An efficient heuristic to dimension large-scale hybrid optoelectronic networks

Abstract

This paper presents a new heuristic to solve efficiently the problem of dimensioning large-size hybrid optoelectronic networks with grooming. It is modeled as a large mixed integer program which cannot be solved to optimality in a reasonable amount of time for networks larger than 10 nodes. The heuristic is based on concepts borrowed from genetic algorithm, tabu search and simulated annealing. The definition of the populations and neighborhoods are discussed in depth along with the intensification and diversification procedures. An application of this heuristic to networks of up to 50 nodes has shown excellent results: The computational time is low and the average optimality gap is generally under 7%.

Introduction

The optimization of telecommunication networks has been of great interest to the operations research community over the last 50 years. During the last decade, the widespread deployment of optical fiber coupled with the development of optical switches has generated much interest in the optimization of all-optical wavelength division multiplexing (WDM) networks. Even though the technology to build such networks is available now, today's networks are still composed of electronic routers and switches linked by optical fibers. While the results of research on all-optical networks seem very promising, they cannot be used directly to design a network with current optoelectronic technologies and we need efficient tools to optimize hybrid networks.

Different models of networks design and the corresponding solution techniques, both exact and approximative, have been proposed throughout the years. Gavish and Neuman [1], Gavish and Altinkemer [2] and Amiri and Pirkul [3], [4] proposed models to solve the routing and capacity assignment problem. The objective was to minimize the link and delay costs of the network while finding the routes and assigning capacity to links at the same time. These models use a traffic matrix that represents the average values of random arrival processes for connection requests or for packets and independent M/M/1 queues at each node for the calculation of the delay. Since the model contains a nonlinear objective function, the solution method was a Lagrangean relaxation with a subgradient optimization. Cuihong [5] used a genetic algorithm instead of an exact method to solve the model of Gavish and Neuman [1]. Ng and Hoang [6] proposed another routing and capacity assignment model, this time based on m-M/M/1 queues, which made their problem a convex multicommodity flow that could be solved to optimality using a flow deviation technique.

Similarly, the design of optical transmission networks has been studied in depth in [7] and in references therein. However, in all these models, no capacity is assigned to the nodes or to any electronic equipment. Costamagna et al. [8] proposed a tabu search heuristic to solve design problems where the general structure is a hierarchy of users, multiplexing centers and exchanges with a spanning tree topology. Their objective was to minimize the cost of optical fibers and the cost of opening multiplexing nodes. In their model, traffic demands and equipment capacity were discrete and deterministic.

More recently, Huang and Copeland [9] proposed to minimize the total cost of a network expressed as the sum of three components: the cost of wavelength links and of wavelength and subwavelength routing ports. Their model also takes into account traffic aggregation at the subwavelength layer to reduce the number of wavelength routing ports. Contrary to most previous models, traffic demands could take fractional values instead of being limited to discrete values.

Other models and techniques have been proposed to solve the telecommunication networks design problem and the references mentioned above are just a small sample of what was done in the field. In this paper, we present a new heuristic to solve the dimensioning of optoelectronic networks with traffic grooming. The basic idea of grooming is to take several flows which have common paths, to electronically multiplex them into one larger flow and then to send this aggregated flow on a dedicated optical channel. By doing so, it is possible to save optical channel or equivalently to carry more traffic with the same equipment. For a good review of previous work on traffic grooming, we refer the reader to Dutta and Rouskas [10]. Grooming-related problems are not limited to flow aggregation. Some models try to reduce the number of optical equipment, such as add-drop multiplexers (ADM) or transceivers, while others try to optimize the location of the grooming nodes. However, to the best of our knowledge, with the exception of the work of Huang and Copeland [9], no one has tried to optimize the dimensioning of optoelectronic networks and the grooming of flows simultaneously.

In this paper, we propose a new heuristic to dimension hybrid optoelectronic networks i.e., networks with electronic nodes and optical links. The problem is to choose from a finite set the right amount of capacity to assign to each optical link, in the form of optical channels, and to each electronic router. An important feature of our model not found elsewhere is that we take into account the modular cost of the routers. This cost depends on the amount of traffic that is groomed and the heuristic tries to find the best tradeoff between optical costs and electronic costs using grooming.

We first give a short description of the problem in Section 2. Section 3 presents the mathematical model behind the design and dimensioning problem. In Section 4, the main ideas of our heuristic are described. Some approximations are discussed, the structures of the neighborhood and of the solutions are presented and the inner workings of the heuristic are thoroughly explained. Numerical results obtained with a commercial solver (CPLEX) and the heuristic are shown in Section 5 which are summarized in the conclusion.