A hybrid strategy based on artificial neural network/genetic algorithms is suggested to optimize the mechanical properties of cellular solids. Three-dimensional void structures are generated using a random sequential addition algorithm in which spherical void particles are positioned in a solid phase matrix with a control of their size distribution and overlapping. This allows us to create an open-cell structure with relative densities in the range 0.1-0.3. Finite element calculation is used to assess the effective Young's modulus as a function of generation parameters. Relative Young's moduli in the three main directions of the solid are isotropic with respect to the generation algorithm constraints and adhere qualitatively to the common theory on effective properties of open-cell structures. Moreover, the effective response is found to be correlated to the randomness of the void structure, which exhibits, in some cases, an ordered cell configuration. In order to quantitatively describe these correlations and to check the sensitivity of the mechanical response to the structural features in addition to sampling and discretization levels, the hybrid strategy described above is considered. The main motivation was to decrease the finite element simulation time by predicting, where possible, the correlations instead of calculating them. In addition, the use of the hybrid strategy informs about the optimal mesh with respect to the generation variables. This strategy proved to be an efficient technique in enhancing the predictions and complementary to the finite element methodology.