Andrew
Cannon
Yuki Osada
Angeline Honggowarsito
Contents
What are Evolutionary Algorithms (EAs
)?
Why are EAs Important?
Categories of EAs
Mutation
Self
Adaptation
Recombination
Selection
Application
Evolutionary
Algorithms
Search methods that mimic the process of natural
evolution
Principle of
“Survival of the Fittest”
In each
generation, select the fittest parents
Re

combine those parents to produce new
offspring
Perform mutations on
the new
offspring
Why
are EAs
Important?
Flexibility
Adaptable Concept to Problems
Problem examples:
Travelling Salesman,
Knapsack, Trading Prediction in Stock Market,
etc
.
Algorithms to solve those problems are either too
specialised or too
generalised
Categories
of
EAs
Genetic Algorithms
Evolutionary Strategies
Evolutionary
Programming
Genetic Programming
More similarities than
differences
Genetic
Algorithms
In 1950s, Biologists
used computers
for biological
system simulation.
First introduced in 1960s by John Holland from
the
University
of Michigan
Modeling
Adaptive Process
Designed to solve discrete/integer optimization
problem
Genetic
Algorithms
Operate
on Binary Strings, binary as the
representation of individuals
Applying
recombination
operator with mutation as
background operator
Evolutionary
Strategies
First developed by Rechenberg in 1973
Solved parameter optimization
problems
Individuals
represented
as a pair
of float

valued
vectors
Apply both
recombination
and
self adaptive
mutation
Evolutionary
Strategies
Similar
to
Genetic
Algorithms
in
recombination
and
mutation
processes
Differences with Genetic
Algorithms
Evolutionary Strategies
are
better
at
finding local
maximum while Genetic
Algorithms are
more
suitable
at
finding global
maximum
Thus, Evolutionary Strategies
are
faster than
Genetic
Algorithms
Evolutionary Strategies
are
represented as real
number vector while
GAs are
represented using
bitstrings
Evolutionary
Programming
Developed by Lawrence Fogel in 1962
Aimed at evolution of Artificial Intelligence in
developing ability to predict changes in
environment
Use Finite State Machine for prediction
Evolutionary
Programming
Predict output of 011101 with
initial state C, produce
output of 110111
No recombination
Representation based on real

valued
vectors
1/1
0/0
0/c
0/1
1/1
1/0
A
B
C
Genetic
Programming
Developed by Koza to allow the program to
evolve by itself during the evolution process
Individuals are represented by Tree or
Graphs
Genetic
Programming
Different from GA,ES,EP where representation
is linear (bit strings and real value vectors),
Tree is non

linear
Size depend on Depth and Width, while other
representations have a
fixed
size
Only requires crossover OR
mutation
Mutation
Binary Mutation:
Flipping the bits, as there
are
only two states of
binary values : 0 and
1
Mutating (0,1,0,0,1) will produce (1,0,1,0,1)
Mutation
Real Value Mutation:
Randomly created value added to the variables
with some predefined mutation rate
Mutation rate and Mutation step need to be
defined
Mutation rate is inversely proportional to the
number of variables (dimensions
)
Sources & References
Eiben A.E 2004, “What is Evolutionary Algorithm”,
Available from: <http://www.cs.vu.nl/~gusz/ecbook/Eiben

Smith

Intro2EC

Ch2.pdf>.[29 August 2012 ].
Michalewicz, Z., Hinterding, R., and Michalewicz, M.,
Evolutionary Algorithms,
Chapter 2 in Fuzzy Evolutionary
Computation, W. Pedrycz (editor), Kluwer Academic, 1997.
T. Bäck, U. Hammel, and H.

P. Schwefel, “Evolutionary
computation: comments on the history and current state”,
IEEE Transactions on Evolutionary Computation 1(1), 1997
X. Yao, “Evolutionary computation: a gentle introduction”,
Evolutionary Optimization, 2002
Whitley, D 2001, “An Overview of Evolutionary Algorithm:
Practical Issues and Common Pitfalls”, Information and
Software Technology, vol.43, pp. 817

831
Self Adaptation
Don’t know what values to assign to parameters
–
so let
them evolve!
Population consisting of real vectors
x
= (x
1
,x
2
,…,x
n
)
We produce offspring by adding random vectors to
them
Step Size
Schwefel (1981): add vectors whose components are
Gaussian random variates with mean 0
What standard deviation should be used?
The standard deviation evolves as the algorithm is
running
Step Size
Represent entities as (
x
,
s
)
–
the individual itself (
x
)
and a step vector (
s
)
We start by producing an offspring
s’
from
s
:
s
i
’ = s
i
exp
(c
n

1/2
N
(0,1)
+ d
n

1/4
N
i
(0,1)
)
n = generation number, c,d>0 constants
We produce an offspring
x’
from
x
:
x
i
’ = x
i
+ s
i
’
N
i
(0,1)
Self Adaptation
Other parameters can evolve using similar ideas
Sources:
Bäck
T, Hammel, U & Schwefel, H

P 1997, ‘
Evolutionary computation:
comments on the history and current state’,
IEEE Transactions on
Evolutionary Computation
, vol. 1, no. 1, pp. 3

17. Available from: IEEE
Xplore Digital Library [23
rd
August 2012].
Beyer, HG 1995, ‘Toward a Theory of Evolution Strategies: Self

