Genetic Algorithms. Aims 09s1: COMP9417 Machine Learning and Data Mining. Biological Evolution. Evolutionary Computation

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1 Aims 09s1: COMP9417 Machine Learning and Data Mining Genetic Algorithms April, 009 Acknowledgement: Material derived from slides for the book Machine Learning, Tom M. Mitchell, McGraw-Hill, This lecture will enable ou to describe and reproduce machine learning approaches ug genetic algorithms. Following it ou should be able to: outline evolutionar computation reproduce the basic form of a genetic algorithm describe a representation for rule learning b a genetic algorithm describe genetic programming [Recommended reading: Mitchell, Chapter 9] [Recommended eercises: 9.1 (9.-9.4) ] COMP9417: April, 009 Genetic Algorithms: Slide 1 Evolutionar Computation Computational procedures patterned after biological evolution Search method that probabilisticall applies operators to set of points in the search space Can be viewed as form of stochastic optimization Biological Evolution Lamarck and others: Species transmute over time Darwin and Wallace: Consistent, heritable variation among individuals in population Natural selection of the fittest Mendel and genetics: A mechanism for inheriting traits genotpe phenotpe mapping COMP9417: April, 009 Genetic Algorithms: Slide COMP9417: April, 009 Genetic Algorithms: Slide 3

2 A Genetic Algorithm GA(F itness, F itness threshold, p, r, m) Initialize: P p random hpotheses Evaluate: for each h in P, compute F itness(h) While [ma h F itness(h)] < F itness threshold Do 1. Select: Probabilisticall select (1 r)p members of P to add to P S. Pr(h i ) = F itness(h i) P p j=1 F itness(h j). Crossover: Probabilisticall select r p pairs of hpotheses from P. For each pair, h 1, h, produce two offspring b appling the Crossover operator. Add all offspring to P s. 3. Mutate: Invert a randoml selected bit in m p random members of P s 4. Update: P P s 5. Evaluate: for each h in P, compute F itness(h) Return hpothesis from P with highest fitness. Represent b Represent b Representing Hpotheses (Outlook = Overcast Rain) (W ind = Strong) IF W ind = Strong Outlook W ind THEN P lat ennis = es Outlook W ind P lat ennis COMP9417: April, 009 Genetic Algorithms: Slide 4 COMP9417: April, 009 Genetic Algorithms: Slide 5 Operators for Genetic Algorithms Initial strings Crossover Mask Offspring Fitness proportionate selection: Selecting Most Fit Hpotheses Single-point crossover: Pr(h i ) = F itness(h i ) p j=1 F itness(h j) Two-point crossover: Tournament selection: Pick h 1, h at random with uniform prob. Uniform crossover: With probabilit p, select the more fit. Rank selection: Point mutation: Sort all hpotheses b fitness Prob of selection is proportional to rank COMP9417: April, 009 Genetic Algorithms: Slide 6 COMP9417: April, 009 Genetic Algorithms: Slide 7

3 GABIL [DeJong et al. 1993] GABIL Learns disjunctive set of propositional rules (competitive with C4.5) Representation: IF a 1 = T a = F THEN c = T ; IF a = T THEN c = F represented b Genetic operators:??? want variable length rule sets want onl well-formed bitstring hpotheses Fitness: F itness(h) = (percent correct(h)) a 1 a c a 1 a c COMP9417: April, 009 Genetic Algorithms: Slide 8 COMP9417: April, 009 Genetic Algorithms: Slide 9 Crossover with Variable-Length Bitstrings Crossover with Variable-Length Bitstrings Start with a 1 a c a 1 a c h 1 : h : If we choose 1, 3, go from: a 1 a c a 1 a c h 1 : 1[ ]0 0 h : 0[1 1] choose crossover points for h 1, e.g., after bits 1, 8. now restrict points in h to those that produce bitstrings with welldefined semantics, e.g., 1, 3, 1, 8, 6, 8. to get crossover result: a 1 a c h 3 : a 1 a c a 1 a c a 1 a c h 4 : COMP9417: April, 009 Genetic Algorithms: Slide 10 COMP9417: April, 009 Genetic Algorithms: Slide 11

4 GABIL Etensions Add new genetic operators, also applied probabilisticall: 1. AddAlternative: generalize constraint on a i b changing a 0 to 1. DropCondition: generalize constraint on a i b changing ever 0 to 1 And, add new field to bitstring to determine whether to allow these a 1 a c a 1 a c AA DC GABIL Results Performance of GABIL comparable to smbolic rule/tree learning methods C4.5, ID5R, AQ14 Average performance on a set of 1 snthetic problems: GABIL without AA and DC operators: 9.1% accurac GABIL with AA and DC operators: 95.% accurac smbolic learning methods ranged from 91. to 96.6 So now the learning strateg also evolves, i.e., learning to learn! COMP9417: April, 009 Genetic Algorithms: Slide 1 COMP9417: April, 009 Genetic Algorithms: Slide 13 Schemas How to characterize evolution of population in GA? Schema = string containing 0, 1, * ( don t care ) Tpical schema: 10**0* Instances of above schema: , ,... Characterize population b number of instances representing each possible schema m(s, t) = number of instances of schema s in pop at time t Consider Just Selection f(t) = average fitness of pop. at time t m(s, t) = instances of schema s in pop at time t û(s, t) = ave. fitness of instances of s at time t Probabilit of selecting h in one selection step Pr(h) = f(h) n i=1 f(h i) = f(h) n f(t) COMP9417: April, 009 Genetic Algorithms: Slide 14 COMP9417: April, 009 Genetic Algorithms: Slide 15

