GEOMETRIC INTERPRETATION OF THE COVERING MODEL OF A TASK AREA, WITH ACCOUNT OF RESTRICTIONS OF SPECIAL TYPE

Abstract

One of the ways to solve the problem of optimal coverage of a region is to develop a general model for covering given areas, taking into account the limitations on the basis of which a method for geometric coverage of given areas will be developed. A general coverage model consists of an objective function and associated constraints. For a more detailed understanding of the constraints of the objective function, a geometric interpretation of the constraints is necessary. The geometric interpretation of tasks makes it possible to visually present their structure, as well as identify features.

In this work, a geometric interpretation of the constraints of the problem of covering areas was carried out, taking into account restrictions of a special kind, namely: a minimum of the area of ​​mutual intersection of the objects of coverage; minimum cross-sectional area of ​​coverage objects and area additions; placement parameters of local coordinate systems of coverage objects Must belong to points in the subregion, taking into account the priority affiliation of the subregion; affiliation of subdomains to coverage objects; restrictions of a special type - that the points belong to the intersection regions of a given number of coverage objects.

The use of this model is possible in the field of civil protection in the tasks of optimal coverage of administrative-territorial units, high-risk facilities and potentially dangerous facilities with areas of departure of operational rescue units (from state, municipal, voluntary), and these high-risk facilities and potentially dangerous facilities should belong to departure areas of several units depending on the call number (which relates to the restriction of a special type).

Further research will focus on improving the coverage model for a given area, taking into account special restrictions, namely, expanding the number in the form of nonlinear, discrete, and piecewise linear expressions.

Key words: coatings, restrictions of a special type, general model, given region, subdomains.