A New Large-Scale Global Optimization Method and Its Application to Lennard-Jones Problems
COLORADO UNIV AT BOULDER DEPT OF COMPUTER SCIENCE
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We describe a new stochastic global optimization algorithm that is oriented towards solving large scale problems, and present the results of applying it to a class of problems in molecular chemistry. Our new algorithm incorporates some full-dimensional random sampling and local minimizations as in existing stochastic methods, but the keys to its success are two new phases that concentrate on selected small dimensional subproblems of the overall problem. These phases constitute a major portion of the computational effort of the new method, and represent a significant departure from existing stochastic methods. Computational results on Lennard-Jones problems show that the new method is considerably more successful than any other method that has tried to solve these problems without using prior knowledge of the solution structure in its algorithm, and that our method finds the presumptive global minimizer in all cases with up to 90 variables as well as in some larger cases. On the other hand, on most problems with over 100 variables, our method does not find as good a solution as has been found by the best special purpose methods for Lennard-Jones problems. This illustrates the inherent difficulty of large scale global optimization.
- Numerical Mathematics
- Statistics and Probability