Distributed Decomposition-Based Approaches in Global Optimization

Abstract

Recent advances in the theory of deterministic global optimization have resulted in the development of very efficient algorithmic procedures for identifying the global minimum of certain classes of nonconvex optimization problems. The advent of powerful multiprocessor machines combined with such developments make it possible to tackle with substantial efficiency otherwise intractable global optimization problems. In this paper, we will discuss implementation issues and computational results associated with the distributed implementation of the decomposition-based global optimization algorithm, GOP, [5], [6]. The NP-complete character of the global optimization problem, translated into extremely high computational requirements, had made it difficult to address problems of large size.The parallel implementation made it possible to successfully tackle the increased computational requirements in in order to identify the global minimum in computationally realistic times. The key computational bottlnecks are identified and properly addressed. Finaly, results on an Intel-Paragon machine are presented for large scale Indefinite Quadratic Programming problems, with up to 350 quadratic variables, and Blending-Pooling Problems, with up to 12 components and 30 qualities.

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