Combining Constraint Programming and Multidimensional Scaling to solve Distance Geometry Problems

In this paper we address the merits of combining constraint propagation, typical of Constraint Programming (CP), with local search to solve problems where each method alone can perform poorly. This combined approach is used in solving distance geometry problems, namely those arisen in the determination of spatial configuration of molecular structures from Nuclear Magnetic Resonance (NMR) data. In this problem, we apply a special purpose constraint propagation with local search optimisation based on a Multidimensional Scaling (MDS) method. In this case the methods are combined by using the CP algorithm to provide an approximate solution, which the MDS algorithm then refines until the desired solution is obtained. Thus we overcome two difficulties in this type of problem: on the one hand, great precision is difficult to achieve with the CP approach due to the combinatorial explosion of enumerating the variable domains; on the other hand, a good initial guess is very important for the efficiency of an MDS algorithm.

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