This chapter investigates Boltzmann selection, a tool for controlling the selective pressure in optimizations using genetic algorithms. An implementation of variable selective pressure, modeled after the use of temperature as a parameter in simulated annealing approaches, is described. The convergence behavior of 112optimization runs is illustrated as a function of selective pressure; the method is compared to a genetic algorithm lacking this control feature and is shown to exhibit superior convergence properties on a small set of test problems. An empirical analysis is presented that compares the selective pressure of this algorithm to a standard selection procedure.
Then, in order to understand these results in a broader context, an analytical discussion of selection procedures used in genetic algorithms is presented. A unified framework for discussing and comparing procedures is developed and used to compare proportional, Boltzmann, power law, and sigma truncation selection procedures. Two properties, translation and scale invariance, are defined and studied for each of these procedures. Selective pressure is investigated for proportional and Boltzmann selection. It is proven that, for a normal distribution of individuals in the optimization space, proportional scaling decreases selective pressure during the course of an optimization run.