Study of the mathematical models of optimal partitioning for particular cases - Firsov, Alexander (Eastern-European Journal of Enterprise Technologies, 2018)
The basic problem of optimal sets partitioning (OSP) for the case, where a segment of a plane curve is a set, was stated. The problem is stated as follows: let us assume there is a segment of a plane curve, it is required to place on it a specified number of sources of a certain resource and allocate each point of the curve to a particular source. In addition, it is necessary to minimize the costs of transportation of a resource is from the sources to the corresponding points of the curve along the shortest route. The basic problem was refined by taking into account geometrical characteristics of the curve. For this, the function of the cost was changed according to such parameters as the length of the curve and its curvature. As a result, new statements of OSP problems were obtained. It was shown that geometric characteristics of the curve correspond to a subject area. Each of the problems was solved by using the known methods and the numerical experiment was conducted. Analysis of the obtained results was carried out. Thus, the general OSP theory was supplemented with the new models that are applicable for solving optimization problems with taking into account surfaces of a relief.