Numerical research of placement problem on lines with forbidden zones and routing communications

Abstract

Abstract This paper discusses of placement problem of connected equipment (facilities) on parallel lines with forbidden zones. You can’t place equipment inside of forbidden zones. The facilities are connected among themselves and with zones by some kind of communications. The communications (routing of communications) between the facilities and between facilities and zones located on adjacent lines pass through the vertical equipment (viaduct). The target is to find the facilities placement on lines outside zones. Facilities do not must intersect among themselves. It is necessary to minimize the total cost of communications facilities among themselves and with zones. Practical usage of this problem is found, for example, in technology in the design of engineering devices. We consider cases when the viaduct placement is fixed and when its optimal placement is found. The goal function’s value for a fixed viaduct with a specified placement step is compared with the goal function for optimal placement of the viaduct. The results of numerical experiments are presented.