A Note on Search by Objective Relaxation

Salman et al. [1] propose a technique called search by objective relaxation for the local access network design problem. In this note we show that this technique can essentially be considered as a stylized branch-and-bound strategy on a mixed-integer programming formulation for the local access network design problem, wherein only a single type of facility can be installed on an edge. This provides an alternate, and somewhat simpler interpretation of their technique. Given the computational success Salman et al. have had in solving large network design problems with SOR, we examine if similar benefits are reaped with the stylized branch-and-bound strategy on the mixed-integer programming formulation. To this end we provide some computational experiments with this stylized branch-and-bound strategy, and compare it with the direct application of a state-of-the-art mixed-integer programming solver to several alternate formulations for the local access network design problem.