This work develops new strategies to robustly apply Thrust Network Analysis (TNA) for the assessment of unreinforced masonry (URM) structures studied within the frame of limit analysis. It formulates and solves a nonlinear optimisation problem on thrust networks considering relevant constraints for the assessment of URM structures. Geometrical and force constraints are include such as the consideration of the structural envelope and bounds on the reaction forces. The objective functions studied correspond to the minimum and maximum horizontal thrusts of the vaults. To evaluate the level of stability of an existing structure, this work develops a methodology to estimate the geometric safety factor (GSF) and the minimum thickness of masonry vaults by solving sequential optimisation problems for increasingly tightened geometrical bounds. This procedure is implemented in the open-source, Python-based tool, named compas_tna and illustrated here on two- and three-dimensional applications that are relevant for the structural analysis of historical constructions.