A genetic algorithm is used to optimize the nuclear fuel reload for a boiling water reactor, and an order coding is proposed for the chromosomes and appropriate crossover and mutation operators. The fitness function was designed so that the genetic algorithm creates fuel reloads that, on one hand, satisfy the constrictions for the radial power peaking factor, the minimum critical power ratio, and the maximum linear heat generation rate while optimizing the effective multiplication factor at the beginning and end of the cycle. To find the values of these variables, a neural network trained with the behavior of a reactor simulator was used to predict them. The computation time is therefore greatly decreased in the search process. We validated this method with data from five cycles of the Laguna Verde Nuclear Power Plant in Mexico.