The paper is devoted to modeling wireless mesh networks (WMN) through mixed-integer programming (MIP) formulations that allow to precisely characterize the link data rate capacity and transmission scheduling using the notion of time slots. Such MIP models are formulated for several cases of the modulation and coding schemes (MCS) assignment. We present a general way of solving the max-min fairness (MMF) traffic objective for WMN using the formulated capacity models. Thus the paper combines WMN radio link modeling with a non-standard way of dealing with uncertain traffic, a combination that has not, to our knowledge, been treated so far by exact optimization models. We discuss several ways, including a method based on the so called compatible or independent sets, of solving the arising MIP problems. We also present an extensive numerical study that illustrates the running time efficiency of different solution approaches, and the influence of the MCS selection options and the number of time slots on traffic performance of a WMN. Exact joint optimization modeling of the WMN capacity and the MMF traffic objectives forms the main contribution of the paper.

Finding optimal routes and spectrum allocation in flexgrid optical networks, known as the RSA problem, is an important design problem in transport communication networks. The problem is TeX -hard, and its intractability becomes profound when network instances with several tens of nodes and several hundreds of demands are to be solved to optimum. In order to deal with such instances, large-scale optimization methods need to be considered. In this work, we present a column (more precisely, path) generation-based method for the RSA problem. The method is capable of finding reasonable sets of lightpaths, avoiding large sets of precomputed paths, and leading to high-quality solutions. Numerical results illustrating effectiveness of the proposed method for obtaining solutions for large RSA problem instances are presented.Peer ReviewedPostprint (published version

In the paper we present integer programming (IP) optimization models for flexgrid elastic optical networks (EON). We consider several different basic assumptions regarding flexibility of EON that lead to a variety of IP formulations differing in precision and complexity. As usual, detailed models aiming at precisely describing technological aspects of EON suffer from tractability issues resulting from their greater complexity and have to be reasonably simplified. To achieve this, we consider cases where the bandwidth is divided into predefined slots, cases where the bandwidth is continuous and can be divided between demands with no restrictions, cases where a list of predefined paths is available, and finally cases where all the paths are indirectly taken into account. We present both compact and non-compact formulations. The non-compact formulations are accompanied with brief description of the dedicated column generation algorithms.

We present an optimization platform for Fiberto-the-Home network design. The platform is capable of minimizing the capital expenditures (CAPEX) of network deployment by optimizing locations of optical equipment, signal splitters and cable cabinets, optimizing cable routes and types of cables as well as the number and types of optical cards and splitters. We present the architecture of the platform, the design process it implements, and the algorithms it deploys. The platform is used to indicate the parts of the design process that require complex optimization with dedicated algorithms and those that can be left to appropriately crafted engineering rules. We indicate that while keeping the computation time acceptable, much of the CAPEX savings can be obtained when locations of optical equipment are thoroughly optimized, cable routes are determined with plain engineering rules, and finally, signal splitting patterns are optimized carefully to lower the fiber count and thus the cost of cables.

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In this paper we consider the problem of optimal partitioning of a traffic demand polytope using a hyperplane. In our model all possible demand matrices belong to a polytope. The polytope can be divided into parts, and different routing schemes can be applied while dealing with traffic matrices from different parts of the polytope. We consider three basic models: Robust‐Routing, No‐Sharing and Dynamic‐Routing. We apply two different partitioning strategies depending on whether the reservation vectors on opposite sides of the hyperplane are required to be identical, or allowed to differ. We provide efficient algorithms that solve these problems. Moreover, we prove polynomiality of some of the considered cases. Finally, we present numerical results proving the applicability of the introduced algorithms and showing differences between the routing strategies.

In this article we prove N P-hardness of two well-known optimization problems related to the design of multicommodity flow networks with two different methods for providing network resiliency against failures: path diversity and flow restoration. Path diversity is a static mechanism that consists of using, for each demand, a number of paths and oversizing the flows assigned to these paths so that for any failure the total surviving flow is not less than the volume of the demand. By contrast, flow restoration is a dynamic mechanism that consists of reassigning the failed flows to backup paths when a failure occurs. Both mechanisms are of practical interest because although flow restoration is in general superior to path diversity in terms of the required amount of resource capacity, it might be too complicated to implement. By providing an appropriate reduction from the fractional graph coloring problem, we show that both problems are N P-hard in the general case of failure scenarios that admit simultaneous failures of multiple links. Finally, we discuss how to efficiently solve the two problems using path generation techniques.

We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully Adjustable Robust Counterpart. It consists in selecting a set of poles whose convex hull contains some projection of the uncertainty set, and computing a recourse strategy for each data scenario as a convex combination of some optimized recourses (one for each pole). We show that the proposed multipolar robust counterpart is tractable and its complexity is controllable. Further, we show that under some mild assumptions, two sequences of upper and lower bounds converge to the optimal value of the fully adjustable robust counterpart. To illustrate the approach, a robust problem related to lobbying under some uncertain opinions of authorities is studied. Several numerical experiments are carried out showing the advantages of the proposed robustness framework and evaluating the benefit of adaptability.