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Markov Vitaly Nikolaevich
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•
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professor
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• Kuban State Technological University
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Articles count: 3
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SYNTHESIS OF A SYSTEM OF OPTIMIZATION OF CONSUMPTION OF NONRENEWABLE RESOURCES
DescriptionThe NPproblem of discrete optimization of consumption of nonrenewed resources is considered. The weights of edges of the graph of resources set cost of consumed resources. It is offered to use the transitions of discrete system conditions on the complete graph with number of vertexes, equal to quantity of discrete resources, for the problem decision. The purpose of such system is construction of a chain of the predetermined length and the minimum weight on the complete graph. The problem factor is factorial growth of number of variants of chains on graph at linear growth of quantity of resources. The main idea consists in a use of found statistical regularities of transition ranks of discrete system at construction of chains with the minimum weight on graphs of the any size. Use of ranks allows to abstract from concrete weights of transitions and to find the property inherent optimum. In this article, the structure of discrete system is presented and its functioning in a mode of analysis of ranged decisions is described. Distinctive feature of the presented system is use of the generator of ranks, the generator ranged chains and the statistics block. They are used for definition of distribution of suboptimum decisions. In addition, the article contains the description of structure and functioning of discrete system in a mode of synthesis of suboptimum decisions on the basis of the found distribution of probabilities of local decisions. Novelty of the offered approach to construction of solvers of NPproblems is in using empirical functions from ranks of local decisions to control the search

Description
The NPproblem of discrete optimization of consumption of nonrenewable resources is considered in the article. It is offered to use transitions of NPsystem conditions on the complete graph with number of vertexes, equal to quantity of discrete resources, for the problem decision. The purpose of such system is construction of a chain of the predetermined length and the minimum weight on the complete graph. The length of a chain defines quantity of the consumed resources. The problem factor is factorial growth of number of variants of chains on graph at linear growth of quantity of resources. The main idea consists in a finding of statistical regularities of ranks of transitions of NPsystem at construction of chains with the minimum weight on graphs of the small size. Use of ranks allows to abstract from concrete weights of transitions, which are variables for each problem of optimization, and to find the patrimonial feature of all optimum decisions. It is offered to use the found regularities to solve the problems of the big dimension. As a result of researches, it has been defined that probabilities of ranks of transitions are described by geometric distribution. In the article, the algorithm of definition of parameter of geometrical distribution for a rank of each transition depending on the initial and consumed quantity of resources is presented. Realization of a method of generating of suboptimum chains is based on use of generators of the pseudorandom numbers setting values of each rank of transition of NPsystem according to geometrical distribution of probabilities. It is offered two variants of generators of ranks of chains to use. Computer experiment has shown useful effect of an offered method at the decision of problems of small and average dimension

Description
The article considers discrete automatic machines with memory, designed for searching the values of parameters of the system optimizing a merit figure of the system, described by some criterion function. The problem of multiple parameter optimization is shown as a problem of discrete optimization by means of representation of values of parameters of the optimized system in the form of a set of discrete values with a specified step of digitization