On the impact of the solution representation for the Internet Protocol Network Design Problem with max‐hop constraints

Abstract

The IP (Internet Protocol) Network Design Problem can be shortly stated as follows. Given a set of nodes and a set of traffic demands, we want to determine the minimum cost capacity installation such that all the traffic is routed. Capacity is provided by means of links of a given capacity and traffic must be loaded on the network according to the OSPF-ECM (Open Shortest Path FirstEqual Commodity Multiflow) protocol, with additional constraints on the maximum number of hops. The problem is strongly NP-Hard, and the literature proposes local search-based heuristics that do not take into account max-hop constraints, or assume a simplified OSPF routing. The core in a local search approach is the network loading algorithm for the evaluation of the neighbor solutions costs. It presents critical aspects concerning both computational efficiency and memory requirements. Starting from a tabu search prototype, we show how these aspects deeply impact on the design of a local search procedure, even at the logical level. We present several properties of the related network loading problem, that allow to overcome the critical issues and lead to an efficient solution evaluation.

The network design problem with relays

“…Soni (2001) considers the HCNDP with partial survivability. De Giovanni et al (2004) present a study on how hop constraints can impact network design solutions.…”

Tailoring neighborhood search for the internet protocol network design problem with reliability and routing constraints

“…In [14], the authors discussed how the OHSPF splitting rule impacts on the solution representation and gave the related solution evaluation algorithms. Starting from these results, the aim of this work is to provide an efficient implementation of the basic components of any neighborhood search method for IPRR.…”

“…Hence, the routing of each commodity must satisfy a specific constraint on the maximum number of links that each of its routing paths should contain (max-hop constraint). It follows that the Open Hop-constrained Shortest Path First-Equal Commodity Multi-path (OHSPF-ECM) splitting rule must be applied: at each node, the incoming flow is evenly split on all the outgoing links belonging to at least one hop-constrained shortest path to the destination (see [14]). Note that the same constraints are also related to the reliability of the routing: the less is the number of hops, the less the commodity is likely to be affected by network failures.…”

“…In [8], a prototypal Tabu Search procedure is proposed, able to solve only small instances of IPRR, due to the difficulty of handling the great amount of memory related to storing shortest paths information. In [14], a compact solution representation is proposed, together with the basic algorithms to perform an efficient network loading and, as a consequence, an efficient neighborhood evaluation, even if no reliability constraints are taken into account.…”

“…Some preliminary studies for IPRR are presented in [8] and [14]. In [8], a prototypal Tabu Search procedure is proposed, able to solve only small instances of IPRR, due to the difficulty of handling the great amount of memory related to storing shortest paths information.…”