Dynamic Problem of Covering a Region Bounded by a Curved Line with Circles

The article considers the analysis of specific discrete optimization problems taking into account dynamics, when changes in parameters, or the so-called "disturbance" of the system, are to be taken into account.Both single-criteria and multi-criteria cases and their application in various areas of microeconomics are considered.Fundamental issues and algorithms of discrete optimization, dynamic programming and graph theory are used to solve these problems.In particular, a multi-parameter dynamic problem of covering a region bounded by a curved line with circular objects with a varying radius is considered.Optimization of the characteristic values of objects is considered as an optimality criterion.The coverage radius, power and spatial parameters of each object are selected as parameters.A mathematical model and an algorithm of polynomial complexity have been developed for this problem.