SOFT COMPUTING Evolutionary Computing

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SOFT COMPUTINGEvolutionary Computing
EC
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What is a GA?
Genetic Algorithms (GAs) are adaptive
heuristic search algorithm based on the
evolutionary ideas of natural selection and
genetics. As such they represent an intelligent
exploitation of a random search used to solve
optimization problems. Although randomized, GAs
are by no means random, instead they exploit
historical information to direct the search into
the region of better performance within the
search space. The basic techniques of the GAs are
designed to simulate processes in natural systems
necessary for evolution, specially those follow
the principles first laid down by Charles Darwin
of "survival of the fittest.". Since in nature,
competition among individuals for scanty
resources results in the fittest individuals
dominating over the weaker ones.
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Evolutionary Algorithms
Evolution Strategies
Genetic Programming
Genetic Algorithms
Classifier Systems
Evolutionary Programming

• genetic representation of candidate solutions
• genetic operators
• selection scheme
• problem domain

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History of GAs

• Genetic Algorithms were invented to mimic some of
  the processes observed in natural evolution. Many
  people, biologists included, are astonished that
  life at the level of complexity that we observe
  could have evolved in the relatively short time
  suggested by the fossil record. The idea with GA
  is to use this power of evolution to solve
  optimization problems. The father of the original
  Genetic Algorithm was John Holland who invented
  it in the early 1970's.

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Classes of Search Techniques
DFS, BFS
Tabu Search
Hill Climbing
Genetic Programming
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Early History of EAs

• 1954 Barricelli creates computer simulation of
  life Artificial Life
• 1957 Box develops Evolutionary Operation (EVOP),
  a non-computerised evolutionary process
• 1957 Fraser develops first Genetic Algorithm
• 1958 Friedberg creates a learning machine
  through evolving computer programs
• 1960s, Rechenverg evolution strategies
• a method used to optimize real-valued parameters
  for devices
• 1960s, Fogel, Owens, and Walsh evolutionary
  programming
• to find finite-state machines
• 1960s, John Holland Genetic Algorhtms
• to study the phenomenon of adaptation as it
  occurs in nature (not to solve specific problems)
• 1965 Rechenberg Schwefel independently develop
  Evolution Strategies
• 1966 L. Fogel develops Evolutionary Programming
  as a means of creating artificial intelligence
• 1967 Holland and his students extend GA ideas
  further

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The Genetic Algorithm

• Directed search algorithms based on the mechanics
  of biological evolution
• Developed by John Holland, University of Michigan
  (1970s)
• To understand the adaptive processes of natural
  systems
• To design artificial systems software that
  retains the robustness of natural systems

• The genetic algorithms, first proposed by Holland
  (1975), seek to mimic some of the natural
  evolution and selection.
• The first step of Hollands genetic algorithm is
  to represent a legal solution of a problem by a
  string of genes known as a chromosome.

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Evolutionary Programming

• First developed by Lawrence Fogel in 1966 for use
  in pattern learning
• Early experiments dealt with a number of Finite
  State Automata
• FSA were developed that could recognise recurring
  patterns and even primeness of numbers
• Later experiments dealt with gaming problems
  (coevolution)
• More recently has been applied to training of
  neural networks, function optimisation path
  planning problems

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Biological 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

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Genotype versus Phenotype

• genotype
• blue print that contains the information to
  construct an
• organism e.g. human DNA
• genetic operators such as mutation and
  recombination
• modify the genotype during reproduction
• genotype of an individual is immutable
• (no Lamarckian evolution)
• phenotype
• physical make-up of an organism
• selection operates on phenotypes
• (Darwins principle survival of the
  fittest)

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Courtesy of U.S. Department of Energy Human
Genome Program , http//www.ornl.gov/hgmis
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Genotype Operators

• recombination (crossover)
• combines two parent genotypes into a new
  offspring
• generates new variants by mixing existing
  genetic material
• stochastic selection among parent genes

• mutation
• random alteration of genes
• maintain genetic diversity

• in genetic algorithms crossover is the major
  operator
• whereas mutation only plays a minor role

