Multi—facility placement on lines with forbidden zones and routing of communications

Abstract

Abstract This article is about placement of interconnected facilities (equipment) in a plane on parallel lines with forbidden zones. Placement of the facilities inside of the forbidden zones is not possible. The facilities are connected to each other and with the zones by some communications. Communications (routing of communications) between the facilities and between the facilities and zones which are placed on different lines (adjacent lines) pass through a fixed vertical component (viaduct). It is need to place the facilities on the lines such a way that the total cost of communications between the facilities and zones will be minimal. There are many practical applications of this problem in science and techniques, for example, when designing engineering devices. Some properties of the problem are formulated. A mathematical model of integer nonlinear programming of the problem is constructed. It is shown that algorithms for solving of a problem with rectangular metric without the viaduct can be used for solving of the problem under consideration.