Parallel two-level simulated annealing

In this paper, we propose a new kind of simulated annealing algorithm called two-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 and implemented on the Thinking Machines CM-5. With the full Lennard-Jones potential function, we were able to get satisfactory results for clusters with as many as 100, 000 atoms. 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 as large as these have never been reported before.