Genetic Algorithms IF offspring inherit traits from their - PDF document

Evolution – Darwin’s Natural Selection • IF there are organisms that reproduce, and Genetic Algorithms • IF offspring inherit traits from their progenitors, and • IF there is variability of traits, and • IF the environment cannot support all members of a growing population, MSE 2400 EaLiCaRA • THEN those members of the population with less- Dr. Tom Way adaptive traits (determined by the environment) will die out, and • THEN those members with more-adaptive traits (determined by the environment) will thrive The result is the evolution of species. 2 Basic Idea Of Principle Of An Example of Natural Selection Natural Selection • Giraffes have long necks . Giraffes with slightly longer necks could feed on leaves of higher branches when all lower ones had been eaten off.  They had a better chance of survival.  Favorable characteristic propagated through generations of “Select The Best, Discard The Rest” giraffes.  Now, evolved species has long necks. NOTE: Longer necks may have been a deviant characteristic (mutation) initially but since it was favorable, was propagated over generations. Now an established trait. So, some mutations are beneficial. 3 4 Evolution Through Natural Selection How Genetic Algorithms Work Initial Population Of Animals • Genetic Algorithms implement optimization Struggle For Existence-Survival Of the Fittest strategies by simulating evolution of species through natural selection. Surviving Individuals Reproduce, Propagate Favorable Characteristics • Iteratively improve a set of possible answers to a problem by combining best Millions Of Years parts of possible answers to form Evolved Species (hopefully) better answers. (Favorable Characteristic Now A Trait Of Species) 5 6 1

Genetic Algorithms Background... • Evolution – Invented by John Holland 1975 – Organisms (animals or plants) produce a number of – Made popular by John Koza 1992 offspring which are almost, but not entirely, like themselves. – Extinction and Adaptation Some of these offspring may survive to their own —some won’t produce offspring of • The “better adapted” offspring are more likely to survive • Over time, later generations become better and better adapted – Genes and Chromosomes • Genes – “instructions” for building an organism • Chromosomes – a sequence of genes – Genetic Algorithms use this same process to “evolve” better programs 7 8 Genetic Algorithm Concept Survival of the Fittest • Genetic algorithm (GA) introduces the • The main principle of evolution used in principle of evolution and genetics into GAs is “ survival of the fittest ”. search among possible solutions to – The good solution survive, while bad ones die. given problem. • This is done by the creation within a machine of a population of individuals represented by chromosomes, in essence a set of character strings, that are analogous to the DNA, that we have in our own chromosomes. 9 10 So what is a genetic algorithm? Basic algorithm • Genetic algorithms are a randomized • Create an initial population, either random or “blank”. heuristic search strategy. • Basic idea: Simulate natural selection, • While the best candidate so far is not a where the population is composed of solution: candidate solutions . – Create new population using successor • Focus is on evolving a population from functions. – Evaluate the fitness of each candidate in the which strong and diverse candidates can population. emerge via mutation and crossover • Return the best candidate found. (mating). 11 12 2

Flowchart of a Genetic Algorithm Crossover Begin • Crossover is the similar to natural Initialize population reproduction. Evaluate Solutions • Crossover combines genetic material T =0 from two parents, N Optimum Solution? in order to produce superior offspring. Selection Y • Few types of crossover: T=T+1 Crossover Stop – One-point – Multiple point. Mutation 13 14 Crossover Crossover • E.g. • E.g. 0 7 0 7 1 6 1 6 2 5 5 2 3 4 3 4 4 3 4 3 5 2 5 2 6 1 6 1 7 0 7 0 Parent 1 Parent 2 15 16 Mutation Mutation • Mutation introduces randomness into the population. Parent • Why ‘Mutation’ 1 1 1 0 1 0 0 0 0 1 – The idea of mutation is to reintroduce divergence into a converging population. • Mutation is performed on small part of population, 0 0 1 0 1 0 1 1 0 1 Child in order to avoid entering unstable state. 17 18 3

Fitness Function Selection • Fitness Function is the evaluation • The selection operation copies a function that is used to evaluated the single individual, probabilistically solutions and find out the better selected based on fitness, into the solutions. next generation of the population. • Fitness of computed for each • Several possible ways individual based on the fitness – Keep the strongest – Keep some of the weaker solutions function and then determine what solutions are better than others. 19 20 Selection Stopping Criteria Survival of The Strongest • Final problem is to decide when to Previous generation stop execution of algorithm. • Two possible ways. 0.93 0.51 0.72 0.31 0.12 0.64 – First approach: • Stop after production of definite number of generations – Second approach: Next generation • Stop when the improvement in average fitness over 0.93 0.72 0.64 two generations is below a threshold 22 21 Simple example – alternating string Basic components • Candidate representation • Let’s try to evolve a length 4 alternating string – Important to choose this well. More work here • Initial population: C1=1000, C2=0011 means less work on the successor functions. • We roll the dice and end up creating C1’ = • Successor function(s) cross (C1, C2) = 1011 and C2’ = cross (C1, – Mutation, crossover C1) = 1000. • Fitness function • We mutate C1’ and the fourth bit flips, giving • Solution test 1010. We mutate C2’ and get 1001. • Some parameters • We run our solution test on each. C1’ is a – Population size solution, so we return it and are done. – Generation limit 23 24 4

Candidate representation Candidate representation example • Let’s say we want to represent a rule for classifying • We want to encode candidates in a way bikes as mountain bikes or hybrid, based on these that makes mutation and crossover easy. attributes: – Make (Bridgestone, Cannondale, Nishiki, or Gary Fisher) • The typical candidate representation is a – Tire type (knobby, treads) – Handlebar type (straight, curved) binary string. This string can be thought of – Water bottle holder ( Boolean ) as the genetic code of a candidate – thus • We can encode a rule as a binary string, where each the term “genetic algorithm”! bit represents whether a value is accepted. – Other representations are possible, but they Make Tires Handlebars Water bottle make crossover and mutation harder. B C N G K T S C Y N 25 26 Candidate representation Successor functions example • Mutation – Given a candidate, return a • The candidate will be a bit string of length 10, slightly different candidate. because we have 10 possible attribute values. • Crossover – Given two candidates, produce • Let’s say we want a rule that will match any bike one that has elements of each. that is made by Bridgestone or Cannondale, has • We don’t always generate a successor for treaded tires, and has straight handlebars. This rule could be represented as 1100011011: each candidate. Rather, we generate a successor population based on the candidates in the current population, Make Tires Handlebars Water bottle weighted by fitness. 1 1 0 0 0 1 1 0 1 1 B C N G K T S C Y N 27 28 Successor functions Fitness function • If your candidate representation is just a • The fitness function is analogous to a heuristic that estimates how close a binary string, then these are easy: candidate is to being a solution. – Mutate(c): Copy c as c’. For each bit b in c’, • In general, the fitness function should be flip b with probability p. Return c’. consistent for better performance. However, – Cross (c1, c2): Create a candidate c such even if it is, there are no guarantees. This is that c[i] = c1[i] if i % 2 = 0, c[i] = c2[i] a probabilistic algorithm! otherwise. Return c. • In our classification rule example, one • Alternatively, any other scheme such that c gets possible fitness function would be information roughly equal information from c1 and c2. gain over training data. 29 30 5