Energy-based pruning devices for the BP algorithm applied to Distance Geometry

The Molecular Distance Geometry Problem (MDGP) is the one of finding an embedding of a molecular graph in the three dimensional space, where graph vertices represent atoms and edges represent known distances between some pairs of atoms. The MDGP is a constraint satisfaction problem and it is generally cast as a continuous global optimization problem. Moreover, under some assumptions, this optimization problem can be discretized and so that it becomes combinatorial, and it can be solved by a Branch & Prune (BP) algorithm. The solution set found by BP, however, can be very large for some instances, while only the most energetically stable conformations are of interest. In this work, we propose and integrate the BP algorithm with two new energy-based pruning devices. Computational experiments show that the newly added pruning devices are able to improve the performance of the BP algorithm, as well as the quality (in terms of energy) of the conformations in the solution set.