Towards a stop criterion for simple genetic algorithm, SGA

Abstract

It is presented an explicit calculation of expected waiting times, EWT, of the Simple Genetic Algorithm, SGA, taken advantage the peculiarity of the totally random situation, (maximum uncertainty) and the basic tools of combinatorics obtaining a theoretical calculation of EWT, for any size from n and l, including for the first time real cases. It is obtained an upper bound for the stop criterion average for the general case of random initial population, with multinomial distribution, and the case of equal probability for the initial states. Also it is studied the EWT for restrictive cases of multiploid populations (greater genetic diversity). The obtained results, in order of magnitude, are valid for any used value of 1-point crossover, א, and uniform mutation, μ,. The obtained results seem be very high, in real cases, as to be considered practical. The results show also that the Markov model of Nix and Vose needs to be conplemented to simulate correctly the optimum performance of the SGA.