Genetic Algorithms and the Variance of Fitness

This paper presents a method for calculat ing the variance of schema fitness using Walsh t ransforms. The computation is important for underst anding the performance of genet ic algorithms (GAs) because most GAs depend on the sam pling of schema fitness in populat ions of modest size, and the variance of schema fitn ess is a primary source of noise that can prevent proper evaluation of building blocks, th ereby causing convergence to oth er-than-global opt ima. The paper also applies these calculations to th e sizing of GA pop ulations and to the adjust ment of the schema th eorem to account for fitness variance; the exte nsion of the variance computation to nonun iform populations is also considered . Taken toget her these results may be viewed as a step along the road to rigorous convergence proofs for recombin ative genet ic algorithms.