Genetic Programming What is it? Genetic Programming Genetic - PDF document

Genetic Programming  What is it? Genetic Programming  Genetic programming (GP) is an automated method for creating a working computer program from a high-level problem statement of a problem.  Genetic programming starts from a high- level statement of “what needs to be done” and automatically creates a computer program to solve the problem. 1 2 Genetic Programming Genetic Programming  John Koza, 1992  “Genetic Programming: On the Programming of Computers by Means of Natural Selection“  www.genetic-programming.com 3 4 Genetic Programming Genetic Programming  In genetic programming:  In Koza’s original work  Problem -- involves not finding a solution,  LISP was used as the programming but instead creating a program that can language find the best solution.  Parse trees were used as the genotype.  Phenotype (solution) is a computer program  Straight-forward genetic mapping  Search space is the set of all possible  Functional program --> parse tree. computer programs. 5 6 1

LISP and parse trees Genetic Programming  GPs fit well within the EA framework (defun o() sqrt (setf A 1.52) (sqtr (* A (* A A ))))  Important distinction: *  Genotype = tree *  Phenotype = LISP program A A A Mitchell 7 8 GPs as EAs Defining your problem  For programs to be be evolved, must define:  To use evolutionary algorithms you must:  Define your problem -- must provide hints to functional  Terminal Set building blocks  Leaves of the parse tree  Define your genotype  Correspond to program inputs  Identify your phenotype  Function Set  Define the genotype -> phenotype translation  Interior nodes of parse tree  Define crossover and mutation operators  Set of functions allowable in program  Define fitness  Should be chosen with relation to problem to be solved.  Determine selection criteria  Can have side effects.  Set population parameters 9 10 Defining your problem GPs as EAs  Sufficiency and Closure  To use evolutionary algorithms you must:  Sufficiency  Define your problem -- must provide hints to functional building blocks  terminals + functions must be able to solve the  Define your genotype -- parse trees problem at hand  Identify your phenotype -- LISP program  Choose your terminal and function set wisely  Define the genotype -> phenotype translation  Closure  Define crossover and mutation operators  Functions should be able to accept as  Define fitness argument any value returned by other  Determine selection criteria functions  Set population parameters  Universal return type. 11 12 2

GPs: Crossover and Mutation GPs: Crossover and Mutation  Crossover crossover mutation  Choose random sub-tree from each parent  Swap them in resultant children  Mutation Before crossover Before mutation  Replace randomly chosen sub-tree with randomly After crossover After mutation generated tree.  Can result in increasing / decreasing the size of the genome.  Note that operation maintain valid individuals. 13 14 GPs and crossover GPs as EAs  To use evolutionary algorithms you must:  Define your problem -- must provide hints to functional building blocks  Define your genotype -- parse trees  Identify your phenotype -- LISP program  Define the genotype -> phenotype translation  Define crossover and mutation operators  Define fitness  Determine selection criteria  Set population parameters 15 16 Fitness GPs as EAs  Evaluate the effectiveness of the  To use evolutionary algorithms you must: program to solve the problem  Define your problem -- must provide hints to functional building blocks  Define your genotype -- parse trees  Identify your phenotype -- LISP program  Two stage fitness:  Define the genotype -> phenotype translation  Run resultant program  Define crossover and mutation operators  Define fitness  Compare to correct / desired results  Determine selection criteria  Set population parameters 17 18 3

GPs as EAs GPs as EAs  In Koza’s original work:  To use evolutionary algorithms you must:  Define your problem -- must provide hints to functional  10% of individuals will move to next building blocks generation  Define your genotype -- parse trees  Probability based on Fitness  Identify your phenotype -- LISP program  Define the genotype -> phenotype translation  90% formed by crossover  Define crossover and mutation operators  Parent chosen probabilistically based on fitness  Define fitness  Koza does not use mutation.  Determine selection criteria  Set population parameters 19 20 Initializing population Trivial example  Randomly creating programs.  From Mitchell  Must assure that trees match valid  Program to compute P, the orbital period programs. of a planet.  Number of function arguments must match.  Parameters A = average distance from the sun.  Usually a limit is set on tree depth of generated program.  Known solution:  P 2 = cA 3  c = constant.  Questions so far 21 22 Trivial example Trivial example  Terminal set:  A = average distance from the sun  Function set:  Typical arithmetic operations:  +, -, *, /, sqrt  Closure -- Note that all take float and return float 23 24 4

