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SOFT COMPUTING
Evolutionary Computing
1
What is a GA?

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.
What is a GA?

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.
Evolutionary Algorithms
Evolution
Strategies
Genetic
Programming
Genetic
Algorithms
Classifier
Systems
Evolutionary
Programming
• genetic representation of candidate solutions
• genetic operators
• selection scheme
• problem domain
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.
Classes of Search Techniques
Search techniques
Calculus-based techniques
Direct methods
Finonacci
Guided random search techniques
Indirect methods
Newton
Evolutionary algorithms
Evolutionary strategies
Genetic Programming
Centralized
Simulated annealing
Genetic algorithms
Parallel
Distributed
Enumerative techniques
Tabu Search
Sequential
Steady-state
Generational
Dynamic programming
Hill Climbing
DFS, BFS
Early History of EAs

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





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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 Algorithms
 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
The Genetic Algorithm




Directed search algorithms based on the mechanics of
biological evolution
Developed by John Holland, University of Michigan (1970’s)
 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 Holland’s genetic algorithm is to represent a
legal solution of a problem by a string of genes known as a
chromosome.
Evolutionary Programming

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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
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
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
(Darwin’s principle : “survival of the fittest”)
Courtesy of U.S. Department of Energy Human Genome Program , http://www.ornl.gov/hgmis
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
Crossover
• crossover applied to parent strings with
probability pc : [0.6..1.0]
• crossover site chosen randomly
• one-point crossover
parent A 1 1 0 1 0
parent B 1 0 0 0 1
offspring A
offspring B
11011
• two-point crossover
parent A 1 1 0 1 0
parent B 1 0 0 0 1
offspring A
offspring B
11 00 0
10000
10 01 1
Mutation
• mutation applied to allele/gene with
probability Pm : [0.001..0.1]
• role of mutation is to maintain genetic diversity
offspring:
11000
Mutate fourth allele (bit flip)
mutated offspring:
1 1 0 10 0
Structure of an Evolutionary Algorithm
mutation
population of genotypes
10111
10011
10001
01001
01001
00111
11001
01011
recombination
f
coding scheme
selection
10011
10
011
001
10001
01001
01
001
011
01011
phenotype space
10001
10001
01011
11001
x
fitness
Pseudo Code of an Evolutionary Alg.
Create initial random population
Evaluate fitness of each individual
yes
Termination criteria satisfied ?
no
Select parents according to fitness
Recombine parents to generate offspring
Mutate offspring
Replace population by new offspring
stop
Roulette Wheel Selection
• selection is a stochastic process
• probability of reproduction pi = fi / Sk fk
• selected parents : 01011, 11010, 10001, 10001
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}
X1
- constants {0.1, 0.2, 0.5 }
tree is parsed from left to right:
(+ X1 (* X2 X3))
X1+(X2*X3)
X2
*
X3
Genetic Programming : Crossover
-
+
parent A
X1
parent B
X2
X1
-
X2
*
X2
/
-
X3
+
offspring A
X2
*
X2
/
X3
X2
-
X1
X3
offspring B
X1
X3
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
Goldberg (1989)

Goldberg D. E. (1989),
Genetic Algorithms in
Search, Optimization,
and Machine Learning.
Addison-Wesley,
Reading.
Michalewicz (1996)

Michalewicz, Z. (1996),
Genetic Algorithms + Data
Structures = Evolution
Programs, Springer.
Vose (1999)

Vose M. D. (1999), The
Simple Genetic
Algorithm :
Foundations and
Theory (Complex
Adaptive Systems).
Bradford Books;
SOFT COMPUTING
Fuzzy-Evolutionary Computing
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Genetic Fuzzy Systems (GFS’s)
• 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
Genetic Fuzzy System for
Data Modeling
Evolutionary
algorithm
genotype
Fuzzy system
parameters
fitness
Evaluation
scheme
phenotype
Fuzzy System
Dataset : xi,yi
Fuzzy Systems
Knowledge Base
Rule base:
Database :
definition of
Definition of
fuzzy membership- fuzzy rules
function
If X1 is A1 and … and Xn is An
then Y is B
a b
c
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
Linear Scaling Functions
Chromosome for linear scaling:
• for each input xi : two parameters ai,bi i=1..n
• for the output y : two parameter a0,b0
Genetic Algorithms:
• encode each parameter by k bit using Gray code
total length = 2*(n+1)*k bit
a0
100101
b0
011111
a1
110101
...
b2*(n+1)
100101
Evolutionary Strategies:
• each parameter ai or bi corresponds to one
object variable xm m : 1… 2*(n+1)
a0
x0,so
b0
x1,s1
a1
x2,s2
...
b2*(n+1)
xm,sm
Descriptive Knowledge Base
• descriptive knowledge base
m
m
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
Approximate Knowledge Base
• each rule employs its own local membership function
R1 : if X is
R1 : if X is
then Y 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
Tuning Membership Functions
• encode each fuzzy set by characteristic parameters
Trapezoid: <a,b,c,d>
Gaussian: N(m,s)
(x)
1
0
(x)
1
a
b
c
s
0
d x
m
x
Triangular: <a,b,c>
(x)
1
0
a
b
c
x
x
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)
Ci
= (ai1, bi1, ci1, . . . , ain, bin, cin, ai, bi, ci, )
each parameter may be binary or real-coded
The chromosome is the concatenation of the
individual segments corresponding to rules :
C1 C2 C3 C 4 . . . Ck
Descriptive Genetic Tuning Process
• the rule base already exists
• assume the i-th variable is composed of Ni terms
Ci
= (ai1, bi1, ci1, . . . , aiNi, biNi, ciNi )
m
ai1, bi1, ci1, ai2,
bi2, ci2
xi
ai3, bi3, ci3
The chromosome is the concatenation of the
individual segments corresponding to variables :
C1 C 2 C3 C4 . . . Ck
Descriptive Genetic Tuning
• in the previous coding scheme fuzzy sets might
change their order and optimization is subject
to the constraints : aij < bij < cij
x1
x2
x3
• encode the distance among the center points
of triangular fuzzy sets and choose the border
points such that S mi = 1
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)
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
Michigan Approach
Population:
11001
00101
10111
11100
01000
11101
:
:
:
:
:
:
X
A6
R1: if x is A1 ….then Y is B1
R2: if x is A2 ….then Y is B2
R3: if x is A3 ….then Y is B3
R4: if x is A4 ….then Y is B4
R5: if x is A5 ….then Y is B5
R6: if x is A6 ….then Y is B6
A1A4
A3
Y
A5
A2
B1
B2
B5
Individual:
B4
B6
B3
Cooperation vs. Competition Problem
• we need a fitness function that measures the
Fitness = number of
correct classifications
minus number of incorrect
classifications
Y
ze
pos
accuracy of an individual rule as well as the
quality of its cooperation with other rules
neg
R2 :: ifif xx is
is small
med. then
Y
is
zero
R1
large
neg.
R3
then
Y
is
R4 : if x is small then Y is zero
pos.
F
=
2.5
F=2.7
F=-0.4
F=-1.6
small medium
large X
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
competitors:
11001 : R1: if x is A1 ….then Y is B1
00101 : R2: if x is A2 ….then Y is B2
11001 : R1: if x is A1 ….then Y is B1
10111 : R3: if x is A3 ….then Y is B3
10111 : R3: if x is A3 ….then Y is B3
11100 : R4: if x is A4 ….then Y is B4
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
removed from the population
Thanks for your attention!
That’s all.
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