A method to reduce the dimension of the initial search space in an optimizati- on problem is proposed. The method consists in the identification of the sub-space with the greatest impact on the cost or fitness function. Optimization is restricted in this sub-space, achieving, thus, a considerable reduction of the computational cost, due to more effective exploration. The Model Reduction is the result of mathematical analysis performed on approximations of the cost/fitness function supplied by Artificial Neural Networks, trained during the optimization process. The Model Reduction is coupled with Genetic Algorithms and performed in a self-adaptive way during the genetic evolution.