an introduction to genetic programming ii - gp... · 5/27/2010 1 an introduction to genetic...
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An Introduction to Genetic Programming
Prof. N. SundararajanSchool of EEE
Nanyang Technological UniversitySingapore
Email: [email protected]
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Prof. N. Sundararajan, NTU
Web Links :
www.geneticprogramming.org
ti i www.genetic-programming.org
Genetic programming code can be found in http://www.geneticprogramming.com/GPpages
/software.html
Text Book :
Koza, John R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge, MA: The MIT Press. 1992 2Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010
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What is Genetic Programming
"Genetic programming is automatic programming. For the first time since theprogramming. For the first time since the idea of automatic programming was first discussed in the late 40's and early 50's, we have a set of non-trivial, non-tailored, computer-generated programs that satisfy. John Holland University of Michigan 1997– John Holland, University of Michigan, 1997
Samuel's exhortation: 'Tell the computer what to do, not how to do it.' "
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General Idea
Use principle of an Evolutionary Algorithm to evolve programsevolve programs
Conventional programming Genetic programming
programinput output Required behavior
GP
programinput outputWritten by you
Automatically evolved 4Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010
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Why GP?
It saves time by freeing the human from having to design complex algorithms Nothaving to design complex algorithms. Not only designing the algorithms but creating ones that give optimal solutions.
Again, Biologically Inspired Computation.
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Challenge ?
"How can computers learn to solveproblems without being explicitlyproblems without being explicitlyprogrammed? In other words, how cancomputers be made to do what is neededto be done, without being told exactly howto do it?"
Attributed to Arthur Samuel (1959)
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CRITERION FOR SUCCESS
"The aim [is] ... to get machines to exhibitbehavior which if done by humans wouldbehavior, which if done by humans, wouldbe assumed to involve the use ofintelligence.“
Arthur Samuel (1983)
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REPRESENTATIONS
Decision trees Binary decision Decision trees
If-then production rules
Horn clauses
Neural nets
Bayesian networks
Binary decision diagrams
Formal grammars Coefficients for
polynomials Reinforcement learning
tables Frames
Propositional logic
Conceptual clusters Classifier systems
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Computer program
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GENETIC PROGRAMMING (GP) GP applies the approach of the genetic
algorithm to the space of possible computer programs
Computer programs are the lingua francafor expressing the solutions to a wide variety of problems
A wide variety of seemingly different problems from many different fields canproblems from many different fields can be reformulated as a search for a computer program to solve the problem.
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GP MAIN POINTS Genetic programming now routinely delivers
high-return human-competitive machine g pintelligence.
Genetic programming is an automated invention machine.
Genetic programming has delivered a progression of qualitatively more substantial results in synchrony with five approximatelyresults in synchrony with five approximately order-of-magnitude increases in the expenditure of computer time.
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GP Issues
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Components of GP
Similar to GA, GP also have six components Population initialization Population initialization Program representation Selection function Genetic operations
Reproduction Crossover Mutation
Fitness function Termination criterion
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GP - Flowchart
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GP Flowchart…
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Genetic ProgrammingGenetic Programming
Solution representation
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Introductory example: credit scoring Bank wants to distinguish good from bad loan
applicantsapplicants
Model needed that matches historical data
ID No of children
Salary Marital status
OK?
ID-1 2 45000 Married 0
ID-2 0 30000 Single 1
ID-3 1 40000 Divorced 1
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Introductory example: credit scoring A possible model: IF (NOC = 2) AND (S > 80000) THEN good ELSE badIF (NOC 2) AND (S 80000) THEN good ELSE bad In general:
IF formula THEN good ELSE bad Only unknown is the right formula, hence Our search space (phenotypes) is the set of formulas Natural fitness of a formula: percentage of well
classified cases of the model it stands forclassified cases of the model it stands for Natural representation of formulas (genotypes) is:
parse trees
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Introductory example: credit scoringIF (NOC = 2) AND (S > 80000) THEN good ELSE bad
can be represented by the following treecan be represented by the following tree
AND
S2NOC 80000
>=
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Formula – Computer program
The best formula is generated using the computer programcomputer program
Formula has two major components AND, =, > - operators NOC, S, constants (2,8000) – Operands
To write any formula, we need Terminals – problem depended variablesTerminals problem depended variables
Like NOC, S
Functions set AND, =, > operators
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Formula representation in computer programs Formula : (NOC = 2) AND (S > 80000) We use tree structure to represent the formula We use tree structure to represent the formula In GP this formula is represented using LISP-S
expression (S stands for symbolic expression) (AND (= NOC 2) (> S 80000))
Here AND, =, > are operators NOC, S, 2, 80000 are operands
Lisp is a family of computer programming languageLisp is a family of computer programming language with a long history and a distinctive fully-parenthesized syntax
Lisp Ref: http://www.apl.jhu.edu/~hall/lisp.html
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Function and Terminal set
The identification of the function set and terminal set for a particular problem (or category of problems) is
ll t i htf dusually a straightforward process. For some problems, the function set may consist of
merely the arithmetic functions of addition, subtraction, multiplication, and division as well as a conditional branching operator.
