This work aims to present a new strategy for the non-overlapping disk packing problem to generate dense random assemblies. The geometric algorithm adopts an advancing front approach that uses new heuristics to determine the next positions for the incoming particles with the support of a polygonal mesh. Furthermore, we propose relocation schemes to improve the packing at the pack s interior and near the container borders. Experiments prove that our algorithm outperforms previous results, w.r.t the desired particle radii distribution function and increases the packing density and mean number of particle contacts.