Transcript Genetic Algorithms: A Tutorial

Genetic Algorithms:
Soft Computing Week 13
“Genetic Algorithms are
good at taking large,
potentially huge search
spaces and navigating
them, looking for optimal
combinations of things,
solutions you might not
otherwise find in a
lifetime.”
- Salvatore Mangano
Computer Design, May 1995
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Genetic Algorithms
The Genetic Algorithm
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Directed search algorithms based on
the mechanics of biological evolution
Developed by John Holland, University
of Michigan (1970’s)
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To understand the adaptive processes of
natural systems
 To design artificial systems software that
retains the robustness of natural systems
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Genetic Algorithms
The Genetic Algorithm (cont.)
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Provide efficient, effective techniques
for optimization and machine learning
applications
Widely-used today in business,
scientific and engineering circles
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Genetic Algorithms
Evolution in the real world
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Each cell of a living thing contains
chromosomes - strings of DNA
Each chromosome contains a set of genes blocks of DNA
Each gene determines some aspect of the
organism (like eye colour)
A collection of genes is sometimes called a
genotype
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Genetic Algorithms
Evolution in the real world
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A collection of aspects (like eye colour)
is sometimes called a phenotype
Reproduction involves recombination of
genes from parents and then small
amounts of mutation (errors) in copying
The fitness of an organism is how
much it can reproduce before it dies
Evolution based on “survival of the
fittest”
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Genetic Algorithms
Start with a Dream…
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Suppose you have a problem
You don’t know how to solve it
What can you do?
Can you use a computer to somehow
find a solution for you?
This would be nice! Can it be done?
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Genetic Algorithms
A dumb solution
A “blind generate and test” algorithm:
Repeat
Generate a random possible solution
Test the solution and see how good it is
Until solution is good enough
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Genetic Algorithms
Can we use this dumb idea?
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Sometimes - yes:
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if there are only a few possible solutions
 and you have enough time
 then such a method could be used
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For most problems - no:
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Too many possible solutions
 No time to try them all
 So this method can not be used
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Genetic Algorithms
A “less-dumb” idea (GA)
Generate a set of random solutions
Repeat
Test each solution in the set (rank them)
Remove some bad solutions from set
Duplicate some good solutions
make small changes to some of them
Until best solution is good enough
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Genetic Algorithms
How do you encode a solution?
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Obviously this depends on the problem!
GA’s often encode solutions as fixed length
“bitstrings” (e.g. 101110, 111111, 000101)
Each bit represents some aspect of the
proposed solution to the problem
For GA’s to work, we need to be able to
“test” any string and get a “score”
indicating how “good” that solution is
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Genetic Algorithms
Adding Sex - Crossover
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Although it may work for simple search
spaces our algorithm is still very simple
It relies on random mutation to find a good
solution
It has been found that by introducing “sex”
into the algorithm better results are obtained
This is done by selecting two parents during
reproduction and combining their genes to
produce offspring
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Genetic Algorithms
Adding Sex - Crossover
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Two high scoring “parent” bit strings
(chromosomes) are selected and with some
probability (crossover rate) combined
Producing two new offspring (bit strings)
Each offspring may then be changed
randomly (mutation)
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Genetic Algorithms
Selecting Parents
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Many schemes are possible so long as better
scoring chromosomes more likely selected
Score is often termed the fitness
“Roulette Wheel” selection can be used
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Genetic Algorithms
Example population
No.
1
2
3
4
5
6
7
8
Chromosome
1010011010
1111100001
1011001100
1010000000
0000010000
1001011111
0101010101
1011100111
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Fitness
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2
3
1
3
5
1
2
Genetic Algorithms
Roulette Wheel Selection
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1
0
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3
2
4
3
1
5
6
3
7
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Rnd[0..18] = 7
Rnd[0..18] = 12
Chromosome4
Chromosome6
Parent1
Parent2
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1
8
2
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Genetic Algorithms
Crossover - Recombination
1011011111
1010000000
Parent1
Offspring1
1001011111
Parent2
Offspring2 1010000000
Crossover
single point random
With some high probability (crossover
rate) apply crossover to the parents.
