR - Web-Document RetrievalApplications in IR - Web-Document Retrieval

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Crossover

Truncation selection

Mutation

yn…y3y2y1xn…x3x2x1

chromosome X chromosome Y

chromosome Z (offspring)

zi = (xi + yi ) / 2 w.p. Pc

chromosome X

chromosome X’

change value w.p. Pm

xn…x3x2x1

xn…x3x2x1zn…z3z2z1


Evolutionary Learning: Evolutionary Learning: Applications in IR – Tag WeightingApplications in IR – Tag Weighting

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Datasets TREC-8 Web Track Data 2GB, 247491 web documents (WT2g) No. of training topics: 10, No. of test topics: 10

Results


Evolutionary Learning : Evolutionary Learning : Applications in IR - Experimental ResultsApplications in IR - Experimental Results

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Time Series Prediction (1)Time Series Prediction (1)Application Example 11Application Example 11

RawTime Series

RawTime Series

Prepro-cessingPrepro-cessing

EvolutionaryNeural Trees

(ENTs)

EvolutionaryNeural Trees

(ENTs)

CombiningNeural TreesCombining

Neural Trees

AutonomousModel Discovery

Combine Neural TreesOutputs

Prediction

[Zhang & Joung, 2000]

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Time Series Prediction (2)Time Series Prediction (2) Experimental Setup for the far-infrared NH3

Laser

Design Paramenters Values Used

population size 200

max generation 50

crossover rate 0.95

mutation rate 0.1

no. of iterations 100

training set size 1000

test set size 1000

size of committee pool 10

no. of committee members 3


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Time Series Prediction (3)Time Series Prediction (3)

Experimental Result

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 201 401 601 801 1001 1201 1401 1601 1801 2001

t

x(t

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000 1200 1400 1600 1800 2000

t

x(t

)

Computed Approximation

Target Function


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Traveling Salesman Problem (1)Traveling Salesman Problem (1)

This is a minimization problem Given n cities, what is the shortest route to each

city, visiting each city exactly once Want to minimize total distance traveled Also must obey the “Visit Once” constraint


99


Encoding represents the order of cities to visit Candidates scored by total distance traveled

1

0

3

2 5

6

4


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Traveling Salesman Problem (TSP) combinatorial optimization problems a salesman seeks the shortest tour through n cities NP-complete problem


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Simple Example with the TSP The “house-call problem”

• Problem: Doctor must visit patients once and only once and return home in the shortest possible path

Difficulty: The number of possible routes increases faster than exponentially

• 10 patients = 191,440 possible routes

• 22 patients = 10,000,000,000,000,000,000,000


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Representation Permutation Representation

• cities are listed in the order in which they are visited[3 2 5 4 7 1 6 9 0 8] : 3 - 2 - 5 - 4 - 7 - 6 - 1 - 9 - 0 - 8• path presentation, order representation• lead to illegal tour if the traditional one-point crossover operator is used

Random Keys Representation• encodes a solution with random numbers from (0, 1)[0.23 0.82 0.45 0.74 0.87 0.11 0.56 0.69 0.78] position i in the list represent city I random number in position I determines the visiting order of city I in a TSP

tour sort random keys in ascending order to get tour

6 - 3 - 7 - 8 - 4 - 9 - 2 - 5 eliminate the infeasibility of the offspring


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Cooperating Robots (1)Cooperating Robots (1)

What is Evolutionary Robotics? An attempt to create robots which evolve using various

evolutionary computational methods Evolve behaviors or competence modules implemented

in various manners: several languages, relay, neuro chips, FPGA’s, etc.

“Intelligence is emergent” Presently, limited to mostly evolution of robot’s control

software. However, some attempts to evolve hardware began.

GA and its variants used. Most current attempts center around {population size=50 ~ 500, generations = 50 ~ 500}


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CLOSED

OPEN !!


Industrial Robots Industrial Robots Autonomous Mobile RobotsAutonomous Mobile Robots

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Cooperating Autonomous Robots


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Why Build Cooperating Robots? Increased scope for missions inherently

distributed in: • Space • Time • Functionality

Increased reliability, robustness (through redundancy)

Decreased task completion time (through parallelism)

Decreased cost (through simpler individual robot design)


107

Cooperating Robots (5)Cooperating Robots (5) Cooperating Autonomous Robots: Application

domain Mining Construction Planetary exploration Automated manufacturing Search and rescue missions Cleanup of hazardous waste Industrial/household maintenance Nuclear power plant decommissioning Security, surveillance, and reconnaissance


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Co-evolving Soccer Softbots (1)Co-evolving Soccer Softbots (1)

At RoboCup there are two "leagues": the "real" robot league and the "virtual" softbot league

