introduction to genetic algorithms. 2 contact information name: 任庆生 office: 教三楼 403 tel:...
TRANSCRIPT
Introduction to Genetic Algorithms
3
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
4
Grading
Homework: 20%
Final project: 80% . The deadline is ???
5
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.
6
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.
7
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.
8
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.
9
Some Examples
Choosing among 1,500 features for OCR.
Scheduling the Chili, NY, annual soccer invitational.
N Queens, Graphs, Salesmen, etc., etc.
10
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.
11
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.
12
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).
13
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...
14
Placing N Non-Attacking Queens
Found by my genetic algorithm!
15
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.
16
100 Non-Attacking Queens in 130 Fitness Evaluations
17
Graph Coloring: Edge Ends Get Different Colors
18
Graph Coloring = Map Coloring
19
Graph Coloring = Map Coloring
20
Traveling Salesman Route Min.
Another classic, hard, NP-complete problem.
We tried cities on a HW 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.
21
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
22
History
Holland
Bagley
Cavicchio
Hollstien
De Jong
Goldberg
Medical image processing
Prisoner’s dilemma
Holland
Others
23
Classes of Search Techniques
F inonacci N ew ton
D irect methods Indirect methods
C alculus-based techniques
E volutionary strategies
C en tralized D istrib u ted
P arallel
S tead y-state G en eration al
S eq u en tia l
G en etic a lgorith m s
E volu tion ary a lgorith m s S imulated annealing
G u id ed ran d om search tech n iq u es
D ynamic programming
E numerative techniques
S earch tech n iq u es
24
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
25
• 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*? ...
x0
f(x) = c d0
x2
x3
x1
26
Local and Global Minimum
– 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.
x
f(x)
• •
• A B C
27
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
28
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
29
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
30
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
31
Outline of This GA Course
The basic frame of genetic algorithm.
More about representation and operators
Theory analysis of GA
Combinatorial Problem
Constraint optimization
32
Outline of This GA Course
Genetic algorithm and Artificial neural network
Parallel GA
Genetic programming
33
Famous Problems & Concepts
N Queens
Traveling salesman
Knight's tour
Bin packing
Scheduling
Function optimization
Graph coloring, Ramsey problems
Satisfiability