In this paper we address the multiperson decision making problem when the preferences of each individual is represented by a generalized additive independent (GAI) utility on a product set (the size of which forbids any attempt of exhaustive enumeration of its elements). We focus our attention on finding an optimal compromise solution when it corresponds to maximize a Choquet integral over the elements on the product set. We propose a fast procedure for the exact determination of this optimal compromise solution. This procedure relies on a ranking algorithm that enumerates top-k-solutions of a GAI-Network until a stop condition is met. Finally, we provide results of numerical experiments that indicate the practical efficiency of our procedure.