A Stochastic/Perturbation Global Optimization Algorithm for Distance Geometry Problems

We present a new global optimization approach for solving exactly or inexactly constrained distance geometry problems. Distance geometry problems are concerned with determining spatial structures from measurements of internal distances. They arise in the structural interpretation of nuclear magnetic resonance data and in the prediction of protein structure. These problems can be naturally formulated as global optimization problems which generally are large and diicult. The global optimization method that we present is related to our previous stochastic/perturbation global optimization methods for nding minimum energy conngurations, but has several key diierences that are important to its success. Our computational results show that the method readily solves a set of artiicial problems introduced by Mor e and Wu that have up to 343 atoms. On a set of considerably more diicult protein fragment problems introduced by Hendrickson, the method solves all the problems with up to 377 atoms exactly, and nds nearly exact solution for all the remaining problems which have up to 777 atoms. These preliminary results indicate that this approach has very good promise for helping to solve distance geometry problems.