Trivial example Trivial example  Sample solutions  Fitness: 25 26 More interesting Example Other GP variants  Block stacking problem  Strongly typed GP  Koza 1992 as described by Mitchell  Gets around the closure idea  Given:  Function arguments are typed  Set of blocks that can either be  Individual generation and genetic  On a stack  On a table. operators must respect the types.  Goal:  Find a program that will place the blocks on the stack in the “correct” order. 27 28 Building Block Example Factoids about Genetic Programming  More elaborate scheme to solve this:  From Koza’s Web site  There are now 36 instances where genetic  Using Strongly Typed GPs programming has produced a human-competitive  Found in [Kochenderfer] result.  15 instances where GP has created an entity that either infringes or duplicates the functionality of a previous patent  6 instances where genetic programming has done the same with respect to a 21st-centry invention  Questions?  2 instances where genetic programming has created a patentable new invention. 29 30 5

Genetic Programming Factoids about Genetic Programming  GPs themselves were patented by Koza:  In Koza’s original work  LISP was used as the programming language  Koza, John R. Non-Linear Genetic Algorithms for Solving Problems.  Parse trees were used as the genotype.  US Patent 4,935,877. Issued June 19, 1990.  Australian Patent 611,350. Issued September 21, 1991.  Straight-forward genetic mapping  Canadian Patent 1,311,561. Issued December 15, 1992.  Functional program --> parse tree.  German patent 3916328.8-53. Issued June 18, 1997.  Not the only way to do genetic programming. 31 32 Genetic Programming GPs as GAs  In genetic programming:  GADS  Problem -- involves not finding a solution,  [Paterson, Livesey] but instead creating a program that can find the best solution.  Phenotype = program  Phenotype (solution) is a computer program  Genotype = n-tuple (array).  Search space is the set of all possible computer programs.  Genotype need not be a parse tree! 33 34 Languages as grammars Phenotype Representation  Grammars for programming languages  Phenotype is a program in a given language  Language is defined by a grammar in BNF.  <stmt> → … | <for-stmt> | <if-stmt> | …  Each production in the grammar is uniquely  <stmt> → { <stmt> <stmt> } | ε numbered.  <if-stmt> → if ( <expr> ) then <stmt>  <for-stmt> → for ( <expr> ; <expr> ; lhs → rhs <expr> ) <stmt> <sexpr> → (GT <sexpr> <sexpr>) 35 36 6

Phenotype Representation Genotype representation  A valid program can be described by a sequence of applications of grammar rules.  Genotype = tuple or array representing this sequence.  Let’s try:  (GT (* -1 X) (* V (ABS V) ) )  Can use “standard” GA operators for tuples for crossover and mutation. 37 38 Genetic Mapping Genetic Mapping  Genetic Repairs Required:  Genetic Repairs Required:  Inapplicable productions.  Inapplicable productions.  Assume after a number of production  Genetic repair: skip the problematic gene and applications (as defined by a genome) the progress to the first gene that has an generated program is: appropriate lhs. (GT <sexpr> <numeral>) What if the the production of the next gene does NOT have a lhs of <sexpr> or <numeral>? 39 40 Genetic Mapping Genetic Mapping  Genetic Repairs Required:  Genetic Repairs Required:  Residual non-terminals  Residual non-terminals  What if…after all productions associated to all  Reject this individual or genes have been applied and there are still  Have each non-terminal have a default terminal non-terminals in the program? value and use this default. 41 42 7