5 Consider Just Selection Probabilit of selecting an instance of s in one step Pr(h s) = = h s p t f(h) n f(t) û(s, t) m(s, t) n f(t) Epected number of instances of s after n selections E[m(s, t 1)] Schema Theorem ( ) û(s, t) f(t) m(s, t) d(s) 1 p c (1 p m ) o(s) l 1 m(s, t) = instances of schema s in pop at time t f(t) = average fitness of pop. at time t û(s, t) = ave. fitness of instances of s at time t p c = probabilit of gle point crossover operator p m = probabilit of mutation operator E[m(s, t 1)] = û(s, t) m(s, t) f(t) l = length of gle bit strings o(s) number of defined (non * ) bits in s d(s) = distance between leftmost, rightmost defined bits in s COMP9417: April, 009 Genetic Algorithms: Slide 16 COMP9417: April, 009 Genetic Algorithms: Slide 17 Genetic Programming Crossover Population of programs represented b trees () COMP9417: April, 009 Genetic Algorithms: Slide 18 COMP9417: April, 009 Genetic Algorithms: Slide 19

6 n e s r Goal: spell UNIVERSAL Terminals: v u Block Problem l a CS ( current stack ) = name of the top block on stack, or F. TB ( top correct block ) = name of topmost correct block on stack NN ( net necessar ) = name of the net block needed above TB in the stack i Primitive functions: Block Problem (MS ): ( move to stack ), if block is on the table, moves to the top of the stack and returns the value T. Otherwise, does nothing and returns the value F. (MT ): ( move to table ), if block is somewhere in the stack, moves the block at the top of the stack to the table and returns the value T. Otherwise, returns F. (EQ ): ( equal ), returns T if equals, and returns F otherwise. (NOT ): returns T if = F, else returns F (DU ): ( do until ) eecutes the epression repeatedl until epression returns the value T COMP9417: April, 009 Genetic Algorithms: Slide 0 COMP9417: April, 009 Genetic Algorithms: Slide 1 Block Problem Learned Program: Trained to fit 166 test problems Ug population of 300 programs, found this after 10 generations: (EQ (DU (MT CS)(NOT CS)) (DU (MS NN)(NOT NN)) ) Genetic Programming More interesting eample: design electronic filter circuits Individuals are programs that transform begining circuit to final circuit, b adding/subtracting components and connections Use population of 640,000, run on 64 node parallel processor Discovers circuits competitive with best human designs COMP9417: April, 009 Genetic Algorithms: Slide COMP9417: April, 009 Genetic Algorithms: Slide 3

7 GP for Classifing Images Fitness: based on coverage and accurac Representation: Primitives include Add, Sub, Mult, Div, Not, Ma, Min, Read, Write, If-Then-Else, Either, Piel, Least, Most, Ave, Variance, Difference, Mini, Librar Mini refers to a local subroutine that is separatel co-evolved Librar refers to a global librar subroutine (evolved b selecting the most useful minis) Biological Evolution Lamarck (19th centur) Believed individual genetic makeup was altered b lifetime eperience But current evidence contradicts this view What is the impact of individual learning on population evolution? Genetic operators: Crossover, mutation Create mating pools and use rank proportionate reproduction COMP9417: April, 009 Genetic Algorithms: Slide 4 COMP9417: April, 009 Genetic Algorithms: Slide 5 Assume Baldwin Effect Individual learning has no direct influence on individual DNA But abilit to learn reduces need to hard wire traits in DNA Then Abilit of individuals to learn will support more diverse gene pool Because learning allows individuals with various hard wired traits to be successful More diverse gene pool will support faster evolution of gene pool Plausible eample: Baldwin Effect 1. New predator appears in environment. Individuals who can learn (to avoid it) will be selected 3. Increase in learning individuals will support more diverse gene pool 4. resulting in faster evolution 5. possibl resulting in new non-learned traits such as instintive fear of predator individual learning (indirectl) increases rate of evolution COMP9417: April, 009 Genetic Algorithms: Slide 6 COMP9417: April, 009 Genetic Algorithms: Slide 7

8 Computer Eperiments on Baldwin Effect Evolve simple neural networks: Some network weights fied during lifetime, others trainable Genetic makeup determines which are fied, and their weight values Results: With no individual learning, population failed to improve over time When individual learning allowed Earl generations: population contained man individuals with man trainable weights Later generations: higher fitness, while number of trainable weights decreased Summar: Evolutionar Programming Conduct randomized, parallel, hill-climbing search through H Approach learning as optimization problem (optimize fitness) Nice feature: evaluation of Fitness can be ver indirect consider learning rule set for multistep decision making no issue of assigning credit/blame to indiv. steps COMP9417: April, 009 Genetic Algorithms: Slide 8 COMP9417: April, 009 Genetic Algorithms: Slide 9