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Crossover

• crossover applied to parent strings with
• probability pc 0.6..1.0
• crossover site chosen randomly

• one-point crossover

• two-point crossover

parent A parent B
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Mutation

• mutation applied to allele/gene with
• probability Pm 0.001..0.1
• role of mutation is to maintain genetic
  diversity

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Structure of an Evolutionary Algorithm
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Pseudo Code of an Evolutionary Alg.
Create initial random population
Evaluate fitness of each individual
yes
Termination criteria satisfied ?
stop
no
Select parents according to fitness
Recombine parents to generate offspring
Mutate offspring
Replace population by new offspring
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Roulette Wheel Selection

• selection is a stochastic process

• probability of reproduction pi fi / Sk fk

• selected parents 01011, 11010, 10001, 10001

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Genetic Programming

• automatic generation of computer programs
• by means of natural evolution see Koza 1999
• programs are represented by a parse tree (LISP
  expression)
• tree nodes correspond to functions
• - arithmetic functions ,-,,/
• - logarithmic functions sin,exp
• leaf nodes correspond to terminals
• - input variables X1, X2, X3
• - constants 0.1, 0.2, 0.5

X1
tree is parsed from left to right ( X1 ( X2
X3)) X1(X2X3)
X3
X2
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Genetic Programming Crossover
parent A
parent B
-

/

offspring B
offspring A
X3
X2
X2
X1
X1
-
X3
X2
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Areas EAs Have Been Used In

• Design of electronic circuits
• Telecommunication network design
• Artificial intelligence
• Study of atomic clusters
• Study of neuronal behaviour
• Neural network training design
• Automatic control
• Artificial life
• Scheduling

• Travelling Salesman Problem
• General function optimisation
  
  
• Bin Packing Problem
• Pattern learning
• Gaming
• Self-adapting computer programs
• Classification
• Test-data generation
• Medical image analysis
• Study of earthquakes

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Goldberg (1989)

• Goldberg D. E. (1989), Genetic Algorithms in
  Search, Optimisation, and Machine Learning.
  Addison-Wesley, Reading.

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Michalewicz (1996)

• Michalewicz, Z. (1996), Genetic Algorithms Data
  Structures Evolution Programs, Springer.

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Vose (1999)

• Vose M. D. (1999), The Simple Genetic Algorithm
  Foundations and Theory (Complex Adaptive
  Systems). Bradford Books

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SOFT COMPUTINGFuzzy-Evolutionary Computing
FEC
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Genetic Fuzzy Systems (GFSs)

• genetic design of fuzzy systems
• automated tuning of the fuzzy knowledge base
• automated learning of the fuzzy knowledge base
• objective of tuning/learning process
• optimizing the performance of the fuzzy system
• e.g. fuzzy modeling minimizing quadratic
  error
• between data set and the fuzzy system
  outputs
• e.g fuzzy control system optimize the
• behavior of the plant fuzzy
  controller

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Genetic Fuzzy System for Data Modeling
fitness
Evolutionary algorithm
Evaluation scheme
genotype
Fuzzy system parameters
phenotype
Dataset xi,yi
Fuzzy System
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Fuzzy Systems
Knowledge Base
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Genetic Tuning Process

• tuning problems utilize an already existing rule
  base
• tuning aims to find a set of optimal parameters
  for
• the database
• points of membership-functions a,b,c,d
• or
• scaling factors for input and output variables

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Linear Scaling Functions

• Chromosome for linear scaling
• for each input xi two parameters ai,bi
  i1..n
• for the output y two parameter a0,b0

• Genetic Algorithms
• encode each parameter by k bit using Gray code
• total length 2(n1)k bit

• Evolutionary Strategies
• each parameter ai or bi corresponds to one
• object variable xm m 1 2(n1)

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Descriptive Knowledge Base

• descriptive knowledge base

m
m
neg ze pos
sm me lg
y
x

• all rules share the same global membership
  functions
• R1 if X is sm then Y is neg
• R2 if X is me then Y is ze
• R3 if X is lg then Y is pos

