A probabilistic database approach to the analysis of genetic algorithms

This paper takes a fresh look at some of the key ideas of genetic algorithms, using concepts drawn from the theory of majorization and probabilistic databases. We show the intimate relationships between GAs and the theory of probabilistic databases. We show how deception is well described using Saari's theorem, and its relationships with the Simpson and other paradoxes in decision theory. Reconstructability, a concept of fundamental importance in databases, is proposed as a useful substitute for deception. The database projection operator is connected with hyperplane partitions, and is used to show the nexus between point crossover operators and the join operator. Using results from probabilistic databases, we show that crossover may be considered as a majorization operator.