The terminal set may consist of the program’s external inputs (independent variables) and numerical constantsnumerical constants.
This function set and terminal set is useful for a wide variety of problems (and corresponds to the basic operations found in virtually every general-purpose digital computer).
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Tree based representation
Trees are a universal form, e.g. consider
A ith ti f l Arithmetic formula
Logical formula
Program
15)3(2
yx
(x true) (( x y ) (z (x y)))g
i =1;while (i < 20){
i = i +1} 23Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010
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Tree based representation – Ex 1
LISP form – (+ (* 2 pi) (- (+ x 3) (/ y (+ 5 1))))
15)3(2form almathematic
yx
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Tree based representation : Ex 2
(x true) (( x y ) (z (x y)))
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Tree based representation – Ex 3
i =1;while (i < 20){
i = i +1}
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Tree based representation
In GA and EP chromosomes are linear structures (bit strings integer string real-structures (bit strings, integer string, realvalued vectors, permutations)
Tree shaped chromosomes are non-linear structures
In GA, and EP the size of the chromosomes is fixed
Trees in GP may vary in depth and width
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Tree based representation
Symbolic expressions can be defined by Terminal set T Function set F (with the arities of function symbols)
Adopting the following general recursive definition:1. Every t T is a correct expression2. f(e1, …, en) is a correct expression if f F, arity(f)=n
and e1, …, en are correct expressions 3. There are no other forms of correct expressions
In general, expressions in GP are not typed (closure property: any f F can take any g F as argument)
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How to write GP?
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CREATING GP - 1
Available functions Available functions F = {+, -, *, %, IFLTE}
IFLTE(a,b,c,d): if a <= b then c else d
Available terminals T = {X, Y, Random-Constants}
The random programs are: The random programs are: Of different sizes and shapes
Syntactically valid
Executable30Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010
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GP Creation - 2
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GP Creation - 3
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GP Creation VIDEO
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Genetic ProgrammingGenetic Programming
Population initialization
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Population initialization
Maximum initial depth of trees Dmax is set Full method (each branch has depth = Dmax): Full method (each branch has depth Dmax):
nodes at depth d < Dmax randomly chosen from function set F
nodes at depth d = Dmax randomly chosen from terminal set T
Grow method (each branch has depth Dmax): nodes at depth d < Dmax randomly chosen from F T nodes at depth d = Dmax randomly chosen from T
Common GP initialisation: ramped half-and-half, where grow & full method each deliver half of initial population
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Genetic ProgrammingGenetic Programming
Lecture – II (Genetic Operations)
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GP GENETIC OPERATIONS
R d ti Reproduction
Mutation
Crossover (sexual recombination)
Architecture-altering operations
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Offspring creation scheme
Compare
GA h i AND t ti GA scheme using crossover AND mutation sequentially (be it probabilistically)
GP scheme using crossover OR mutation (chosen probabilistically)
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Offspring creation scheme
Compare
GA h i AND t ti GA scheme using crossover AND mutation sequentially (be it probabilistically)
GP scheme using crossover OR mutation (chosen probabilistically)
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GP flowchartGA flowchart40Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010
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MUTATION OPERATION
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MUTATION OPERATION
Select 1 parent probabilistically based on fitness Pick point from 1 to NUMBER-OF-POINTS Delete subtree at the picked point Grow new subtree at the mutation point in same
way as generated trees for initial random population (generation 0)
The result is a syntactically valid executable programP t th ff i i t th t ti f th Put the offspring into the next generation of the population
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CROSSOVER OPERATION
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Example Crossover operation
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Crossover fragments
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Crossover reminders
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Two offspring's
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CROSSOVER OPERATION - summary
Select 2 parents probabilistically based on fitness Randomly pick a number from 1 to NUMBER-OF-POINTS for y p
1st parent
Independently randomly pick a number for 2nd parent
The result is a syntactically valid executable program
Put the offspring into the next generation of the population
Identify the subtrees rooted at the two picked points
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REPRODUCTION OPERATION
S l t t b bili ti ll b d Select parent probabilistically based on fitness
Copy it (unchanged) into the next generation of the population
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Genetic ProgrammingGenetic Programming
Selection function
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GP – Selection function
Selection Function
Objective: Select search nodes from existing population to find new search nodes. Types of selection functions
Roulette wheel selection and its extensions Scaling techniques, Tournament Ranking methods
Normalized Geometric Ranking Method: Arrange the search nodes in descending order of their Arrange the search nodes in descending order of their
fitness value. Selection probability (q) – To select best search node Rank of jth search node rj
Probability of selecting jth search node : N
r
jq
qqs
j
11
1 1
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Normalized Geometric Ranking
Consider three solutions u, v and w.