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Approximate Knowledge Base

• each rule employs its own local membership
  function

R1 if X is then Y is
R1 if X is then Y is
R1 if X is then Y is

• tradeoff more degrees of freedom and therefore
• better approximation but intuitive meaning of
• fuzzy sets gets lost

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Tuning Membership Functions

• encode each fuzzy set by characteristic
  parameters

Trapezoid lta,b,c,dgt
Gaussian N(m,s)
?(x)
?(x)
1
1
s
0
0
x
a
b
c
d
x
m
Triangular lta,b,cgt
?(x)
1
0
x
a
b
c
x
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Approximate Genetic Tuning Process

• a chromosome encodes the entire knowledge base,
• database and rulebase

Ri if x1 is Ai1 and xn is Ain then y is Bi
encoded by the i-th segment Ci of the
chromosome using triangular membership-functions
(a,b,c)

(ai1, bi1, ci1, . . . , ain, bin, cin, ai, bi,
ci, )
Ci
each parameter may be binary or real-coded
The chromosome is the concatenation of the
individual segments corresponding to rules
C1
C2
C3
C4
Ck
. . .
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Descriptive Genetic Tuning Process

• the rule base already exists

• assume the i-th variable is composed of Ni terms

(ai1, bi1, ci1, . . . , aiNi, biNi, ciNi )
Ci
m
A1 A2 A3
xi
ai1, bi1, ci1, ai2, bi2, ci2 ai3, bi3,
ci3
The chromosome is the concatenation of the
individual segments corresponding to variables
C1
C2
C3
C4
Ck
. . .
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Descriptive Genetic Tuning

• in the previous coding scheme fuzzy sets might
• change their order and optimization is
  subject
• to the constraints aij lt bij lt cij

A1 A2 A3
x1 x2 x3

• encode the distance among the center points
• of triangular fuzzy sets and choose the
  border
• points such that S mi 1

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Fitness Function for Tuning

• minimize quadratic error among training data
  (xi,yi)
• and fuzzy system output f(xi)
• E Sumi (yi-f(xi))2
• Fitness 1 / E (maximize fitness)

• minimize maximal error among training data
  (xi,yi)
• and fuzzy system output f(xi)
• E maxi (yi-f(xi))2
• Fitness 1 / E (maximize fitness)

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Genetic Learning Systems

• genetic learning aim to
• learn the fuzzy rule base
• or
• learn the entire knowledge base

• three different approaches
• Michigan approach each chromosome represents
• a single rule
• Pittsburgh approach each chromosome represents
• an entire rule base / knowledge base
• Iterative rule learning each chromosome
  represents
• a single rule, but rules are injected one
  after the
• other into the knowledge base

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Michigan Approach
Population
Individual
11001 R1 if x is A1 .then Y is B1
00101 R2 if x is A2 .then Y is B2
10111 R3 if x is A3 .then Y is B3
11100 R4 if x is A4 .then Y is B4
01000 R5 if x is A5 .then Y is B5
11101 R6 if x is A6 .then Y is B6
B4
X
Y
B5
A4
A1
B1
A5
A3
B6
A2
A6
B2
B3
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Cooperation vs. Competition Problem

• we need a fitness function that measures the
• accuracy of an individual rule as well as the
  
• quality of its cooperation with other rules

Fitness number of correct classifications
minus number of incorrect classifications
Y
pos
ze
neg
small
medium
large
X
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Michigan Approach

• steady state selection
• pick one individual at random
• compare it with all individuals that cover
• the same input region
• remove the relatively worst one from the
• population
• pick two parents at random independent of
• their fitness and generate a new offspring

11001 R1 if x is A1 .then Y is B1
00101 R2 if x is A2 .then Y is B2
10111 R3 if x is A3 .then Y is B3
11100 R4 if x is A4 .then Y is B4
01000 R5 if x is A5 .then Y is B5
11101 R6 if x is A6 .then Y is B6