Lagrangian decomposition, metaheuristics, and hybrid approaches for the design of the last mile in fiber optic networks

Abstract. We consider a generalization of the (Price Collecting) Steiner Tree Problem on a graph with special redundancy requirements for customer nodes. The problem occurs in the design of the last mile integer linear program and apply Lagrangian Decomposition to obtain relatively tight lower bounds as well as feasible solutions. Furthermore, a Variable Neighborhood Search and a GRASP approach are described, utilizing a new construction heuristic and special neighborhoods. In particular, hybrids of these methods are also studied and turn out to often perform superior. By comparison to previously published exact methods we show that our approaches are applicable to larger problem instances, while providing high quality solutions together with good lower bounds

Lexicographical minimization of routing hops in hop-constrained node survivable networks

In this paper, we address a hop-constrained node survivable traffic engineering problem in the context of packet switched networks with source based routing. Consider a telecommunications network with given link capacities that was dimensioned for a set of commodities, with estimated demand values, such that each commodity demand is routed through a set of node disjoint service and backup paths, all with at most H hops. When the network is put in operation, the real demand values might be different from the initial estimated ones. So, we aim to determine a set of hop-constrained service and backup paths for each commodity, with known demand values, such that the whole set of paths does not violate the link capacities. The traffic engineering goal is related with the hop minimization of only the service paths. We aim to minimize the number of routing hops in a lexicographical sense, i.e., minimize the number of service paths with the worst number of hops; then, among all such solutions, minimize the number of service paths with the second worst number of hops; and so on. We address two traffic engineering variants: in the first variant, all service paths of each commodity are accounted for in the objective function while in the second variant only the worst service path of each commodity is accounted for in the objective function. We first present and discuss three classes of Integer Linear Programming hop-indexed models- disaggregated, mixed and aggregated — for both variants. Then, we prove that, although the three classes are not equivalent, they provide the same Linear Programming relaxation bounds for each variant. Finally, we present computational results showing that, as a consequence, the more compact aggregated models are more efficient in obtaining the optimal integer solutions

Benders Decomposition for the Hop-Constrained Survivable Network Design Problem

Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia [Gouveia, L. 1998. Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints. INFORMS J. Comput. 10(2) 180–188], we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the large number of variables and constraints. We show that our Benders cuts contain constraints used in previous studies to formulate the problem for L = 2, 3, 4, as well as new inequalities when L ≥ 5. Whereas some recent works on Benders decomposition study the impact of the normalization constraint in the dual subproblem, we focus here on when to generate the Benders cuts. We present a thorough computational study of various branch-and-cut algorithms on a large set of instances including the real-based instances from SNDlib. Our best branch-and-cut algorithm combined with an efficient heuristic is able to solve the instances significantly faster than CPLEX 12 on the extended formulation.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Location Problems in Telecommunications

Language of publication: enInternational audienceno abstrac