A Hybrid VNS for Connected Facility Location

Abstract

The connected facility location (ConFL) problem generalizes the facility location problem and the Steiner tree problem in graphs. Given a graph G = (V,E), a set of customers ${\cal D} \subseteq V$, a set of potential facility locations ${\cal F} \subseteq V$ (including a root r), and a set of Steiner nodes in the graph G = (V,E), a solution (F,T) of ConFL represents a set of open facilities $F\subseteq \cal F$, such that each customer is assigned to an open facility and the open facilities are connected to the root via a Steiner Tree T. The total cost of the solution (F,T) is the sum of the cost for opening the facilities, the cost of assigning customers to the open facilities and the cost of the Steiner tree that interconnects the facilities.

We show how to combine a variable neighborhood search method with a reactive tabu-search, in order to find sub-optimal solutions for large scale instances. We also propose a branch-and-cut approach for solving the ConFL to provable optimality. In our computational study, we test the quality of the proposed hybrid strategy by comparing its values to lower and upper bounds obtained within a branch-and-cut framework.