Adaptation’,
Evolutionary Computation
, vol. 3, no. 3, pp. 311

348.
Saravanan, N, Fogel, DB & Nelson, KM 1995, ‘A comparison of methods for
self

adaptation in evolutionary algorithms’,
BioSystems
, vol. 36, no. 2, pp.
157

166. Available from: Science Direct [26
th
August 2012].
Schwefel, H

P 1981,
Numerical Optimization of Computer Models
,
Wiley,
Chichester.
Recombination
Produce offspring from 2 or more entities in the
original population
Most easily addressed using bitstring representations
One
P
oint Crossover
Entities are represented in the population as bitstrings
of length
n
Randomly select a crossover point
p
from 1 to
n
(inclusive)
Take the substring formed by the first
p
bits of the first
string and append to it the last
n

p
bits of the second
string to give offspring
One
P
oint Crossover
Bitstrings of length 8:
01011100 and 00001111
Choose crossover point of 6
Take the first 6 bits from
010111
00
Take the last 2 bits from 000011
11
Form the offspring
010111
11
Uniform Crossover
Form a new offspring from 2 parents by selecting bits
from each parent with a particular probability
For example, given strings:
11001011 and 01010101
Select bits from the first string with probability ½
Uniform Crossover
Rolled a die 8 times: 2, 3, 6, 6, 3, 1, 3, 5
Whenever the result is 3 or less, take a bit from the
first string, otherwise, take a bit from the second
string:
23
66
313
5 23
66
313
5
11
00
101
1 and 01
01
010
1
Produce offspring:
11
01
101
1
Other Variants
Multiple crossover points
Multiple parents
Probabilistic application
Source:
Bäck T, Hammel, U & Schwefel, H

P 1997, ‘
Evolutionary
computation: comments on the history and current state’,
IEEE
Transactions on Evolutionary Computation
, vol. 1, no. 1, pp. 3

17.
Available from: IEEE Xplore Digital Library [23
rd
August 2012].
Selection
How individuals and their offspring from one
generation are selected to fill the next generation
May be probabilistic or deterministic
Proportional Selection
Probabilistic method
Assume that fitness f(x)>0 for every entity x in the
population
p(y) = f(y) / (sum of f(x) for every x)
Tournament Selection
Probabilistic method
Select q individuals randomly from the population
with uniform probability
The best individual of this set goes into the next
generation
Repeat until the next generation is filled
(
μ
,
λ
)

Selection
Deterministic method
From a generation of
μ
individuals,
λ
>
μ
offspring are
produced
The next generation is produced from the
μ
fittest
individuals of the
λ
offspring
The fittest member of the next generation may not be
as fit as the fittest member of the previous generation
(
μ
+
λ
)

Selection
Deterministic method
From a generation of
μ
individuals,
λ
offspring are
produced
The next generation is produced from the
μ
fittest
individuals from the
μ
+
λ
parents and offspring
The fittest members will always survive
Selection
Best method (or methods) will be problem specific
Sources:
Bäck
T 1994, ‘
Selective pressure in evolutionary algorithms: a
characterization of selection mechanisms’,
Proceedings of the First
IEEE Conference on Evolutionary Computation
, pp. 57

62. Available
from: IEEE Xplore Digital Library [28
th
August 2012].
Bäck
T, Hammel, U & Schwefel, H

P 1997, ‘
Evolutionary computation:
comments on the history and current state’,
IEEE Transactions on
Evolutionary Computation
, vol. 1, no. 1, pp. 3

17. Available from: IEEE
Xplore Digital Library [23
rd
August 2012].
Travelling Salesman Problem (TSP)
Travelling salesman problem:
This is a hard problem (NP

hard, "at least as hard as
the hardest problems in NP
")
The
DP solution is
O(n
2
.2
n
)
Genes are a sequence representing the order that the
cities are visited
in
Example: [0 5 3 4 8 2 1 6 7 9
]
Crossover in TSP
A possible crossover: The greedy crossover.
"Greedy crossover selects the first city of one parent,
compares the cities leaving that city in both parents, and
chooses the closer one to extend the tour. If one city has
already appeared in the tour, we choose the other city. If
both cities have already appeared, we randomly select a
non

selected city."
Sources:
J. J. Grefenstetts, R. Gopal, B. Rosmaita, and D. Van Gucht.
Genetic Algorithms for the Traveling Salesman problem
. In
Proceedings of an International Conference on Genetic
Algorithms and Their Applications, pages 160
–
168, 1985
.
Mutation in TSP
A possible mutation: The greedy

swap.
"The basic idea of greedy

swap is to randomly select two
cities from one chromosome and swap them if the new
(swapped) tour length is shorter than the old one"
Sources:
S. J. Louis, R. Tang.
Interactive Genetic Algorithms for
the Travelling Salesman Problem.
Genetic Adaptive
Systems Lab, University of Neveda, Reno. 1999.
Applications
EAs are a very powerful computational
tool
EAs find application in:
bioinformatics
phylogenetics
computational
science
engineering
economics
chemistry
manufacturing
mathematics
physics and other
fields
Applications
Computer

automated design
Automotive design
Design composite materials and aerodynamic shapes to provide faster,
lighter, more fuel efficient and safer
vehicles
No
need to spend time in labs working with
models
Engineering design
Optimise the design of many tools/components ie.
turbines
Applications
Game playing
Sequence of actions can be learnt to win a
game
Encryption and code breaking
Telecommunications
DP problems:
Travelling salesman problem
Plan for efficient routes and scheduling for travel planners.
Knapsack problem
Sources
T. Bäck, U. Hammel, and H.

P. Schwefel,
“Evolutionary computation: comments on the
history and current state”, IEEE Transactions
on Evolutionary Computation 1(1), 1997
X. Yao, “Evolutionary computation: a gentle
introduction”, Evolutionary Optimization,
2002
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