A new branch-and-cut approach for the generalized regenerator location problem

Abstract

In optical networks, a signal can only travel a maximum distance (called optical reach) before its quality deteriorates, needing regenerations by installing regenerators at network nodes. Such an optical reach is an important property of a transmission system, which is a necessary ingredient for enabling optical bypass and thus significantly affects optical network design. In this paper, we study the generalized regenerator location problem (GRLP) where we are given a set S of candidate locations for regenerator placement and a set T of network nodes required to communicate with each other. The GRLP is to find a minimal number of network nodes for regenerator placement, such that for each node pair in T, there exists a path of which no subpath without internal regenerators has a length greater than the given optical reach. Starting with an existing set covering formulation of the problem, we first study the facial structure of the associated polytope. Making use of these polyhedral results, we then present a new branch-and-cut solution approach to solve the GRLP to optimality. With benchmark instances and newly generated instances, we finally evaluate our approach and compare it with an existing method. Computational results demonstrate efficacy of our approach.