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Параллельная оптимизация

One of the prospective trends in improving optimization process efficiency is the use of computers with multiple processors. In this case, the reduction of elapsed (clock) computing time can be achieved through solution time reduction by means of parallel computations "inside" the model, as well as by adaptive organization of the optimization process for parallel computations. The first approach implies the use (or development) of mathematical analysis models suitable for using parallel processors. The latter makes it necessary to develop or to modify the corresponding optimization methods.

We have developed the new optimization algorithm, which uses parallel processors. Our algorithm allows us to reach the speed-up parameter value that exceeds the total number of operational CPUs. Например, при использовании 20 CPU может быть достигнуто ускорение процесса поиска оптимального решения в 40 и более раз. Наши алгоритмы позволяют максимально использовать имеющиеся в распоряжении пользователя вычислительные ресурсы, так как число одновременно используемых процессоров не зависит от размерности задачи оптимизации. Так, при 10 варьируемых параметрах возможно использование 1, …,20,..100 и более CPU. Использование наших алгоритмов параллельной оптимизации позволяет ставить и реально решать задачи оптимизации, когда для вычисления одного значения критерия оптимизации необходимы часы, либо даже десятки часов процессорного времени (например, 3D CFD ). Объединение наших параллельных процедур с алгоритмами многоуровневой оптимизации позволяет существенно расширить область решения сложных практических проблем.
Схема IOSO алгоритма параллельной оптимизации
Master processor carries out operation of the main IOSO unit. This unit is called data analysis and moving strategy unit. Within the frameworks of the given unit, analysis of stored information is performed for the variables, constraints, and optimization criteria. The neighborhood of the current solution is selected, the promising areas for further search are determined, and formulation of the sequence of the next operations is performed. Three possible actions could be performed in the end of the current iteration:

I) Optimization process termination. This is performed by the stop-criterion activation when working in automatic operation mode, or if a researcher terminates the process when working in an interactive operation mode.

II) Experiment design generation. This involves generation of a set of points in the initial search area (at the initial stage of optimization), or in a promising sub-region of the search area. Then, for this set of points, both the optimization criteria calculations and parallel constraints calculations are performed by slave processors. The obtained information is transmitted back to the unit of data analysis and moving strategy and the next iteration is started.

III) The most probable action is the following:

a) Synthesis of the response surface functions for optimization criteria and constraints. These functions differ in both structure and search area. The synthesis is performed with the help of slave processors.

b) Optimization of the obtained approximation functions using slave processors. The result of this step is a set of points which are candidate solutions of the initial optimization problem.

c) Evaluation of true values of optimization criteria and constraints for the candidate solutions using slave CPUs. The obtained information is transmitted back to the data analysis and moving strategy unit, and the next iteration is started.

The main difference between the developed parallel optimization algorithm and the basic IOSO algorithm is in the information received by the data analysis and moving strategy unit. This information is not for a single point only, but for a whole set of points, the number of which is equal to the number of slave processors. This can affect the algorithm work efficiency. To evaluate this effect, a testing of the developed algorithm has been carried out.

© Сигма Технология 2001. E-mail: company@iosotech.com