The network design problem with relays

Abstract

The network design problem with relays (NDPR) is defined on an undirected graph G = (V, E, K), where V = {1, . . . , n} is a vertex set, E = {(i, j) : i, j 2 V, i < j} is an edge set. The set K = {(o(k), d(k))} is a set of communication pairs (or commodities): o(k) 2 V and d(k) 2 V denote the origin and the destination of the kth commodity, respectively. With each edge (i, j) are associated a cost c ij and a length d ij . With vertex i is associated a fixed cost f i of locating a relay at i. The NDPR consists of selecting a subset E of edges of E and of locating relays at a subset V of vertices of V in such a way that: (1) the sum Q of edge costs and relay costs is minimized; (2) there exists a path linking the origin and the destination of each commodity in which the length between the origin and the first relay, the last relay and the destination, or any two consecutive relays does not exceed a preset upper bound k. This article develops a lower bound procedure and four heuristics for the NPDR. These are compared on several randomly generated instances with |V| 6 1002 and |E| 6 1930.

Regenerator Location Problem and survivable extensions: A hub covering location perspective

“…The lack of costs in pure service-oriented hub center and hub covering models have found more reasonable applications in telecom than in transportation. Confirming this analysis of Campbell and O'Kelly (2012), RLP literature discussed in this paper as well as a closely related network design problem with relays of Cabral et al (2007), Laporte and Pascoal (2011) and Kewcharoenwong and Uster (2014) seem to be confined to the field of telecommunications. In this regard, we shall attempt to describe transportation-related settings and motivations where RLP and its close variants can be of interest.…”

Electric vehicles: A review of network modelling and future research needs

“…The length between two consecutive relays does not exceed a pre-set upper bound. 46 The problem of energy-efficient routing of EVs has been addressed, and the polynomial time algorithms have been developed in the literature by considering the limited cruising range and regenerative braking (i.e. the EV increases its level of energy when braking) capabilities of EVs which is actually a special case of the constrained SPP.…”

Wide area telecommunication network design: application to the Alberta SuperNet

“…The heuristic we employ to solve the TDP was developed by Cabrai et al (2007). It works on the directed graph in which each edge has been replaced by two opposite arcs.…”

“…The heuristic is based on a procedure put forward by Takahashi and Matsuyama (1980) for the STP, which constructs a sub network in a greedy fashion, one (o(k), d(k)) pair at a time for every k e Kf. Because of the constraint imposed on the interspacing of shelters, the (o(k),...,d{k)) paths are con structed by using the auxiliary pseudo-polynomial procedure suggested by Cabrai et al (2005) some of its nodes in such a way that the interspacing con straint is satisfied. When applied to a particular (o(k), d(k)) pair, the SPPR problem is denoted as SPPR(&).…”