The Role of Selection in Genetic Algorithms

Genetic Algorithms have gained wide popularity due to their conceptual simplicity and their ability to obtain approximate solutions for complex searching and optimization problems. Their wide applicability contrasts with their rather undeveloped theoretical basis. In particular, the convergence of genetic algorithms has been one of the most challenging theoretical issues in the evolutionary computation area. We provide a careful analysis of the structure of the classical genetic algorithm. We demonstrate that, when a Genetic Algorithm is used to maximize a function, selection is the process that assures convergence to the global optimum (asymptoticly in the limit) for the tness of the population. Our results have several practical implications; among these, the number of generations up to which reasonable improvement could be expected may be approximated ahead or during the working of the genetic algorithm.