An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms

The frequency with which various elements of the search space of a given evolutionary algorithm are sampled is affected by the family of recombination (reproduction) operators. The original Geiringer theorem tells us the limiting frequency of occurrence of a given individual under repeated application of crossover alone for the classical genetic algorithm. Recently, Geiringer's theorem has been generalized to include the case of linear GP with homologous crossover (which can also be thought of as a variable length GA). In the current paper we prove a general theorem which tells us that under rather mild conditions on a given evolutionary algorithm, call it A, the stationary distribution of a certain Markov chain of populations in the absence of selection is unique and uniform. This theorem not only implies the already existing versions of Geiringer's theorem, but also provides a recipe of how to obtain similar facts for a rather wide class of evolutionary algorithms. The tec...

• Type: Journal
• Year: 2006
• Where: EC
• Authors: Boris Mitavskiy, Jonathan E. Rowe
• Keywords: Classical Genetic Algorithm, EC 2006, ECommerce, Evolutionary Algorithms, Genetic Algorithms