Hybrid Lagrangian relaxation for bandwidth-constrained routing: knapsack decomposition

Authors:
Wided Ouaja;Barry Richards
Affiliations:
Imperial College London, London, UK;Imperial College London, London, UK
Venue:
Proceedings of the 2005 ACM symposium on Applied computing
Year:
2005

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Abstract

To deliver quality of service, internet service providers are seeking effective solutions to optimize their networks. One of the main tasks is to optimally route a set of traffic demands, each along a single path, while satisfying their bandwidth requirements and without exceeding edge capacities. This is an integer multicommodity flow problem, which is known to be NP-hard. To solve this problem efficiently, a new complete and scalable hybrid solver (HLR) integrating Lagrangian relaxation and constraint programming has been proposed. It exploits the shortest path decomposition of the problem and has been shown to yield significant benefits over several other algorithms, such as CPLEX and well-known routing heuristics. In this paper we explore an alternative dualization within the same hybrid. We present a variant of HLR, adapted to the knapsack decomposition of the problem. Although this relaxation seems less natural, experimental results show that it has some advantages. The paper provides an interesting insight of where the benefits may lie, in particular for larger and harder cases where the ratio of total demand to available capacity is higher.