Selection Methods Choosing the individuals in the population that will create offspring for the next generation. Richard P. Simpson

Methods often used Fitness-Proportionate Selection (Roulette Wheel) Fitness-Proportionalte Selection (Stochastic Universal Sampling) Sigma Scaling Elitism Boltzmann Selection Rank Selection Tournament Selection Steady-State Selection

Fitness-Proportionate Selection (Roulette Wheel) Used originally by Holland Here the expected number of times an individual will bes selected to reproduce is that individual’s fitness divided by the average fitness of the population Let T= sum of the expected values of the individuals in the population. Choose a random number between 0 and T Loop through the individuals in the pop. summing the expected values until the sum is greater than r. Select the individual that puts the sum over this limit.

Fitness-Proportionate Selection (Roulette Wheel) This methods results in the expected number of offspring for each individual Does not work well for small populations To correct this SUS(stochastic universal sampling) has been proposed. Here one spins the wheel one using N equally spaced points to select N parents.

SUS(stochastic universal sampling) Fitness-proportionate selections main problem Early in the search the fitness variance in the population is high. The highly fit individuals will multiply quickly and soon dominate the pop. This is called premature convergence, ie exploration is slows rapidly. Often finds non optimal hills. Fitness-Proportionate Selection (Roulette Wheel) The rate of evolution depends on the variance of fitnesses in the population.

Sigma Scaling Used to address the previous problem In these cases raw fitness values are mapped to expected values so as to make the GA less susceptible to premature convergence. Here an attempt is made to keep selection pressure relatively constant over the course of the run. Sigma scaling, an individual’s expected value is a function of its fitness, the population mean, and the population standard deviation. standard deviation at time t mean fitness fitness

Elitism Kenneth De Jong (1975) Can be used with many of the other selection methods. Here a certain percent of the population is carried forward to the next population. This implies that the best individual ever discovered will appear in the final generations population. Sometimes elitism significantly improves performance, depends on the problem.

Boltzmann Selection Sometimes we would like to vary the selection pressure over a run. We could start with low selection pressure and increase it as we progress from generation to generation. This implies that we are searching more during the initial generations of the run and evolving faster toward the end of the run.

Rank Selection This is another attempt to prevent premature convergence. The individuals are sorted according to fitness. Ranking avoids giving the far largest share of offspring to a small group of highly fit individuals, and thus reduces the selection pressure when the fitness variance is high. before after

Baker’s ranking method Individuals are ranked according to fitness. the user chooses the expected value Max of the individual with rank N, and Min, the expected value of the individual with rank 1. Constrants Max>=0 and Sum of ExpVal =N 1<= Max<=2 and Min= 2 - Max

Truncation Selection In truncation selection individuals are sorted according to their fitness. Only the best individuals are selected for parents. These selected parents produce uniform at random offspring. The parameter for truncation selection is the truncation threshold Trunc. Trunc indicates the proportion of the population to be selected as parents and takes values ranging from 50%-10%. Individuals below the truncation threshold do not produce offspring.

Tournament Selection Two individuals are chosen at random from the population.. A random number r between 0 and 1 is chosen. If r<k (where k is a parameter say.75) the more fit individual is selected otherwise the least fit is selected. Do this twice to retrieve to parents. Fitness-proportionate methods require two passes thru the pop. for each generation. One to determine the average and one to compute the expected value of each individual. This is a very efficient method that works quite well and suits itself to parallel solutions.

Fitness Uniform Selection(FUSS)

Population Search Space