CONSTRUCTION OF SPECIAL OBJECTIVE FUNCTIONS IN THE OPTIMIZATION OF GEOMETRIC MODELS OF WATER SUPPLY SYSTEMS

Abstract

In the process of designing external water supply systems, the technical and economic aspects of their construction and subsequent operation should be taken into account. These indicators should be as attractive as possible from a financial and economic point of view. Accordingly, when it comes to the costs of construction and maintenance with subsequent repairs, their specific values should be minimized. If we are talking about economic characteristics associated with projected volumes of savings, then they should be maximum. In the classical approach, the optimization of the water supply system requires the construction of an objective function, the extrema of which will be found and investigated in the search for the best geometric parameters of this system.

If we consider as the objective function the cost of construction and further operation of the entire length of the pipelines of the water supply network, as the sum of the costs for its individual sections between the branch nodes, then to determine the cost of each such section, it will be necessary to set specific indicators of the corresponding costs per unit length of the pipeline. However, such specific indicators will be different in different parts of the territory, depending on the complexity of the terrain, the presence or absence of other engineering systems or structures, as well as on geotechnical conditions.

Ultimately, it will be necessary to construct a special continuous distribution function for specific indicators of the cost of the construction and operation of the links of the water supply system as a discrete geometric model on a plane — a planar or non-planar graph. Based on the corresponding objective function, it is proposed to carry out the process of forming a discrete geometric model by performing successive approximations in the calculations.

Keywords: water supply systems, discrete geometric modeling, radial basis functions.