Benders decomposition algorithms for the fixed-charge relay network design in telecommunications

In translucent networks, signal regenerators that operate based on optical/electrical/optical (O/E/O) conversion are employed to handle the problems of physical impairments and resulting signal quality issues in long-distance transmissions. Regenerators are placed at the relay nodes in a translucent network in such a way that the optical signals are not transmitted farther than a threshold distance without a 3R regeneration (reamplification-reshaping-retiming). In this study, we consider a fixed-charge relay network design (FCRND) problem whose applications are found mainly in long distance translucent optical telecommunication networks. From a modeling perspective, FCRND combines prominent features of the uncapacitated single-assignment hub location (location of relays points) and the fixed-charge network design problems (choice of transmission links in the network and routing of signals) while additionally considering distance-based coverage constraints. We devise Benders decomposition based solution methodologies in which the algorithmic performance is further enhanced by devising strengthened and disaggregated Benders cuts, surrogate constraints for the master problem, and an upper bound heuristic to both obtain and tighten optimality Benders cuts. We obtain solutions within 2.0 % of optimality in very reasonable times as we illustrate in our computational study.