ACM Transactions on Mathematical Software (TOMS)
Bayesian stopping rules for multistart global optimization methods
Mathematical Programming: Series A and B
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
The design and analysis of parallel algorithms
The design and analysis of parallel algorithms
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
A parallel Monte Carlo search algorithm for the conformational analysis of proteins
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
An optional hypercube direct N-body solver on the connection machine
Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Recent advances in global optimization
Minimizing the Lennard-Jones potential function on a massively parallel computer
ICS '92 Proceedings of the 6th international conference on Supercomputing
A discrete-continuous algorithm for molecular energy minimization
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Experiments with simulated annealing
DAC '85 Proceedings of the 22nd ACM/IEEE Design Automation Conference
Global Optimization on Funneling Landscapes
Journal of Global Optimization
Applying Two-Level Simulated Annealing on Bayesian Structure Learning to Infer Genetic Networks
CSB '04 Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference
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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.