Combining Lagrangian Decomposition with Very Large Scale Neighborhood Search for Capacitated Connected Facility Location

We consider a generalized version of the rooted Connected Facility Location problem (ConFL) which occurs when extending existing communication networks in order to increase the available bandwidth for customers. In addition to choosing facilities to open and connecting them by a Steiner tree as in the classic ConFL, we have to select a subset of all potential customers and assign them to open facilities respecting given capacity constraints in order to maximize profit. We present two exact mixed integer programming formulations and a Lagrangian decomposition (LD) based approach which uses the volume algorithm. Feasible solutions are derived using a Lagrangian heuristic. Furthermore, we present two hybrid variants combining LD with local search and a very large scale neighborhood search. By applying those improvement methods only to the most promising solutions, we are able to compute much better solutions without increasing the necessary runtime too much. As documented by our computational results, our hybrid approaches compute high quality solutions with tight optimality gaps in relatively short time.