How do you do this with GP? GP breeding strategies: homogeneous and heterogeneous Decision of the basic set of function with which to evolve players Creation of an evaluation environment for our GP individuals


Co-evolvingCo-evolving Soccer Softbots Soccer Softbots With Genetic With Genetic ProgrammingProgramming

109


Initial Random Population


110


Kiddie Soccer


111


Learning to Block the Goal


112


Becoming Territorial


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Evolvable Hardware (1)Evolvable Hardware (1)

EVOLVABLE HARDWARE

HARDWARE IMPLEMENTATION OF EVOLVABLE SOFTWARE (i.e. GP)

Reconfigurable logic is too slow to make it worthwhile


114


FPGAs Bad, because they are designed for

conventional electronic design Good, because they can be abused and allow

the exploitation of the physics

FPMAs Field Programmable Matter Arrays

WHAT WE NEED


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Can we, by evolving the voltages configure the material to carry out a useful function?

KEY REQUIREMENT

Removing the voltage must cause the material

to relax to its former state

wires Chemical substrate

A single piece of material

Region to which voltage may be applied


What is a FPMA?What is a FPMA?

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XC6216 FPGA


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The Evolvable Hardware Robot Controller

The logic functions are evolved, and implemented in a RAM chip

A allows a signal to be either synchronised to a clock of evolved frequency, or passed straight through asynchronously, all under genetic control.

All evaluations performed using the REAL HARDWARE

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Evolvable Hardware (6)Evolvable Hardware (6)Application Example 15Application Example 15

119

4. Current Issues4. Current Issues

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Innovative Techniques for ECInnovative Techniques for EC

Effective Operators Novel Representation Exploration/Exploitation Population Sizing Niching Methods Dynamic Fitness Evaluation

Multi-objective Optimization Co-evolution Self-Adaptation EA/NN/Fuzzy Hybrids Distribution Estimation Algorithms Parallel Evolutionary Algorithms Molecular Evolutionary Computation

121

1000-Pentium Beowulf-Style 1000-Pentium Beowulf-Style Cluster Computer for Parallel GPCluster Computer for Parallel GP

122

Molecular Evolutionary Molecular Evolutionary ComputingComputing

011001101010001 ATGCTCGAAGCT

123

Applications of EAs Applications of EAs

Optimization Machine learning Data mining Intelligent Agents Bioinformatics Engineering Design Telecommunications Evolvable Hardware Evolutionary Robotics

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5. References and URLs5. References and URLs

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Journals & ConferencesJournals & Conferences

Journals: Evolutionary Computation (MIT Press) Trans. on Evolutionary Computation (IEEE) Genetic Programming & Evolvable Hardware

(Kluwer) Evolutionary Optimization

Conferences: Congress on Evolutionary Computation (CEC) Genetic and Evolutionary Computation Conference

(GECCO) Parallel Problem Solving from Nature (PPSN)

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WWW ResourcesWWW Resources

• Genetic Programming Notebook• http://www.geneticprogramming.comsoftware, people, papers, tutorial, FAQs

• Hitch-Hiker’s Guide to Evolutionary Computation• http://alife.santafe.edu/~joke/encore/wwwFAQ for comp.ai.genetic

• Genetic Algorithms Archive• http://www.aic.nrl.navy.mil/galistRepository for GA related information, conferences, etc.

• EVONET European Network of Excellence on Evolutionary Comp. : http://www.dcs.napier.ac.uk/evonet

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BooksBooks

• Bäck, Th., Evolutionary Algorithms in Theory and Practice, Oxford

University Press, New York, 1996.• Mitchell, M., An Introduction to Genetic Algorithms, MIT Press, Cambridge, MA, 1996.• Fogel, D., Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, IEEE Press, NJ, 1995. • Schwefel, H-P., Evolution and Optimum Seeking, Wiley, New York, 1995.• Koza, J., Genetic Programming, MIT Press, Cambridge, MA, 1992.• Goldberg, D., Genetic Algorithms in Search and Optimization, Addison- Wesley, Reading, MA, 1989.• Holland, J., Adaptation in Natural and Artificial Systems, Univeristy of Michigan Press, Ann Arbor, 1975.• Rechenberg, I., Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Frommann-Holzboog Verlag, Stuttgart, 1973. • Fogel, L.J., Owens, A.J, and Walsh, M.J., Artificial Intelligence through Simulated Evolution, John Wiley, NY, 1966.

For more information:For more information:

http://scai.snu.ac.kr/http://scai.snu.ac.kr/

evolutionary computation ( 진 화 연 산 ) 장 병 탁 서울대 컴퓨터공학부 e-mail:...

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