Research Properties Sets of Effective Criteria Values in the Optimization Problem Engineering Network

Abstract

The problem of choosing a project for a developing engineering network is considered. A mathematical model of a developing engineering network, which even at the design stage allows us to take into account the possibility of expanding or reconstructing the system in case new customers are added to the target product, which is a two-criteria block programming problem with separable criterion functions. In the proposed mathematical model, the first criterion reflects the need to minimize financial costs construction and operation of the network, in order to ensure portability of the target product delivered at the time of designing. The second criterion expresses the requirement of minimizing financial costs for the future development of the system in the future from the achieved level, provided that the vector of the system’s development is known before the engineering network design starts. Taking into account the criteria preference vector, which allows you to take into account the inequality of both cost criteria in the constructed mathematical model and makes it possible comparing criteria of different orders makes it possible to replace the two-criterion optimization problem of choosing a project of a developing engineering network with a single-criterion mathematical programming problem without changing the set of solutions to the problem. The properties of the set of effective vectors of criteria values, which arise when solving a single-criteria optimization problem of choosing an engineering network project variant with a variation of all possible values of the criteria preference vector, have been formulated and investigated, which will make it possible to build dialogue procedures, during the execution of which the approximation of the set of values of the problem criteria will be carried out.