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Genetic Programming Primer

ami hauptman

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Outline Intro GP definition

Human Competitive Results Representation

Advantages GP operators

The GP Individual The GP experiment Example – symbolic regression Additional Concepts

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Intro Representation is a crucial issue in problem-solving

Part of the solution Generic GAs

Linear (bit-vector) solutions Fixed length

Problems: Often difficult and unnatural Limited search; Length may be unknown

Examples – TSP; AI; … Very few “real world” implementations

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Towards a Variant A : Computer programs fundamental models in CS B : “Computer programs are the best model for computer programs” Conclusion… (A Λ B ) Why not implement GA individuals as programs?

Implemented in…

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Genetic Programming [GP] Evolutionary search in program space Tree-structured representation Non tree-based program

representations exist (e.g. Machine-Code GA)

Introduced by Cramer [1985] Developed by Koza [1992] Active and highly successful field

Conferences Patents And especially…

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Human-Competitive Results

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Human-Competitive Results Increasing in the field of genetic and

evolutionary computation

An automatically created result is “human-

competitive” if (www.human-

competitive.org): Patent (invention)

New scientific result

Solution to long-standing problem

Wins / Holds its own in regulated competition

with human contestant (= live player or human-

written program)

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Human-Competitive Results Over 40 to date Examples:

Evolved antenna for use by NASA (Lohn, 2004) Automatic quantum computer programming

(Spector, 2004) Several analog electronic circuits (Koza et al.,

mid 90s till today): amplifiers, computational circuits, …

MAJOR motivation: As of 2004, yearly contest

WITH CASH PRIZES!

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Outline Intro GP definition

Human Competitive Results Representation

Advantages GP operators

The GP Individual The GP experiment Example – symbolic regression Additional Concepts

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Representations Individuals as LISP programs (S-

expressions) Why trees?

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Advantages of trees

Before Genetic operators Powerful representation (+ 1 2 (IF (> TIME 10) 3 4)) Simple

No: local vars, types … Individual Solution

Saves precious time

Recursive - size may vary Main advantage:

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Outline Intro GP definition

Human Competitive Results Representation

Advantages GP operators

The GP Individual The GP experiment Example – symbolic regression Additional Concepts

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Genetic Operators

Reproduction – as before Crossover, Mutation -

now tree operators S-expressions closed under most (tree)

operators Generate VALID individuals Unlike C programs…

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GP Operators - Crossover BINARY

1) Randomly select 2 nodes

2) Swap underlying sub-trees S.t. depth constraints (if applicable)

FATHER MOTHER OFFSPRING1 OFFSPRING2

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GP Operators - Mutation UNARY

1) Select mutation point

2) Remove entire sub-tree and grow a new one

Again – depth constraints

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Genome What’s inside the tree… Genome contains functions and

terminals Functions - Internal nodes

Varying complexity Examples: +, -, And, Or, If, IFLTE, ADFs

Terminals - Leaves Constants or “sensors”; Actions Generally more domain dependant Examples: Variables, Constants, 0-

params functions, ERCs

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Example 1 Logic expression

AND

AND

Y X

ORNOTX

Z

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Example 2 Series of instructions

Progn2

IF

Wall_is_near 90

Rotate_Right

Advance_5 Advance_10

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More realistic trees…

Tree 0: (If3 (Or2 (Not (Or2 (And2 OppPieceAttUnprotected NotMyKingInCheck) (Or2 NotMyPieceAttUnprotected 100*Increase))) (And2 (Or3 (And2 OppKingStuck NotMyPieceAttUnprotected) (And2 OppPieceAttUnprotected OppKingStuck) (And3 -1000*MateInOne OppKingInCheckPieceBehind NotMyKingStuck)) (Or2 (Not NotMyKingStuck) OppKingInCheck))) NumMyPiecesUNATT (If3 (< (If3 (Or2 NotMyPieceAttUnprotected NotMyKingInCheck) (If3 NotMyPieceAttUnprotected #NotMovesOppKing OppKingInCheckPieceBehind) (If3 OppKingStuck OppKingInCheckPieceBehind -1000*MateInOne)) (If3 (And2 100*Increase 1000*Mate?) (If3 (< NumMyPiecesUNATT (If3 NotMyPieceAttUnprotected -1000*MateInOne OppKingProxEdges)) (If3 (< MyKingDistEdges #NotMovesOppKing) (If3 -1000*MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) (If3 NotMyKingStuck -100.0 OppKingProxEdges))) (If3 OppKingInCheck (If3 (Or2 NotMyPieceAttUnprotected NotMyKingInCheck) (If3 (< MyKingDistEdges #NotMovesOppKing) (If3 -1000*MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) (If3 (And3 -1000*MateInOne NotMyPieceAttUnprotected 100*Increase) (If3 (< NumMyPiecesUNATT (If3 NotMyPieceAttUnprotected -1000*MateInOne OppKingProxEdges)) (If3 (< MyKingDistEdges #NotMovesOppKing) (If3 -1000*MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) -1000*MateInOne)) (If3 (< (If3 100*Increase MyKingDistEdges 100*Increase) (If3 OppKingStuck OppKingInCheckPieceBehind -1000*MateInOne)) -100.0 (If3 (And2 NotMyPieceAttUnprotected -1000*MateInOne) (If3 (< NumMyPiecesUNATT (If3 NotMyPieceAttUnprotected -1000*MateInOne OppKingProxEdges)) (If3 (< MyKingDistEdges #NotMovesOppKing) (If3 -1000*MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) (If3 OppPieceAttUnprotected NumMyPiecesUNATT MyFork)))))

