We analyze the global structure of the worldwide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the worldwide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multicommunity structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints and that geopolitical considerations have to be taken into account. We identify each city's global role based on its pattern of intercommunity and intracommunity connections, which enables us to obtain scale-specific representations of the network.

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The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles

Numerous transportation applications as diverse as capital investment decision-making, vehicle fleet planning, and traffic light signal setting all involve some form of (discrete choice) network design. In this paper, we review some of the uses and limitations of integer programming-based approaches to network design, and describe several discrete and continuous choice models and algorithms. Our objectives are threefold—to provide a unifying view for synthesizing many network design models, to propose a unifying framework for deriving many network design algorithms, and to summarize computational experience in solving design problems. We also show that many of the most celebrated combinatorial problems that arise in transportation planning are specializations and variations of a generic design model. Consequently, the network design concepts described in this paper have great potential application in a wide range of problem settings.

Network Design and Transportation Planning: Models and Algorithms

http://www3.eng.cam.ac.uk/~hj231/Papers/rostering.pdf

Staff scheduling and rostering: A review of applications, methods and models

In network design, the gap between theory and practice is woefully broad. This book narrows it, comprehensively and critically examining current network design models and methods. You will learn where mathematical modeling and algorithmic optimization have been under-utilized. At the opposite extreme, you will learn where they tend to fail to contribute to the twin goals of network efficiency and cost-savings. Most of all, you will learn precisely how to tailor theoretical models to make them as useful as possible in practice. Throughout, the authors focus on the traffic demands encountered in the real world of network design. Their generic approach, however, allows problem formulations and solutions to be applied across the board to virtually any type of backbone communication or computer network. For beginners, this book is an excellent introduction. For seasoned professionals, it provides immediate solutions and a strong foundation for further advances in the use of mathematical modeling for network design. (Less)

Routing, Flow, And Capacity Design In Communication And Computer Networks

http://www.optimization-online.org/DB_FILE/2003/06/670.pdf

A stochastic programming approach for supply chain network design under uncertainty

This paper proposes methodology for improving the performance of Benders decomposition when applied to mixed integer programs. It introduces a new technique for accelerating the convergence of the algorithm and theory for distinguishing “good” model formulations of a problem that has distinct but equivalent mixed integer programming representations. The acceleration technique is based upon selecting judiciously from the alternate optima of the Benders subproblem to generate strong or pareto-optimal cuts. This methodology also applies to a much broader class of optimization algorithms that includes Dantzig-Wolfe decomposition for linear and nonlinear programs and related “cutting plane” type algorithms that arise in resource directive and price decomposition. When specialized to network location problems, this cut generation technique leads to very efficient algorithms that exploit the underlying structure of these models. In discussing the “proper” formulation of mixed integer programs, we suggest criteri...

Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria

A capacitated node routing problem, known as the vehicle routing or dispatch problem, has been the focus of much research attention On the other hand, capacitated arc routing problems have been comparatively neglected Both classes of problems are extremely rich in theory and applications Our intent in this paper is to define a capacitated arc routing problem, to provide mathematical programming formulations, to perform a computational complexity analysis, and to present an approximate solution strategy for this class of problems In addition, we identify several related routing problems and develop tight lower bounds on the optimal solution

Capacitated arc routing problems

The Steiner tree problem on a directed graph (STDG) is to find a directed subtree that connects a root node to every node in a designated node setV. We give a dual ascent procedure for obtaining lower bounds to the optimal solution value. The ascent information is also used in a heuristic procedure for obtaining feasible solutions to the STDG. Computational results indicate that the two procedures are very effective in solving a class of STDG's containing up to 60 nodes and 240 directed/120 undirected arcs. The directed spanning tree and uncapacitated plant location problems are special cases of the STDG. Using these relationships, we show that our ascent procedure can be viewed as a generalization ofboth the Chu-Liu-Edmonds directed spanning tree algorithm and the Bilde-Krarup-Erlenkotter ascent algorithm for the plant location problem. The former comparison yields a dual ascent interpretation of the steps of the directed spanning tree algorithm.

A dual ascent approach for steiner tree problems on a directed graph

The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling. We develop a family of dual-ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location, Steiner network and directed spanning tree problems. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints show that the dual-ascent procedure and an associated drop-add heuristic generate solutions that, in almost all cases, are guaranteed to be within 1 to 4% of optimality. Moreover, the procedure requires no more than 150 seconds on an IBM 3083 computer. The test problems correspond to dense and sparse networks, including some models that arise in freight transport.

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Richard T. Wong

Papers

Network Design and Transportation Planning: Models and Algorithms

Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria

Capacitated arc routing problems

A dual ascent approach for steiner tree problems on a directed graph

A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design