The problem of covering the fields by the circles in the task of optimization of observation points for ground videomonitoring systems of forest fires

Abstract

The problem of covering the area by circles, mathematical model of the coating offers a new coverage criteria based on which analytically describes the range of permissible solutions of the problem. Based on the analysis of the properties of the model, it is shown that the solution of the problem can be reduced to the solution of problems of nonlinear programming sequence. At the moment, there are systems of video monitoring forest land. An important class of geometric design problems is problems of irregular covering the field by geometric objects, as well as regular. In the problems of covering it is set up a claim that all points of the field were covered by geometric objects, while the conditions of non-intersection of objects between themselves and their placement in the field may be violated. One problem with the design of terrestrial video monitoring systems is to optimize the placement of observation points. optimal placement of towers problem can be formulated as a coating task. An approach to the placement of towers terrestrial video monitoring of forest fires, the main stage of which is set forth search method local extremum in the problem coverage area circles of varying radius. There is build a mathematical model to optimize the placement of variable radius circle and on its basis – the development of methods of solution and proposed an approach to obtaining a local extremum of covering problem.