Transcript Document

Introduction to Genetic Algorithms
Contact Information
Name: 任庆生
Office: 教三楼403
Tel: 62932089
E-mail: [email protected]
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Reference
刘勇，康立山，陈毓屏，非数值并行算法(二)—遗传算法，科
学出版社，1995
陈国良，王煦法，庄镇泉，王东生，遗传算法及其应用，人民
邮电出版社，1996
David E. Goldberg, Genetic Algorithms in Search, Optimization,
and Machine Learning, Addison-Wesley Publishing Company,
1989
Holland J H, Adaptation in Natural and Artificial Systems, The
MIT Press,1995
ftp.cs.sjtu.edu.cn/ren-qs/教学/遗传算法
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Grading
Homework: 20%
Final project: 80% . The deadline is ???
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Course Overview
An introduction to emulating the problem solving according to
nature's method: via evolution, selective breeding, "survival of
the fittest". We will present the fundamental algorithms and
present several examples, especially some problems that are
hard to solve otherwise.
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Dealing with Hard (NP-Complete) Problems
Some Problems We Just Don't Know How to Solve Efficiently!
. . . but we do know how to critique a “solution”.
Coloring graphs is hard, but counting colors and violations is easy
(a violation is two adjacent vertices with the same color).
Finding the shortest salesman's path is hard, but measuring a path is easy.
Scheduling examinations or assigning teachers to classes is hard, but
counting the conflicts (ideally there are none) is easy.
Computer programs are hard to write, but counting bugs is easy.
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GAs Emulate Selective Breeding
Designing tender chickens is hard; taste-testing them is easy.
Designing thick-skinned tomatoes is hard; dropping is easy.
So, the breeders iterate:
• Selection: find which one is better and which one is worse.
• Crossover: Let the better members breed.
• Mutation: X-ray them.
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Darwin’s Theory of Evolution
A process called natural selection, ‘selects’ individuals best adapted to
the environment. Those fittest survive longest
Characteristics, encoded in genes are transmitted to offspring and tend
to propagate into new generations
An offspring’s characteristics are partially inherited from parents and
partly the result of new genes created during the reproduction
process
In sexual reproduction (crossover), the chromosomes of offspring are a
mix of their parents. Traits found in parents are passed on to their
offspring
Variations (mutations) are present naturally in all species producing
new traits. Over long periods of time, variations can accumulate
and produce new species.
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Some Examples
Choosing among 1,500 features for OCR.
Scheduling the Chili, NY, annual soccer invitational.
N Queens, Graphs, Salesmen, etc., etc.
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Subsetting 1,500 OCR Features
The polynet OCR engine trains and executes rapidly.
Performance was competitive.
We wanted to embed it in hardware, but it used 1,500 features.
We could deal with 300 features.
So, we bred high-performance feature subsets.
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Soccer Scheduling
Bill Gustafson's MS Project, May, 1998
The Chili Soccer Association hosts an annual soccer tournament.
131 teams, 209 games, 14 fields, 17 game times.
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Soccer Scheduling Hard Constraints
A field can have one game at a time.
A team can only play one game at a time.
Teams must play on appropriate size fields.
Late games must be played on lighted fields.
A team must rest one game period (two is better) between games.
Teams can only play when they can be present (some cannot come
Friday evening).
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Soccer Scheduling Soft Constraints
A team's games should be distributed evenly over the playing days.
Teams should play in at most two playing areas.
Each team should play at least once in the main playing area.
Teams should play in areas where they have a preference.
Games should finish as early as possible on Sunday.
Etc...
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Placing N Non-Attacking Queens
Found by my genetic algorithm!
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Placing N Non-Attacking Queens
Queens attack on chess-board rows, columns, and diagonals.
Any permutation in N rows avoids row & column attacks.
Exhaustive search works for N  10, but N! grows rapidly.
A GA can place 1,000 Queens in 1,344 fitness evaluations.
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100 Non-Attacking Queens in 130 Fitness
Evaluations
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Graph Coloring: Edge Ends Get Different
Colors
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Graph Coloring = Map Coloring
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Graph Coloring = Map Coloring
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Traveling Salesman Route Min.
Another classic, hard, NP-complete problem.
We tried cities on a HW grid, so best distance is known.
Perfection is hard to achieve.
A clever algorithm costs O(cities2) to evaluate a fittness.
But, we get pretty good answers.
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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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History
Holland
Bagley
Cavicchio
Hollstien
De Jong
Goldberg
Medical image processing
Prisoner’s dilemma
Holland
Others
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Classes of Search Techniques
Search techniques
Calculus-based techniques
Direct methods
Finonacci
Guided random search techniques
Indirect methods
Newton
Evolutionary algorithms
Evolutionary strategies
Dynamic programming
Genetic algorithms
Parallel
Centralized
Simulated annealing
Enumerative techniques
Distributed
Sequential
Steady-state Generational
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Traditional Optimization Method
• The Problem:
Minimize f(x), with x  X  Rn
f(x): Continuously differentiable
Q. How does an optimization algorithm work?
• Analogy:
– A blind person with a stick goes down a hill
– Knows the current elevation and the slope
– Can measure a few more points, one at a time and at a cost
– Wants to decide which direction to go, and by how far to
reach the bottom
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f(x) = c
d0
x2
x1
x3
x0
• Mathematically
– Start with an initial point x0, evaluate f(x0), f(x0) (2f(x0))
– Based on the information, select a search direction “d0”
emanating from x0
– Find the next point x1 along the direction d0, and evaluate f(x1),
f(x1) (2f(x1))
– Repeat the above, and successfully generate x2, x3, .., such that f(x)
is decreased at each iteration  Iterative Descent
• Key Questions?
– Which direction to go? How far? Is the algorithm guaranteed to
reach x*? How fast to reach x*? ...
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Local and Global Minimum
f(x)
A
•
•
B
• C
x
– Which of the above is a local minimum point? Global minimum?
How to mathematically define these terms?
– Local minimum: A, B, and C. Global: C
– f(x*)  f(x)  x with ||x – x*|| <   x* is a local minimum
– f(x*)  f(x) x  X  x* is a global minimum
– Minimum is strict if “” is replaced by “<”
– For traditional optimization method, we can always get local ones
– For GA we can get the global one in theory.
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Comments about GA
Stochastic algorithm
randomness has an essential role in genetic algorithms
both selection and reproduction needs random procedures
Consider population of solutions
evaluates more than a single solution at each iteration
assortment, amenable for parallelisation
Robustness
Ability to perform consistently well on a broad range of
problem types
no particular requirements on the problems before using GAs
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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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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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Uses of GAs
GAs (and SAs): the algorithms of despair. Use a GA when
you have no idea how to reasonably solve a problem
calculus doesn't apply
generation of all solutions is impractical
but, you can evaluate posed solutions
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Outline of This GA Course
The basic frame of genetic algorithm.
More about representation and operators
Theory analysis of GA
Combinatorial Problem
Constraint optimization
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Outline of This GA Course
Genetic algorithm and Artificial neural network
Parallel GA
Genetic programming
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Famous Problems & Concepts
N Queens
Traveling salesman
Knight's tour
Bin packing
Scheduling
Function optimization
Graph coloring, Ramsey problems
Satisfiability
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