Multiperiod network design with incremental routing

Abstract

In this paper, we study a special case of multiperiod network design (MPND) problems, multiperiod network design with incremental routing (MPNDI), as applied to the transmission layer of an optical network. We optimize simultaneously the network architecture and the link dimensioning under discrete cost functions in order to route all traffic demands in line with traffic growth over a discrete time horizon. Because of operational requirements, routing paths used at a given period to route some traffic demands have to be preserved over subsequent periods; this is called incremental routing with respect to incremental flow. To handle the high dimensionality, a compact formulation omitting explicitly written flow variables is given. We examine the dominant polyhedron of the incremental multicommodity flow and provide a polyhedral study of it. Finally, a solution approach taking advantage of the polyhedral structure of MPNDI is proposed, and computational results for a range of instances with 8 and 10 nodes are provided.

Robust network design: Formulations, valid inequalities, and computations

“…In multi-period or multi-hour network design [44,62], an explicit finite set of demand matrices is given, and the network is designed in such a way that each of the demand matrices can be routed nonsimultaneously within the installed capacities (potentially expanding the network capacity in every period). In this context, Oriolo [55] introduces the concept of dominated demand matrices.…”

A fast hybrid primal heuristic for multiband robust capacitated network design with multiple time periods

“…From a modeling point of view, this generalization requires to add a new index t ∈ T to the decision variables, to represent routing and capacity installation decisions taken in each period. This is a simple modeling operation, which, however, greatly increases the size and complexity of the problem as pointed out in our computational section and by Gavros and Raghavan (2012) and Lardeux et al (2007) e ∈ E, t ∈ T (3)…”

“…We immediately stress that, though the problem of optimally designing networks over multiple time periods is not new and can be traced back at least to the seminal work by Christofides and Brooker (1974), to the best of our knowledge, the MP-CNDP has received very little attention and just a few works have investigated it -essentially, Lardeux et al (2007) and Gavros and Raghavan (2012). Checking literature, several other works dealing with multiperiod design of networks can be found (just to make a couple of examples, Gendrau et al 2006 andGupta andGrossmann 2012): however, all these works consider problems that are application-specific or are sensibly different from the more general setting that we consider here and we thus avoid a more detailed discussion of them (Gendrau et al (2006) study capacity expansion problem in access networks with tree topology, whereas Gupta and Grossmann (2012) consider the design of utility networks modeled by non-linear mathematical programs).…”

Applications of Evolutionary Computation

“…Moreover, traffic uncertainty is taken into account to protect design solutions against deviations of the traffic input data, that may compromise feasibility and optimality of solutions. To the best of our knowledge, the (MP-NDP) has received little attention and just a few works have investigated it (primarily, [18] and [16]). These works point out the difficulty of solving multiperiod problems already for just two periods and (easier) splittable-flow routing [18], and for a pure routing problem in satellite communications [16].…”