UDC 621.396
The block task of targeting (CR) carriers in the disarming strategic operation of the attacking side's nuclear forces is being studied. The article is a further development in terms of accounting for the blockiness arising from the grouping of attack carriers by range and belonging to one of the parts of the nuclear triad. The minimum mathematical expectation of the number of warheads (BB) of the defend-ing side (in megaton terms) is used as an efficiency criteri-on, which, with a given guarantee, will be delivered in re-sponse to the attacking targets. The relationship between the blocks of the CR matrix is carried out using a penalty function that takes into account the difference in the values of the target variables in the intersecting parts of neighbor-ing blocks. The results of a numerical experiment to verify the practical convergence of B.T.Polyak's method in a model example are presented and the acceleration coeffi-cient due to parallelization is calculated. To test the hypothesis that the asymptotic acceleration coefficient will be equal, it is necessary to use a multipro-cessor computing complex (MVC) with parallel data transmission to processors. This research is supposed to be carried out in a separate paper. The results of the statisti-cal experiment show that the acceleration coefficient is greater than unity, and subsequently asymptotically equal to n, which has so far been proven only theoretically. It is shown that the posed block CR problem can be solved by the method of B.T.Polyak. The main result of the work is the decomposition of the problem based on the method of B.T.Polyak, which can serve as a methodological basis for parallelizing the problem.
block assignment problem, penalty for mismatch of block assignment, decomposition method based on B.T.Polyak's algorithm, parallelization of the problem based on decomposition
Работа основана на результатах из [1], [2] и является ее дальнейшим развитием в части учета блочности, возникающей из группирования носителей нападения по дальности действия и принадлежности к одной из частей ядерной триады. Такие задачи распределения целевых каналов по групповым целям применительно к задачам флота изучались в [3]. Поставленная в [4] блочная задача ЦР может быть решена методом Б.Т.Поляка [4]. Основным результатом работы является декомпозиция задачи на основе метода Б.Т. Поляка, который может служить методической основой распараллеливания задачи. Классическая постановка задачи целераспредееления изучалась нами в [5].
В общетеоретическом плане блочные постановки задачи о назначении могут использоваться как основа построения соответствующих цифровых платформ распределения заданий по исполнителям [6, 7]. Поэтому декомпозиция блочных ТЗ, к которым относится задача ЦР в обезоруживающей СОЯС [8], поставленная в [9], является новой и актуальной задачей, а ее решение методом Б.Т.Поляка может служить основой для построения соответствующей схемы распараллеливания, основанной на численном методе решения.
II. Блочная задача ЦР носителей в обезоруживающей СОЯС
Следуя [10] предположим, что исходя из принятого нашим государством (сторона ) ненападения первым на другие страны, когда противник наносит удар первым (наиболее тяжелые условия для обороняющегося), в качестве показателя эффективности боевых действий стороны
целесообразно принять количество боевых блоков (ББ) обороняющейся стороны
, которое с заданной гарантией
будет доставляться в ответных действиях к объектам нападающего
. При этом нападающий будет стремится минимизировать количество ядерных средств в ответных действиях обороняющегося
:
|
. |
(1) |
где
|
. |
(2) |
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