Optimization Models and Algorithms for Network Problems of Resours’ Distribution

The efficient algorithms for nonlinear programming problems for calculating networks have been offered, as well as the new network models to determine the optimal flows and distribution of resources have been constructed. The problems with nonlinear objective functions of general form and network structure of restrictions, which allow reaching quite a wide range of networks using common approach, were considered. For calculations the modifications of well-known methods of nonlinear programming were applied.

Dynamic Models with a Generalized Conservation Law to Control the Flows Distribution in Networks

This paper considers general principles for constructing and investigating mathematical models of natural resources flow distribution along the energy network. Based on classical and generalized conservation laws we construct the complex of dynamic models for flow distribution in networks taking into account the ability to create reserves of energy resources and the uncertainty of information objectively inherent in large power systems. Also, we exemplify the issues of water traffic control in the channels of water irrigation systems and gas pipelines.

Optimization of Storehouses Filling in Flow Distribution Problems

The present paper aims to construct the mathematical model of transportation and distribution of a certain item among consumers. This model takes into account stocking in tanks for temporary storage. To that end, we propose the algorithms based on the effective methods of nonlinear programming. Due to the general problem statement, these algorithms can be used for calculation of various types of distribution networks.

Flow distribution for complex ring topology networks

This study makes a case for the nonlinear flow distribution problem, whose dimension is equal to the quantity of arcs of a network that is transformed to a problem without restrictions, whose dimension depends on the quantity of the closed cycles of a network. To solve the problem of the small dimension, we employ the effective nonlinear programming methods.