Inverse optimization in high-speed networks

Abstract

A general approach is presented for handling the following inverse optimization problem: given solutions to each member of a family of combinatorial optimization tasks on a common underlying set, find a positive linear objective function (weighting) on the common underlying set that simultaneously makes each solution optimal in its own optimization task. Our motivation stems from the inverse shortest path problem that is made practically important in high-speed telecommunication networks by the Asynchronous Transfer Mode Forum's Private Network–Network Interface architecture, in which route finding can be based on administrative weights. Different variants of the problem are investigated, including uniqueness requirements and reserve routes.