EE459 I ntroduction to Artificial I ntelligence Genetic Algorithms Practical Issues: Selection

‘Roulette’ Problems The basic ‘roulette’ selection, in which each individual is assigned a probability of selection according to their fitness in proportion to total fitness, suffers from a number of problems suppose the fitness varies from e.g. -10 to +10 we could add 10 (or 11), but suppose we don’t know the lower bound of fitness as the solution is nearly reached, all fitnesses will be roughly the same, so have roughly equal chance, e.g. four individuals with x= 29, 29, 30, 30 when maximising x 2 over [0 31] have fitness proportions 0.242, 0.242, 0.258, 0.258

Fitness Scaling A frequently used solution is to ‘scale’ the fitness function in some way Fitness scaling alters (transforms) the fitness in some way, such that the fitness of an average individual is still average below average individuals have low fitness above average individuals have high fitness There are two main methods used linear scaling sigma scaling

Linear Scaling For the population, find the average (mean) fitness the minimum (min) fitness Scale by the equation f min f mean f max

Sigma Scaling For the population, find the average (mean) fitness the standard deviation (std) of fitness Scale by the equation Has a very similar effect to linear scaling, except when there are outliers

Elitism If selection of the next generation is left to chance, then there is always a possibility that the best individual in the population does not survive the GA may ‘wander off’ from a good solution In ‘elitist’ strategies, the best individual always survives to the next generation there are minor variations possible the best individual survives to the next generation and is then is the pool for crossover, mutation, etc. the best individual survives to the next generation and is ‘protected’ from any genetic operators

Overlapping Populations As a further refinement, it is also possible to not replace the entire population at each generation straight overlapping a proportion of the population –e.g. 50% survives unchanged, the other 50% undergo operators elitist overlapping temporarily allow the population size to grow by adding in new individuals (all the old ones remain) the old and the new then ‘fight’ for survival In practice, any variation that you can think of!

Other Selection Mechanisms Proportional selection calculate the fitness proportions as before multiply the fitness proportion by the population size round this to the nearest integer that many of the individual survive Tournament selection to select a new population of size N, from N repeat N times pick two individuals at random from the population the one with the highest fitness survives supposedly mirrors natural competition more closely