The multi-layered network design problem

We address the problem of designing a network built on several layers. This problem occurs in practical applications but has not been studied extensively from the point of view of global optimisation, since the problem of designing a single-layered network is complex. An example of an application is the design of a virtual network (Internet Protocol) built on a sparse optical transport network. We suggest a mathematical formulation without any flow variables or path variables, based on metric inequalities. We give numerical results for two-layered network instances obtained with a global method giving optimal solutions and we compare them with approximate results obtained by solving the problem in two steps.