A Lagrangean Relaxation and Subgradient Framework for the Routing and Wavelength Assignment Problem in WDM Networks

Zhang, Yiming; Yang, O.W.W.; Liu, Haomei

doi:10.1109/jsac.2004.833851

Cited by 40 publications

(18 citation statements)

References 18 publications

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“…The Wavelength Graph (WG) model is used for routing in two-layer networks [26]. This graph corresponds to the logical network, and is derived from the physical network considering its topology, and capabilities of physical devices.…”

Section: Problem Formulation and The Goal Of Researchmentioning

confidence: 99%

Methods for physical impairment constrained routing with selected protection in all-optical networks

2013

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In this paper, we investigate the problem of survivable all-optical routing in WDM networks with physical impairments. One of the recent key issues in survivable optical network design refers to maximization of the ratio of routeable demands while keeping the overall network cost low. In WDM networks, this goal can be achieved by routing as many demands in all-optical way as possible. Based on the latest technical trends driven by deployment costs, technical constraints, and backward compatibility, this will not mean that all demands will be routed in all-optical way in the near future.Nowadays, operators are mostly willing to dedicate only a given ratio of their power budget to all-optical routing. This in turn implies a new problem to be solved: operators have to find a way to select demands that should be routed in all-optical way and which should not. The problem gets even more complicated, if we add demand protection issues.In this paper, we introduce and evaluate methods able to maximize the number of demands routed with protection in all-optical way in capacity-constrained networks with limitations on path lengths according to physical impairments.

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Section: Problem Formulation and The Goal Of Researchmentioning

confidence: 99%

Methods for physical impairment constrained routing with selected protection in all-optical networks

2013

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“…The parameters µ and q U are changed adaptively as the algorithm converges. The details of the methods to speed up the convergence can be found in [55,56].…”

Section: Solving the Dual Problemmentioning

confidence: 99%

“…The heuristic algorithm to search for a feasible RWA for a lightpath is the same as MEWA in [56], and is omitted here for simplicity.…”

Section: Constructing a Feasible Rwa And Routing Schemementioning

confidence: 99%

“…If the stopping criterion is not reached, the Lagrange multipliers are updated (Section 5.4), and another iteration of computation is launched. There are various criteria that can be used to terminate the algorithm, such as the duality gap [56], the number of iterations, the time of computation and the objective function value, etc. In the current implementation, we stop the algorithm when the duality gap does not decrease for 1000 iterations.…”

Section: Constructing a Feasible Rwa And Routing Schemementioning

confidence: 99%

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A Lagrangian-Relaxation Based Network Profit Optimization For Mesh SONET-Over-WDM Networks

Zhang

Yang

et al. 2005

Photon Netw Commun

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Abstract. In Wavelength Division Multiplexing (WDM) networks, the huge capacity of wavelength channels is generally much larger than the bandwidth requirement of individual traffic streams from network users. Traffic grooming techniques aggregate low-bandwidth traffic streams onto high-bandwidth wavelength channels. In this paper, we study the optimization problem of grooming the static traffic in mesh Synchronous Optical Network (SONET) over WDM networks. The problem is formulated as a constrained integer linear programming problem and an innovative optimization objective is developed as network profit optimization. The routing cost in the SONET and WDM layers as well as the revenue generated by accepting SONET traffic demands are modelled. Through the optimization process, SONET traffic demands will be selectively accepted based on the profit (i.e., the excess of revenue over network cost) they generate. Considering the complexity of the network optimization problem, a decomposition approach using Lagrangian relaxation is proposed. The overall relaxed dual problem is decomposed into routing and wavelength assignment and SONET traffic routing sub-problems. The subgradient approach is used to optimize the derived dual function by updating the Lagrange multipliers. To generate a feasible network routing scheme, a heuristic algorithm is proposed based on the dual solution. A systematic approach to obtain theoretical performance bounds is presented for an arbitrary topology mesh network. This is the first time that such theoretical performance bounds are obtained for SONET traffic grooming in mesh topology networks. The optimization results of sample networks indicate that the proposed algorithm achieves good sub-optimal solutions. Finally, the influence of various network parameters is studied.

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“…Some of these techniques are: Linear Programming (LP) relaxation [5,28,43]; Randomised Rounding [5,28,29]; Column Generation [31]; and Lagrangian relaxation [39,42,54].…”

Section: Introductionmentioning

confidence: 99%

A bicriteria routing model for multi-fibre WDM networks

et al. 2009

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All-optical WDM networks are characterised by multiple metrics (hop-count, cost, delay, available bandwidth, loss probability, reliability), but generally routing algorithms only optimise one metric. Having in mind the inherent limitations of this type of approach, it seems potentially advantageous in the development of multicriteria models capable of explicitly representing the different performance objectives and enabling to treat in a consistent manner the trade off among the various criteria. A bicriteria model for obtaining a topological path (unidirectional or symmetric bidirectional) for each lightpath request in a WDM network is proposed. The first criterion is related to bandwidth usage in the links (or arcs) of the network. The second criterion is the number of links (hops) of the path. The model resolution approach uses a k-shortest path algorithm as well as preference thresholds defined in the objective function space, combined with a Chebyshev distance to a reference point (which changes with the analysed preference region). The solution of this bicriteria model is a non-dominated topological path. A heuristic procedure is then used to assign wavelengths to the links. The performance of the bicriteria model is analysed by comparing it with two monocriterion approaches, using two test networks.

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A Lagrangean Relaxation and Subgradient Framework for the Routing and Wavelength Assignment Problem in WDM Networks

Cited by 40 publications

References 18 publications

Methods for physical impairment constrained routing with selected protection in all-optical networks

Methods for physical impairment constrained routing with selected protection in all-optical networks

A Lagrangian-Relaxation Based Network Profit Optimization For Mesh SONET-Over-WDM Networks

A bicriteria routing model for multi-fibre WDM networks

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