an introduction to genetic programming ii - gp... · 5/27/2010 1 an introduction to genetic...

5/27/2010

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An Introduction to Genetic Programming

Prof. N. SundararajanSchool of EEE

Nanyang Technological UniversitySingapore

Email: [email protected]

1Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010

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.' "



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.



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)



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



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.



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



GP - Flowchart


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GP Flowchart…


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

… 17Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010


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

>=



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



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


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)))



Tree based representation – Ex 3

i =1;while (i < 20){

i = i +1}


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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




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?



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



GP Creation - 3


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GP Creation VIDEO



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



Lecture – II (Genetic Operations)


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GP GENETIC OPERATIONS

R d ti Reproduction

Mutation

Crossover (sexual recombination)

Architecture-altering operations



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)



GP flowchartGA flowchart40Workshop on Bio-Inspired Computing, VTU, Mysore, 7-10, June 2010

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MUTATION OPERATION



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



Example Crossover operation


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Crossover fragments



Crossover reminders


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Two offspring's



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



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



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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Fitness and Termination functions



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 %



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



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.



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



Data set


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Regression problem



GP Set - Definitions


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Regression Problem - Generation – 0





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Creation of Generation 1 from Generation 0



Creation of Generation 1 from Generation 0


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Regression problem - Generation 2



Best Solution


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Observation



Observation…


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GP – Classification problem



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



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



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



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



GP - Discussion


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GP – Discussion



Expert System Like Rule Base


an introduction to genetic programming ii - gp... · 5/27/2010 1 an introduction to genetic...

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