A P q (t, k, n) q-packing design is a selection of k-subspaces of F n q such that each t-subspace is contained in at most one element of the collection. A successful approach adopted from the Kramer-Mesnermethod of prescribing a group of automorphisms was applied by Kohnert and Kurz to construct some constant dimension codes with moderate parameters which arise by q-packing designs. In this paper we recall this approach and give a version of the Kramer-Mesner-method breaking the condition that the whole q-packing design must admit the prescribed group of automorphisms. Afterwards, we describe the basic idea of an algorithm to tackle the integer linear optimization problems representing the q-packing design construction by means of a metaheuristic approach. Finally, we give some improvements on the size of P 2 (2, 3, n) q-packing designs.