The fitness values are The fitness values are Fu = 200, Fv = 150, Fw =
100 The rank of solutions are
ru = 1, rv = 2, rw = 3 Selection Probability
q = 0.2 Probability of selection are
Su = 0.4098, Sv = 0.3279 and Sw = 0.2623
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Genetic ProgrammingGenetic Programming
Fitness and Termination functions
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Fitness function
y
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Fitness Function
Given set of input patterns and target vectors (U T) find the input output relationship such(U,T), find the input-output relationship such that
For Function Approximation Fitness = - MSE
For Classification Problem Fitness = overall accuracy in %
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Termination Function
Koza (1992) has shown that in GP the evolution is a never-endingprocess, and hence a termination criterion is needed.
The termination criterion for GP is generally based on the problem or is limited by the number of generations.
In GP, a user-defined fitness function has to be maximized for his/her application. Thus, at the end of a GP run, we have a current population of individuals (computer programs), and also the fittest individual (computer program) that appeared during the run.
The fittest individual that has evolved for the given problem is its solution or desired mathematical model.
In our GP runs, we have used maximum number of generations (50,000) or (95% classification criterion or MSE < 0.002 for function approximation problem).
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FIVE MAJOR PREPARATORY STEPS
FOR GP
Determining the set of terminals D t i i th t f f ti Determining the set of functions Determining the fitness measure Determining the parameters for the run Determining the method for designating a result and the
criterion for terminating a run
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GP CYCLE
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Some Application
Prediction and Classification Image and Signal Processing, Target detection, g g g, g ,
Optimization Engineering, BAe wing, GE turbofan. Scheduling,
vehicle routing Financial Trading, Currency trading, Stock market
prediction (Horse race betting) Robots and Autonomous Agents, Artificial Life
E i i l i R b lki fl i h d Economic simulations, Robot walking, flying, hand-eye co-ordination Artistic, Flocking, Craig Reynolds' Film Oscar.
Architecture.
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Genetic ProgrammingGenetic Programming
ILLUSTRATIVE GP Example
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Problem definition - Regression
Given some points in R2, (x1, y1), … , (xn, yn) Find function f(x) s.t. i = 1, …, n : f(xi) = yi Find function f(x) s.t. i 1, …, n : f(xi) yi
Possible GP solution: Representation by F = {+, -, /, sin, cos}, T = R {x} Fitness is the error All operators standard pop.size = 1000, ramped half-half initialisation Termination: n “hits” or 50000 fitness evaluations
reached (where “hit” is if | f(xi) – yi | < 0.0001)
The high-level goal of this problem is to find a program whose output is equal to the values of the polynomial x4+x3+x2+x
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Data set
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Regression problem
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GP Set - Definitions
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Regression Problem - Generation – 0
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Regression Problem - Generation – 0
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Regression Problem - Generation – 0
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Regression Problem - Generation – 0
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Creation of Generation 1 from Generation 0
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Creation of Generation 1 from Generation 0
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Regression problem - Generation 2
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Best Solution
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Observation
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Observation…
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GP – Classification problem
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GP – Rule Generation
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Example – Two Class Problem
Find the best expression approximating the I/O relationshipI/O relationship
Decision (GPCE – GP classifier expression) IF GPCE(x) 0 THEN Y = +1, x class-1
IF GPCE(x) < 0 THEN Y = –1, x class-1,
For Multi-class (n-class) problem Convert into n two class problem
One Vs ALL
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Two – Class Problem
Consider a two-class problem with two inputs x1and x2and x2.
Here, we assume the following: when 10 x1 25, and 10 x2 25, these samples
belong to class-1. When 30 x1 45 and 30 x2 45, these samples
belong to class-2.
We have randomly generated 10 data points each from class-1 and class-2 samples.
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GP Expressions
Run-1
GPCE-1: (ADD (MUL (MUL –8 (DIV x1 47))(DIVGPCE 1: (ADD (MUL (MUL 8 (DIV x1 47))(DIV(SUB x2 62) –5))
The equivalent mathematical expression (mathematicalmodel) is given by
This expression (GPCE-1) can be further simplified as
5
62
478 21 xx
4.122.01702.0 21 xx
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GP Expressions
Run-2GPCE 2 (DIV (DIV 17 )(ADD 28 ) GPCE-2: (DIV (DIV –17 x1)(ADD –28 x2)
The equivalent mathematical model is
This expression (GPCE-3) is simplified as
2
1
28
17
x
x
28
17
21 xx
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Pictorial Representation
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Weld Classification Problem
Purushothaman, S., and Srinivasa, Y. G., 1998, A Procedure for training artificial neural network with application to tool wear monitoring, International Journal of Production Research, 36, 635-651.
In their experimental study, in the ranges of various parameters, speed, feed, and depth of cut data are collected on axial force, radial force, tangential force and flank wear bandwidth.
In this case, getting an analytical model from the input-output data for classification of tool wearing monitoring is difficult.
The input features are x1(speed), x2(feed), x3(depth of cut), x4(axial force), x5(radial force) and x6(tangential force)
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GP Expression
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GP - Discussion
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