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1Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
“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
Genetic Algorithms:Genetic Algorithms:A TutorialA Tutorial
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2Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
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
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3Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
The Genetic Algorithm (cont.)
Provide efficient, effective techniques for optimization and machine learning applications
Widely-used today in business, scientific and engineering circles
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4Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Classes of Search Techniques
F i n o n a c c i N e w t o n
D i r e c t m e t h o d s I n d i r e c t m e t h o d s
C a l c u l u s - b a s e d t e c h n i q u e s
E v o l u t i o n a r y s t r a t e g i e s
C e n t r a l i z e d D i s t r i b u t e d
P a r a l l e l
S t e a d y - s t a t e G e n e r a t i o n a l
S e q u e n t i a l
G e n e t i c a l g o r i t h m s
E v o l u t i o n a r y a l g o r i t h m s S i m u l a t e d a n n e a l i n g
G u i d e d r a n d o m s e a r c h t e c h n i q u e s
D y n a m i c p r o g r a m m i n g
E n u m e r a t i v e t e c h n i q u e s
S e a r c h t e c h n i q u e s
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5Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
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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6Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Simple Genetic Algorithm
{
initialize population;
evaluate population;
while TerminationCriteriaNotSatisfied{
select parents for reproduction;
perform recombination and mutation;
evaluate population;}
}
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7Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
The GA Cycle of Reproduction
reproduction
population evaluation
modification
discard
deleted members
parents
children
modifiedchildren
evaluated children
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8Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Population
Chromosomes could be:♦ Bit strings (0101 ... 1100)♦ Real numbers (43.2 -33.1 ... 0.0 89.2) ♦ Permutations of element (E11 E3 E7 ... E1 E15)♦ Lists of rules (R1 R2 R3 ... R22 R23)♦ Program elements (genetic programming)♦ ... any data structure ...
population
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9Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Reproduction
reproduction
population
parents
children
Parents are selected at random with selection chances biased in relation to chromosome evaluations.
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10Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Chromosome Modification
modificationchildren
Modifications are stochastically triggered Operator types are:
♦ Mutation♦ Crossover (recombination)
modified children
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11Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Mutation: Local Modification
Before: (1 0 1 1 0 1 1 0)
After: (0 1 1 0 0 1 1 0)
Before: (1.38 -69.4 326.44 0.1)
After: (1.38 -67.5 326.44 0.1)
Causes movement in the search space(local or global)
Restores lost information to the population
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12Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Crossover: Recombination
P1 (0 1 1 0 1 0 0 0) (0 1 0 0 1 0 0 0) C1
P2 (1 1 0 1 1 0 1 0) (1 1 1 1 1 0 1 0) C2
Crossover is a critical feature of genetic
algorithms:♦ It greatly accelerates search early in
evolution of a population♦ It leads to effective combination of schemata
(subsolutions on different chromosomes)
*
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13Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Evaluation
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
evaluation
evaluatedchildren
modifiedchildren
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14Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Deletion
Generational GA:entire populations replaced with each iteration
Steady-state GA:a few members replaced each generation
population
discard
discarded members
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15Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
An Abstract Example
Distribution of Individuals in Generation 0
Distribution of Individuals in Generation N
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16Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
A Simple Example
“The Gene is by far the most sophisticated program around.”
- Bill Gates, Business Week, June 27, 1994
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17Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
A Simple Example
The Traveling Salesman Problem:
Find a tour of a given set of cities so that ♦ each city is visited only once♦ the total distance traveled is minimized
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18Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Representation
Representation is an ordered list of city
numbers known as an order-based GA.
1) London 3) Dunedin 5) Beijing 7) Tokyo
2) Venice 4) Singapore 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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19Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Crossover
Crossover combines inversion and
recombination:
* *
Parent1 (3 5 7 2 1 6 4 8)
Parent2 (2 5 7 6 8 1 3 4)
Child (5 8 7 2 1 6 3 4)
This operator is called the Order1 crossover.
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20Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Mutation involves reordering of the list:
* *
Before: (5 8 7 2 1 6 3 4)
After: (5 8 6 2 1 7 3 4)
Mutation
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21Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
TSP Example: 30 Cities
0
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0 10 20 30 40 50 60 70 80 90 100
x
y
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22Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Solution i (Distance = 941)
TSP30 (Performance = 941)
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0 10 20 30 40 50 60 70 80 90 100
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23Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Solution j(Distance = 800)
TSP30 (Performance = 800)
0
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0 10 20 30 40 50 60 70 80 90 100
x
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24Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Solution k(Distance = 652)
TSP30 (Performance = 652)
0
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0 10 20 30 40 50 60 70 80 90 100
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25Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Best Solution (Distance = 420)
TSP30 Solution (Performance = 420)
0
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0 10 20 30 40 50 60 70 80 90 100
x
y
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26Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Overview of Performance
TSP30 - Overview of Performance
0
200
400
600
800
1000
1200
1400
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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Generations (1000)
Dis
tan
ce
Best
Worst
Average
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27Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
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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28Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Issues for GA Practitioners
Choosing basic implementation issues:♦ 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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29Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Benefits of Genetic Algorithms
Concept is easy to understand Modular, separate from application Supports multi-objective optimization Good for “noisy” environments Always an answer; answer gets better
with time Inherently parallel; easily distributed
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30Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Benefits of Genetic Algorithms (cont.)
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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31Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
When to Use a GA 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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32Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
Some GA Application Types
Domain Application Types
Control gas pipeline, pole balancing, missile evasion, pursuit
Design semiconductor layout, aircraft design, keyboardconfiguration, communication networks
Scheduling manufacturing, facility scheduling, resource allocation
Robotics trajectory planning
Machine Learning designing neural networks, improving classificationalgorithms, classifier systems
Signal Processing filter design
Game Playing poker, checkers, prisoner’s dilemma
CombinatorialOptimization
set covering, travelling salesman, routing, bin packing,graph colouring and partitioning
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33Wendy WilliamsMetaheuristic Algorithms
Genetic Algorithms: A Tutorial
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