A direct numerical optimization method is developed to approximate the one-sector stochastic growth model. The feedback investment policy is parameterized as a neural network and trained by a genetic algorithm to maximize the utility functional over the space of time-invariant investment policies. To eliminate the dependence of training on the initial conditions, at any generation, the same stationary investment policy (the same network) is used to repeatedly solve the problem from differing initial conditions. The fitness of a given policy rule is then computed as the sum of payoffs over all initial conditions. The algorithm performs quite well under a wide set of parameters. Given the general purpose nature of the method, the flexibility of neural network parametrization and the global nature of the genetic algorithm search, it can be easily extended to tackle problems with higher dimensional nonlinearities, state spaces and/or discontinuities. © Springer Science+Business Media, Inc. 2006.