MIP-based heuristic approaches for the capacitated edge activation problem: the effect of non-compactness

The capacitated edge activation (CEA) problem consists of activating a minimum cost set of capacitated edges to ensure the routing of some traffic demands. Most of the MIP-based heuristics proposed for network design problems are based on the so-called flow formulation that includes both activation and routing variables. Indeed, there also exists a capacity formulation that includes only activation variables. This formulation is, however, non-compact. Here, we investigate the price to pay to use the non-compact capacity formulation instead of the compact flow formulation in a MIP-based rounding heuristic for the CEA problem. Both splittable and unsplittable flows are considered. The experiments show that, indeed, the capacity formulation requires more time and solves less instances than the flow formulation, due to the time spent in separating feasibility cuts, in particular for unsplittable flows.