Summary: Here is a new genetic algorithm. It is built by perturbing randomly a two operator crossover-selection scheme. A new selection mechanism is used. The random vanishing perturbations are twofold: local perturbations of the individuals (mutations) and loosening of the selection pressure. When the population size is greater than a critical value which depends strongly on the optimization problem, their delicate asymptotic interaction ensures the convergence (possibly in finite time) of the population toward the ideal attractor whose populations contain all the maxima of the fitness function.