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Genetic Algorithms
Mutation
mutate
1011001111
Offspring1
1011011111
Offspring1
Offspring2
1010000000
Offspring2 1000000000
Original offspring
Mutated offspring
With some small probability (the mutation rate) flip
each bit in the offspring (typical values between 0.1
and 0.001)
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Genetic Algorithms
Back to the (GA) Algorithm
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Generate a population of random
chromosomes
Repeat (each generation)
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Calculate fitness of each chromosome
Repeat
» Use roulette selection to select pairs of parents
» Generate offspring with crossover and mutation
Until a new population has been produced
Until best solution is good enough
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Genetic Algorithms
Many Variants of GA
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Different kinds of selection (not roulette)
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Different recombination
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Multi-point crossover
3 way crossover etc.
Different kinds of encoding other than bitstring
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Tournament
Elitism, etc.
Integer values
Ordered set of symbols
Different kinds of mutation
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Genetic Algorithms
Many parameters to set
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Any GA implementation needs to decide on a
number of parameters: Population size (N),
mutation rate (m), crossover rate (c)
Often these have to be “tuned” based on
results obtained - no general theory to
deduce good values
Typical values might be: N = 50, m = 0.05, c =
0.9
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Genetic Algorithms
Why does crossover work?
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A lot of theory about this and some
controversy
Holland introduced “Schema” theory
The idea is that crossover preserves “good
bits” from different parents, combining them
to produce better solutions
A good encoding scheme would therefore try
to preserve “good bits” during crossover and
mutation
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Genetic Algorithms
Classes of Search Techniques
Search techniques
Calculus-based techniques
Direct methods
Finonacci
Indirect methods
Newton
Enumerative techniques
Guided random search techniques
Evolutionary algorithms
Evolutionary strategies
Dynamic programming
Genetic algorithms
Parallel
Centralized
Simulated annealing
Distributed
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Sequential
Steady-state
Generational
Genetic Algorithms
Components of a GA
A problem to solve, and ...
 Encoding technique
(gene, chromosome)
 Initialization procedure
(creation)
 Evaluation function
(environment)
 Selection of parents
(reproduction)
 Genetic operators
(mutation, recombination)
 Parameter settings
(practice and art)
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Genetic Algorithms
Simple Genetic Algorithm
{
initialize population;
evaluate population;
while TerminationCriteriaNotSatisfied
{
select parents for reproduction;
perform recombination and mutation;
evaluate population;
}
}
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Genetic Algorithms
The GA Cycle of Reproduction
reproduction
children
modified
children
parents
population
modification
evaluation
evaluated children
deleted
members
discard
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Genetic Algorithms
Population
population
Chromosomes could be:
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Bit strings
Real numbers
Permutations of element
Lists of rules
Program elements
... any data structure ...
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(0101 ... 1100)
(43.2 -33.1 ... 0.0 89.2)
(E11 E3 E7 ... E1 E15)
(R1 R2 R3 ... R22 R23)
(genetic programming)
Genetic Algorithms
Reproduction
reproduction
children
parents
population
Parents are selected at random with
selection chances biased in relation to
chromosome evaluations.
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Genetic Algorithms
Chromosome Modification
children
modification
modified children
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Modifications are stochastically triggered
Operator types are:
 Mutation
 Crossover (recombination)
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Genetic Algorithms
Evaluation
modified
children
evaluated
children
evaluation
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The evaluator decodes a chromosome and
assigns it a fitness measure
The evaluator is the only link between a
classical GA and the problem it is solving
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Genetic Algorithms
Deletion
population
discarded members
discard
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Generational GA:
entire populations replaced with each iteration
Steady-state GA:
a few members replaced each generation
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Genetic Algorithms
An Abstract Example
Distribution of Individuals in Generation 0
Distribution of Individuals in Generation N
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Genetic Algorithms
A Simple Example
“The Gene is by far the most sophisticated program around.”
