Large scale optimization in survivable WDM mesh networks: Tutorial proposal (DRCN 2009)

Abstract

Design and planning of survivable WDM networks involve different decision and optimization problems under network, traffic, and cost constraints. The high bandwidth brought by WDM access technology has incited network operators to extensive deployment of WDM in both access and backbone networks. Edges of networks have been pushed and transport capacity significantly increased, making the design and planning tasks harder. Consequently, efficient and scalable tools are, more than ever, needed to help network designers. Most of the design and planning problems arising in survivable optical WDM network are large scale optimization and hard combinatorial ones that cannot be tackled efficiently with the classical Integer Linear Programming (ILP) approaches. The Column Generation (CG) technique is an efficient optimization tool which has been shown to be very effective for solving particular classes of large scale systems. Indeed, combined with classical ILP tools, the CG technique offers a valuable tool for the design of highly efficient global search heuristics with an indication on the distance to the globally optimal solution when exact solution is not possible. However, it requires special care at the mathematical modeling step. The objective of this tutorial is to provide in-depth learning on the use of CG and ILP tools throughout different network design examples arising in survivable WDM networks, showing that such tools are highly efficient and scalable. Nowadays, network connectivity with high bandwidth is stretched to reach places that were isolated some years ago. In order to meet the everincreasing demands for high bandwidth, optical WDM technology has been deployed in different telecommunication networks. The heterogeneity of traffic and the explosive growth of demands for high bandwidth services have shaped several network topologies, and raised several other network planning and design issues such as, e.g., survivability. However, with the expansion of network sizes and transport capacities, operators are increasingly concerned with the issue of how to efficiently perform planning and design for such large scale systems. In this tutorial, we focus on the efficient and scalable design of survivable WDM networks, where recent studies have reported outstanding solution of the optimization problems arising therein. Authors have been successful in adopting large scalable optimization tools based on the Column Generation (CG) technique. The 386 2009 7th International Workshop on the Design of Reliable Communication Networks main objective of the tutorial is to provide an in-depth learning on CG optimization techniques in the context of the design of survivable WDM networks. We will elaborate on the different optimization steps of using CG tools including modeling approaches, effective solution schemes, and performance evaluations. Both classical Integer Linear Programming (ILP) approaches and CG are two techniques that basically use the same optimization algorithms to achieve the same solutions, but in different ways, i.e., explicit vs. implicit management of all the variables (or columns). While classical ILP techniques are quickly becoming no scalable when the size of the optimization systems is increasing, CG offers a way to deal efficiently with large scale systems and for the ILP tools to remain scalable, at the expense of more modeling efforts, meaning a decomposition of the initial problem into more compact and easy to solve problems. The scalability of CG based technique lies in the fact that not all the data are used during the optimization process, but only a limited fraction that is incrementally added dynamically during the optimization process, and only under the condition that it allows an improvement of the value of the current solution. Moreover, in some optimization problems, getting all the input data is impossible, e.g., all potential alternate paths or all potential protection cycles (p-cycles) in a graph corresponding to a medium or large backbone optical network. The solution space that is considered in CG is often much smaller than in ILP schemes as identical solutions up to a permutation of some of the parameters (e..g, wavelengths) are eliminated. This results from the increased modeling effort that need to be made in order to use CG techniques, that is a decomposition of the initial set of constraints among difficult smaller and easier to manage subproblems. The elegance and the efficiency of the CG technique comes from the fact that not all subproblems need to be solved exactly in order to end up with the globally optimal solution. When the globally optimal solution remains unreachable for heavy resource requirements, CG offers a new interesting and widely underused (or underestimated) heuristic framework where the search is done globally and hence, much more efficiently than with the local search of the classical heuristics or metaheuristics. All those features will be advertised and illustrated throughout examples in the tutorial. We will review the recent work where the researchers have investigated the use of CG in the context of survivable WDM networks. Work has be done with the two protection paradigms: The classical sequential/joint working 2009 7th International Workshop on the Design of Reliable Communication Networks 387 and disjoint backup path paradigm, and the Protected Working Capacity Envelope (PWCE) introduced by Grover (2004). We will give detailed insights on how-to set up their associated CG optimization formulations, and how to solve them efficiently combining CG and ILP tools. We will discuss very recent results where the authors have investigated different candidate protection structures (linear path, p-cycles, FIPP p-cycles . . . ) for both paradigms. This last piece of work illustrates very clearly the modeling flexibility induced by CG techniques and consequently its effectiveness to solve large scale Integer Linear Programs. We will provide two particular examples, i.e., p-cycle based PWCE and FIPP p-cycles, where CG has been highly successful, achieving much faster running times (reduced by a factor of 10 up to 1000), in spite of providing globally optimal or near optimal solution instead of heuristic or approximate solutions (with a 10 to 30 % improved accuracy) than any previous algorithm. Quantitative comparisons of different design and performance parameters are provided for additional applications arising in the design of survivable WDM networks, comparing the two protection paradigms, as well as the link/path protection schemes vs. the p-cycle based protection ones, and finally the impact of the symmetrical vs asymmetrical traffic assumptions on the performances. 388 2009 7th International Workshop on the Design of Reliable Communication Networks