*† ‡ § This paper is concerned with the development of the numerical optimization method for anisogrid lattice composite adapters consisting of regular, dense and symmetric systems of hoop and geodesic ribs made by automatic filament winding. Optimisation is performed by means of numerical minimization of the shell mass with respect to five design variables which characterize the lattice structure, i.e., the number of geodesic ribs, the number of hoop ribs, the shell thickness and the widths of hoop and geodesic ribs. Design constraints are analytically formulated and allow for the main failure modes for axially compressed conical lattice structures, i.e., material failure under compression of geodesic ribs, local buckling of geodesic ribs and global buckling of the shell. Application of the proposed numerical optimization method results in about 15% weight saving for the lattice structure with respect to the existing adapters designed analytically and, respectively, in the corresponding increase of the space launcher efficiency.