- Bill Gates, Business Week, June 27, 1994
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Genetic Algorithms
A Simple Example
The Traveling Salesman Problem:
Find a tour of a given set of cities so that
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each city is visited only once
 the total distance traveled is minimized
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Genetic Algorithms
Representation
Representation is an ordered list of city
numbers known as an order-based GA.
1) London
2) Venice
3) Dunedin
4) Singapore
5) Beijing 7) Tokyo
6) Phoenix 8) Victoria
CityList1
(3 5 7 2 1 6 4 8)
CityList2
(2 5 7 6 8 1 3 4)
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Genetic Algorithms
Crossover
Crossover combines inversion and
recombination:
Parent1
Parent2
Children1
Children2
(3 5 7 2 1 6 4 8)
(2 8 7 6 8 1 3 4)
(3 5 7 6 8 1 3 4)
(2 8 7 2 1 6 3 4)
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Genetic Algorithms
Mutation
Mutation changing the list:
Before:
*
*
(5 8 7 2 1 6 3 4)
After:
(5 8 6 2 1 7 3 4)
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Genetic Algorithms
TSP Example: 30 Cities
100
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y
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x
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Genetic Algorithms
Solution i (Distance = 941)
TSP30 (Performance = 941)
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y
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0
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Genetic Algorithms
Solution j(Distance = 800)
TSP30 (Performance = 800)
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y
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Genetic Algorithms
Solution k(Distance = 652)
TSP30 (Performance = 652)
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Genetic Algorithms
Best Solution (Distance = 420)
TSP30 Solution (Performance = 420)
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Genetic Algorithms
Overview of Performance
TSP30 - Overview of Performance
1600
1400
Distance
1200
1000
800
600
400
200
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Generations (1000)
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Best
Worst
Average
Genetic Algorithms
Considering the GA Technology
“Almost eight years ago ...
people at Microsoft wrote
a program [that] uses
some genetic things for
finding short code
sequences. Windows 2.0
and 3.2, NT, and almost all
Microsoft applications
products have shipped
with pieces of code created
by that system.”
- Nathan Myhrvold, Microsoft Advanced
Technology Group, Wired, September 1995
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Genetic Algorithms
Issues for GA Practitioners
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Choosing basic implementation issues:
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representation
population size, mutation rate, ...
selection, deletion policies
crossover, mutation operators
Termination Criteria
Performance, scalability
Solution is only as good as the evaluation
function (often hardest part)
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Genetic Algorithms
Benefits of Genetic Algorithms
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Concept is easy to understand
Modular, separate from application
Supports multi-objective optimization
Good for “noisy” environments
Always has an answer; answer gets
better with time
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Genetic Algorithms
Benefits of Genetic Algorithms (cont.)
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Many ways to speed up and improve a
GA-based application as knowledge
about problem domain is gained
Easy to exploit previous or alternate
solutions
Flexible building blocks for hybrid
applications
Substantial history and range of use
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Genetic Algorithms
When to Use a GA
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Alternate solutions are too slow or overly
complicated
Need an exploratory tool to examine new
approaches
Problem is similar to one that has already been
successfully solved by using a GA
Want to hybridize with an existing solution
Benefits of the GA technology meet key problem
requirements
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Genetic Algorithms
Some GA Application Types
Domain
Application Types
Control
gas pipeline, pole balancing, missile evasion, pursuit
Design
Scheduling
semiconductor layout, aircraft design, keyboard
configuration, communication networks
manufacturing, facility scheduling, resource allocation
Robotics
trajectory planning
Machine Learning
Signal Processing
designing neural networks, improving classification
algorithms, classifier systems
filter design
Game Playing
poker, checkers, prisoner’s dilemma
Combinatorial
Optimization
set covering, travelling salesman, routing, bin packing,
graph colouring and partitioning
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Genetic Algorithms
Conclusions
Question:
‘If GAs are so smart, why ain’t they rich?’
Answer:
‘Genetic algorithms are rich - rich in
application across a large and growing
number of disciplines.’
- David E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning
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Genetic Algorithms