Intro to AI Genetic Algorithm Ruth Bergman Fall 2002

Imitating Nature Aspect of the evolution of organisms: The organisms that are ill-suited for an environment have little chances to reproduce (natural selection) Conversely, the best fitting have more chances to survive and reproduce

Imitating Nature Reproduction: Offspring are similar to their parents Random mutations occur and they can bring to better (or worse) fitting individuals “The Origin of the Species on the Basis of Natural Selection” C. Darwin (1859) Encoding: An organism is fully represented by its DNA string, that is a string over a finite alphabet (4 symbols) Each element of this string is called gene

Genetic Algorithm (GA) Developed by John Holland in the early 70’s Optimization and machine learning techniques inspired from the process of natural evolution and evolutionary genetics –Solutions are encoded as chromosomes –Search proceeds through maintenance of a population of solutions –Reproduction favors “better” chromosomes –New chromosomes are generated during reproduction through processes of mutation and cross over, etc.

GA Framework selection mutation cross over population ABCDABCD Fitness evaluation Search space reproduction

GA Procedure Start with a population of N individuals 1.Apply the fitness function to all the individuals 2.Select the pairs of individuals for reproduction (repetition allowed). 3.Each pair generates two children (reproduction with cross-over) 4.Apply a random mutation to the children. The children become the next generation 5.Apply steps 1,2,3 until some termination criteria applies

Encoding Scheme An individual (an organisms) is intended to be a possible solution for the problem you want to solve An individual is represented by a binary string. Such a string is intended to be the complete description of the individual Example: Suppose you have to find a number between 0 and 255, which binary representation contains the same number of 1s and 0s. A individual is a string of 8 bits, ex: h == 126

Fitness Function A fitness function is a function that says how good is a solution, i.e. how well an individual fit the environment Example note that the fitness function gets the minimum value (i.e. 0) when or and the maximum value (i.e. 8) when

The Initial Population

Optimization  local optimum 방지 GA Search Method Hill-climbing Method cf.

Selection Roulette wheel selection –compute each individual’s contribution to the global fitness as –The choice of the pairs for reproduction consists of randomly choosing the individuals (with replacement) with distribution given by P encodingfitness P(-) ABCDABCD Roulette Wheel

Crossover –Randomly choose a cross over point “c”, i.e. a number between 1 and n – return two children: one composed by the first c bits of the first parent and the last n-c bits of the second parent, the other composed by the first c bits of the second parent and the n-c bits of the first parents c

Mutation mutation on individuals: some of the children’s bits are changed (with a small, independent probability maximum found

Stopping Criteria Convergence: –A population is said to converge when all the genes have converged, I.e. when the value of every bit is the same at least in the 95% of the individuals in the population Since convergence is not guaranteed, we must consider other stopping criteria: –Number of generations –Almost constant value of the best fitting individual –Almost constant value of the average fitness of the population

Parameter Settings Population size –How many chromosomes are in population Too few chromosome  small part of search space Too many chromosome  GA slow down –Recommendation : 20-30, Probability of crossover –How often will be crossover performed –Recommendation : 80% -95% Probability of mutation –How often will be parts of chromosome mutated –Recommendation : 0.5% - 1%

Genetic Programming One of the central challenges of CS is to get a computer to do what needs to be done, without telling it how to do it –Automatic programming (or program synthesis) GP is a branch of genetic algorithms Main difference between GP and GA –Representation of the solution (computer program) GA: a string of numbers –fixed-length character strings GP: computer program (lisp or scheme) –Represent hierarchical computer programs of dynamically varying sizes and shapes