1. A communication network designing circuit for multiple point communication service for permitting arbitrary communication within a predetermined range by providing a traffic amount of data inflowing from an ingress node through which data flow in from other network and a traffic amount of data flowing out from an egress node through which data is fed to other network, in an object network consisted of a plurality of nodes and connected to other network, comprising: setting means for setting a mathematical programming problem for deriving said multiple point communication service; and optimizing means for solving the mathematical programming problem set by said setting means and obtaining a path for said multiple point communication service.