A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing

This work studies the build-up method for the global minimization problem for molecular conformation, especially protein folding. The problem is hard to solve for large molecules using general minimization approaches because of the enormous amount of required computation. We therefore propose a build-up process to systematically construct the optimal molecular structures. A prototype algorithm is designed using the anisotropic effective energy simulated annealing method at each build-up stage. The algorithm has been implemented on the Intel iPSC/860 parallel computer, and tested with the Lennard-Jones microcluster conformation problem. The experiments showed that the algorithm was effective for relatively large test problems, and also very suitable for massively parallel computation. In particular, for the 72-atom Lennard-Jones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.     

Molecular conformation on the CM-5 by parallel two-level simulated annealing

In this paper, we propose a new kind of simulated annealing algorithm calledtwo-level simulated annealing for solving certain class of hard combinatorial optimization problems. This two-level simulated annealing algorithm is less likely to get stuck at a non-global minimizer than conventional simulated annealing algorithms. We also propose a parallel version of our two-level simulated annealing algorithm and discuss its efficiency. This new technique is then applied to the Molecular Conformation problem in 3 dimensional Euclidean space. Extensive computational results on Thinking Machines CM-5 are presented. With the full Lennard-Jones potential function, we were able to get satisfactory results for problems for cluster sizes as large as 100,000. A peak rate of over 0.8 giga flop per second in 64-bit operations was sustained on a partition with 512 processing elements. To the best of our knowledge, ground states of Lennard-Jones clusters of size as large as these have never been reported before.Also a researcher at the Army High Performance Computing Research Center, University of Minnesota, Minneapolis, MN 55415     

Optimization methods for computing global minima of nonconvex potential energy functions

The minimization of potential energy functions plays an important role in the determination of ground states or stable states of certain classes of molecular clusters and proteins. In this paper we introduce some of the most commonly used potential energy functions and discuss different optimization methods used in the minimization of nonconvex potential energy functions. A very complete bibliography is also given.Also a researcher at the Army High Performance Computing Research Center, University of Minnesota, Minneapolis, MN 55415     

Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography

The simulated annealing (SA) algorithm is a well-established optimization technique which has found applications in many research areas. However, the SA algorithm is limited in its application due to the high computational cost and the difficulties in determining the annealing schedule. This paper demonstrates that the temperature parallel simulated annealing (TPSA) algorithm, a parallel implementation of the SA algorithm, shows great promise to overcome these limitations when applied to continuous functions. The TPSA algorithm greatly reduces the computational time due to its parallel nature, and avoids the determination of the annealing schedule by fixing the temperatures during the annealing process. The main contributions of this paper are threefold. First, this paper explains a simple and effective way to determine the temperatures by applying the concept of critical temperature (T_C). Second, this paper presents systematic tests of the TPSA algorithm on various continuous functions, demonstrating comparable performance as well-established sequential SA algorithms. Third, this paper demonstrates the application of the TPSA algorithm on a difficult practical inverse problem, namely the hyperspectral tomography problem. The results and conclusions presented in this work provide are expected to be useful for the further development and expanded applications of the TPSA algorithm.