EE749 I ntroduction to Artificial I ntelligence Genetic Algorithms The Simple GA

Principles of Genetic Algorithms Genetic algorithms (GA’s) are iterative, adaptive, general-purpose search strategies They are driven by the following principles evolution operates on chromosomes chromosomes are strings of genes chromosomes define the characteristics of an individual less fit individuals tend not to survive (natural selection) offspring inherit properties from their parents by the process of reproduction individuals that are more successful reproduce more

I ndividuals Each possible candidate solution is an individual A set of possible solutions is maintained a population of individuals Each individual consists of a string of symbols from a fixed set of symbols (an alphabet) in the simple GA, the symbols are ‘0’ and ‘1’ each variable is represented by a binary string each variable is the equivalent of a biological gene the total string of genes is a chromosome

Fitness Functions Each chromosome is evaluated and assigned a value known as its fitness value the chromosome is split into its constituent genes each gene is decoded to give the corresponding variable’s value the variables are used to evaluate the fitness function The fitness value is used to determine the individual’s rate of reproduction the higher the fitness, the more change of being selected Each iteration is called a generation

GA Overview At each generation, each individual is evaluated by a fitness function and assigned a fitness value the fitness value somehow measures how good the individuals is as a solution to the problem New individuals are produced by selecting individuals from the current population on the basis of their fitness values Some individuals within the population may be altered by the application of genetic operators This is repeated until a decision is made to stop

GA Outline Let P represent a population and P(t) represent the state of population P at time t Then Initialise P(t = 0);/* P(0) is the starting population */ Evaluate P(t = 0);/* evaluate each individual */ WHILE ( NOT termination condition ) DO Generate P(t + 1) from P(t); /* by a process of reproduction */ t = t + 1; Evaluate P(t); END (* while*)

Selection Strategy Determine how many new offspring to produce there are many variations, but in the simple GA we produce a new population of the same size as the old Determine which individuals are to be used again, there are variations, but the simplest is termed ‘roulette’ selection each individual is assigned a probability based on their fitness as a straight proportion of overall fitness individuals are randomly picked, according to their fitness proportion, to survive into the next generation

‘Roulette’ Example For example: f(x) = x 2, x = [0, 31] No.Stringxx2x2 psps  Range     The following random numbers are generated : 0.521, 0.968, 0.112, so individuals 2, 4, 1, 4 survive to the next generation

Genetic Operators Reproduction produces a new generation selected according to fitness, but it does not introduce any new variation into the population genetic operators are applied to generate variation The two operators used in the simple GA are crossover mutation Each operator is applied to each newly selected individual with a certain probability it’s very hard to guess what these probabilities should be

Crossover Two individuals are chosen randomly a crossover point is selected at random the strings are swapped to the right of crossover point For example OLD 1 = OLD 2 = and position five is chosen, giving NEW 1 = NEW 2 =

Mutation One individual is chosen randomly one or more mutation points are selected at random the symbols in the string are changed (somehow) in simple GA with binary ‘0’s and ‘1’s, the bit is ‘flipped’ For example OLD = is selected for mutation at points 2, 4 and 8 NEW =

Operator Probabilities The probability of applying each operator is application dependent and is usually discovered empirically (i.e. by trying several alternatives) As a heuristic (‘rule of thumb’) crossover often applied so that 50 to 75% of the individuals in the population undergo crossover i.e to 0.75 probability of being applied mutation often applied to each bit with prob. 1 / (total number of bits) e.g. 10 individuals of 10 bits = 100 bits; p mutate = 0.01 per bit