Variable Neighborhood Search for Capacitated Connected Facility Location

The Capacitated Connected Facility Location Problem (CConFL) is an NPhard combinatorial optimization problem which arises in the design of last mile communication networks (fiber-to-the-curb scenarios) [1]. Formally, we are given an undirected, weighted graph G = (V,E), with edge costs ce ≥ 0, ∀e ∈ E. The node set V = {r}∪F ∪T is the disjoint union of the root node r, potential facility locations F , and possible Steiner nodes T . Each facility i ∈ F has associated opening costs fi ≥ 0 and a maximum assignable capacity Di ∈ N. Furthermore, we are given a set of potential customers C, with individual capacity demands dk ∈ N and prizes pk ≥ 0, ∀k ∈ C, the latter corresponding to the expected profit when supplying customer k. Each customer k ∈ C may be assigned to one facility of a subset Fk ⊆ F , with assignment costs ai,k ≥ 0, ∀i ∈ Fk. A solution to CConFL S = (RS , TS , FS , CS , αS) consists of a Steiner Tree (RS , TS), RS ⊆ V , TS ⊆ E, connecting the set of opened facilities FS ⊆ F and the root node r. CS ⊆ C is the set of customers feasibly (i.e. respecting the capacity constraints) assigned to facilities FS , whereas the actual mapping between customers and facilities is described by αS : CS → FS . The objective value of a feasible solution S is given by c(S) = ∑ e∈TS ce+ ∑ i∈FS fi+ ∑ k∈CS aαS(k),k+ ∑ k∈C\CS pk, and we aim to identify a most profitable solution minimizing this function. This variant of CConFL has already been tackled by exact methods based on mixed integer programming [2] and hybrid approaches based on Lagrangian relaxation [1]. Here, we present the first pure metaheuristic approach, which computes high quality solution faster than existing approaches.