Download EAs

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
0/c
initial state C, produce
output of 110111
B
No recombination
0/0
1/1
0/1
Representation based on real-
valued vectors
A
C
1/0
1/1
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/EibenSmith-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 = (x1,x2,…,xn)
 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:
si’ = si exp(cn-1/2N(0,1) + dn-1/4Ni(0,1))
n = generation number, c,d>0 constants
 We produce an offspring x’ from x:
xi’ = xi + si’Ni(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 [23rd 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 [26th 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 Point 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 Point Crossover
 Bitstrings of length 8:




01011100 and 00001111
Choose crossover point of 6
Take the first 6 bits from 01011100
Take the last 2 bits from 00001111
Form the offspring 01011111
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:
23663135 23663135
11001011 and 01010101
 Produce offspring: 11011011
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 [23rd 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 [28th 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 [23rd 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(n2.2n)
 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