The Schema Theorem and the Misallocation of Trials in the Presence of Stochastic Effects

Traditional selection in genetic algorithms has relied on reproduction in proportion to observed fitness. There has been recent interest in assessing the result of proportional selection on schemata in the presence of random effects (e.g., noisy evaluation of solutions). The analysis presented here indicates, in contrast with previous literature, that the introduction of noise to the evaluation of solutions can change the expected sampling of schemata, even when the noise is zero mean. Unfortunately, this “misallocation of trials” can also result simply from random initialization of a population.