1 Genetic Programming Primer ami hauptman

2 Outline  Intro  GP definition  Human Competitive Results  Representation  Advantages  GP operators  The GP Individual  The GP experiment  Example – symbolic regression  Additional Concepts

3 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

4 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…

5 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…

6 Human-Competitive Results

7  Increasing in the field of genetic and evolutionary computation  An automatically created result is “human- competitive” if (  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)

8 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!

9 Outline  Intro  GP definition  Human Competitive Results  Representation  Advantages  GP operators  The GP Individual  The GP experiment  Example – symbolic regression  Additional Concepts

10 Representations  Individuals as LISP programs (S- expressions)  Why trees?

11 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:

12 Outline  Intro  GP definition  Human Competitive Results  Representation  Advantages  GP operators  The GP Individual  The GP experiment  Example – symbolic regression  Additional Concepts

13 Genetic Operators  Reproduction – as before  Crossover, Mutation -  now tree operators  S-expressions closed under most (tree) operators  Generate VALID individuals  Unlike C programs…

14 GP Operators - Crossover  BINARY 1) Randomly select 2 nodes 2) Swap underlying sub-trees  S.t. depth constraints (if applicable) FATHER MOTHER OFFSPRING1 OFFSPRING2

15 GP Operators - Mutation  UNARY 1) Select mutation point 2) Remove entire sub-tree and grow a new one  Again – depth constraints

16 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

17 Example 1  Logic expression AND Y X OR NOT X Z

18 Example 2  Series of instructions Progn2 IF Wall_is_near 90 Rotate_Right Advance_5Advance_10

19 More realistic trees… Tree 0: (If3 (Or2 (Not (Or2 (And2 OppPieceAttUnprotected NotMyKingInCheck) (Or2 NotMyPieceAttUnprotected 100*Increase))) (And2 (Or3 (And2 OppKingStuck NotMyPieceAttUnprotected) (And2 OppPieceAttUnprotected OppKingStuck) (And *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) (If *MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) (If3 NotMyKingStuck OppKingProxEdges))) (If3 OppKingInCheck (If3 (Or2 NotMyPieceAttUnprotected NotMyKingInCheck) (If3 (< MyKingDistEdges #NotMovesOppKing) (If *MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) (If3 (And *MateInOne NotMyPieceAttUnprotected 100*Increase) (If3 (< NumMyPiecesUNATT (If3 NotMyPieceAttUnprotected -1000*MateInOne OppKingProxEdges)) (If3 (< MyKingDistEdges #NotMovesOppKing) (If *MateInOne *MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) -1000*MateInOne)) (If3 (< (If3 100*Increase MyKingDistEdges 100*Increase) (If3 OppKingStuck OppKingInCheckPieceBehind -1000*MateInOne)) (If3 (And2 NotMyPieceAttUnprotected -1000*MateInOne) (If3 (< NumMyPiecesUNATT (If3 NotMyPieceAttUnprotected -1000*MateInOne OppKingProxEdges)) (If3 (< MyKingDistEdges #NotMovesOppKing) (If *MateInOne -1000*MateInOne NotMyPieceATT) (If3 100*Increase #MovesMyKing OppKingInCheckPieceBehind)) NumOppPiecesATT) (If3 OppPieceAttUnprotected NumMyPiecesUNATT MyFork))))) GP-EndChess

20 Outline  Intro  GP definition  Human Competitive Results  Representation  Advantages  GP operators  The GP Individual  The GP experiment  Example – symbolic regression  Additional Concepts

21 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:

22 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

23 Flowchart of GP

24 Example - Symbolic regression Independent variable X Dependent variable Y

25 Preparatory Steps Objective: 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

26 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 2 nd argument  Needed to avoid BAD individuals

27 Generation 0  4 Random Individuals (later: creation)  More complex than actual  transformed

28 Fitness  f(x) = x 2 +x+ 1 x + 1x x

29 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

30 Generation 1 - Fitness IDEAL

31 Outline  Intro  GP definition  Human Competitive Results  Representation  Advantages  GP operators  The GP Individual  GP experiments  Example – symbolic regression  Additional Concepts

32 Additional Concepts  Competitive Evaluation  Ephemeral Random constants (ERCs)  Strongly Typed GP (STGP)

33 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

34 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

35 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

36 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