Parallel global optimization: numerical methods, dynamic scheduling methods, and application to molecular configuration

Abstract : Global optimization problems are computationally extensive problems that arise in many important applications. The solution of very large practical global optimization problems, which may have thousands of variables and huge numbers of local minimizers, is not yet possible. It will require efficient numerical algorithms that take advantage of the properties of the particular application, as well as efficient utilization of the fastest available computers, which will almost certainly be highly parallel machines. This paper summarizes our research efforts in this direction. First, we describe general purpose adaptive, asynchronous parallel stochastic global optimization methods that we have developed, our computational experience with them. Second, we describe several alternative dynamic scheduling algorithms that are required to control such dynamic parallel algorithms on distributed memory multiprocessors, and compare their performance in the context of our parallel in the context of our parallel global optimization methods. Third, we discuss the application and refinement of these methods to global optimization problems arising from the structural optimization of chemical molecules, and present preliminary computational results on some problems with between 15 and 100 variables. This work includes the development of new algorithmic features that are motivated by the molecular configuration problem but are applicable to a wider class of large scale, partially separable global optimization problems.