• GP-EndChess

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Outline Intro GP definition

Human Competitive Results Representation

Advantages GP operators

The GP Individual The GP experiment Example – symbolic regression Additional Concepts

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The GP experiment Preparatory steps: Determine set of terminals & functions Determine fitness measure Determine run parameters

Population size Operator probabilities Tree depths …

Set up end of run criteria Run the experiment

start with initial population:

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Creating the Initial Population

3 Methods Depth=m Grow

F.e. node – randomly select function or terminal

varying depths Full

All of same depth Ramped-half-and-half

Divide population to max_depth-1 parts For each part: half by grow; half by full Preferred by Koza

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Flowchart of GP

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Example - Symbolic regression

Independent variable X

Dependent variable Y

-1.001.00

-0.800.84

-0.600.76

-0.400.76

-0.200.84

0.001.00

0.201.24

0.401.56

0.601.96

0.802.44

1.003.00

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Preparatory StepsObjective:Find a computer program with one

input (independent variable X) whose output equals the given data

1Terminal set:T = {X, Random-Constants}

2Function set:F = {+, -, *, %}

3Fitness:The sum of the absolute value of the differences between the candidate program’s output and the given data, where (-1 < X < 1)

4Parameters:Population size M = 4

5Termination:An individual emerges whose sum of absolute errors is less than 0.1

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Notes Complexity of function = ?

Size of solution unknown More points more difficult

Depth constraints Can limit complexity Needed anyway

Typically size of pop >= 50 “%” function

is “/” excluding zero in 2nd argument Needed to avoid BAD individuals

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Generation 0

4 Random Individuals (later: creation) More complex than actual

transformed

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Fitness

f(x) = x2 +x+ 1

x + 1 x2 + 1 2 x

4.4 6.00 9.48 15.4

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Generation 1

Copy of (a)

Mutant of (c) picking “2” as mutation point

First offspring of crossover of (a) and (b) picking “+” of parent (a) and left-most “x” of parent (b) as crossover points

Second offspring of crossover of (a) and (b) picking “+” of parent (a) and left-most “x” of parent (b) as crossover points

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Generation 1 - Fitness

4.4 6.0 15.4 0 - IDEAL

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Outline Intro GP definition

Human Competitive Results Representation

Advantages GP operators

The GP Individual GP experiments Example – symbolic regression Additional Concepts

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Additional Concepts

Competitive Evaluation Ephemeral Random constants

(ERCs) Strongly Typed GP (STGP)

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Competitive Evaluation (not only in GP) Important in games ! Fitness depends on peers; relative

E.g. compete against k peers Optional – count score for both

Easier progress at start – weak opps

Avoid over-generalization and early convergence

Still need absolute measure

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ERCs Sometimes constants not known in

advance E.g. symbolic regression

ERC (terminal) node – init to a random constant stay

Mutate-ERC operator (low prob.) Change to other constant

Typically-range for constants

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Strongly Typed Genetic Programming (STGP)

Montana [1995] Node data types may vary; casting

not enough Impose structural constraints Assigning (pseudo) types to

functions & terminals Sometimes more than one Typically actual (implementation)

types are all real numbers

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STGP Example

Include both Boolean and Float terminals True, False, zero-arg Predicates ERCs, float zero-arg functions

Some used as both – “Query” Important predicate Returns a large float if true

If function Children: Boolean, Float, Float

Query can be at each child location of If