Tournament Selection, Iterated Coupon-Collection Problem, and Backward-Chaining Evolutionary Algorithms

Tournament selection performs tournaments by first sampling individuals uniformly at random from the population and then selecting the best of the sample for some genetic operation. This sampling process needs to be repeated many times when creating a new generation. However, even upon iteration, it may happen not to sample some of the individuals in the population. These individuals can therefore play no role in future generations. Under conditions of low selection pressure, the fraction of individuals not involved in any way in the selection process may be substantial. In this paper we investigate how we can model this process and we explore the possibility, methods and consequences of not generating and evaluating those individuals with the aim of increasing the efficiency of evolutionary algorithms based on tournament selection. In some conditions, considerable savings in terms of fitness evaluations are easily achievable, without altering in any way the expected behaviour of such algorithms.