Genetic Algorithms

Biological Evolution Lamarck and others: Darwin: Species “transmute” over time Darwin: Consistent, heritable variation among individuals in population Natural selection of the fittest

Why GAs? Evolution is known to be a successful, robust method for adaptation within biological systems. GAs can search spaces of hypotheses containing complex interacting parts. GAs have been applied successfully to a variety of learning tasks and optimization problems GAs admit a natural implementation on massively parallel computers.

GAs - High Level Overview Begin with a collection of initial hypotheses – a population Then score the hypotheses (individuals) in the current population using a fitness function. A new population is is then generated by probabilistically selecting the most fit individuals from the current population (survival of the fittest). Some of these selected individuals are carried forward into the next generation intact. Others are are used as basis for creating new offspring individuals by applying genetic operations of crossover and mutation.

Formally GA(Fitness, Fitness threshold, p, r,m) • Initialize: P ← p random hypotheses • Evaluate: for each h in P, compute Fitness(h) • While [max Fitness(h)] < Fitness threshold 1. Select: Probabilistically select (1 − r)p members of P to add to Ps. 2. Crossover: Probabilistically select r·p/2 pairs of hypotheses from P. For each pair, <h1, h2>, produce two offspring by applying the Crossover operator. Add all offspring to Ps. 3. Mutate: Invert a randomly selected bit in m·p random members of Ps 4. Update: P ← Ps 5. Evaluate: for each h in P, compute Fitness(h) • Return the hypothesis from P that has the highest fitness.

Individual Selection Roulette-Wheel Selection: Choose members from a population in a way that is proportional to their fitness. Population’s total fitness score is represented by a pie chart, or roulette wheel. Assign a slice of the wheel to each member of the population. Size of the slice is proportional to that individual fitness score. Select a member by spinning the ball and selecting the one at the point it stops. Tournament Selection: Two members are chosen at random from a population. With some predefined probability p the more fit of these two is then selected, and with probability 1-p the less fit hypothesis is selected. Sometimes TS yields a more diverse population that RS.

Representing Hypotheses (Outlook = Overcast  Rain)  (Wind = Strong) by Outlook Wind 011 10 IF Wind = Strong THEN PlayTennis = yes Outlook Wind PlayTennis 111 10 10 Don’t care for Outlook here.

Operators for Genetic Algorithms

GABIL [DeJong et al. 1993] Learn a set of rules Representation: Each hypothesis is a set of rules To represent a set of rules, the bit-string representation of individual rules are concatenated Example IF a1 = T AND a2 = F THEN c = T; IF a2 = T THEN c = F a1 a2 c a1 a2 c 10 01 1 11 10 0

GABIL Fitness function: Fitness(h) = (correct(h))2 correct(h): the percent of all training examples correctly classified

GABIL: Genetic operators Use the standard mutation operator Crossover: extension of the two-point crossover operator want variable length rule sets want only well-formed bitstring hypotheses Crossover with variable-length bitstrings 1. choose two crossover points for h1. Let d1 (d2) be the distance to the rule boundary immediately to its left. 2. now restrict points in h2 to those that have the same d1 and d2 value

GABIL: Crossover a1 a2 c a1 a2 c h1 : 10 01 1 11 10 0 Suppose crossover points for h1, are after bits 1, 8 (d1=1;d2=3) a1 a2 c a1 a2 c h1 : 1[0 01 1 11 1]0 0 Allowed pairs of crossover points for h2 are <1;3>, <1;8>, <6;8>. If pair <1;3> is chosen, a1 a2 c a1 a2 c h2 : 0[1 1]1 0 10 01 0 the result is:

GABIL: Crossover a1 a2 c h3 : 11 10 0 a1 a2 c a1 a2 c a1 a2 c