Introduction to linear and nonlinear programming

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

Topographic distance and watershed lines

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

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

Nonlinear Programming: A Unified Approach

This paper is intended as a survey in the area of network synthesis and optimum network design, which, in view of the importance and variety of the underlying applications, has attraced, since the early 1960s, much interest in the Operations Research community. Indeed, if the first models were studied in connection with telecommunication networks, the range of applications kept on getting broader and broader, including transportation networks, computer and teleprocessing networks, energy transport systems, water distribution networks, etc. However, beyond the apparent diversity of practical situations involved, most of these applications can be accounted for (modulo possibly a few minor adaptations), by a rather limited number of basic models. One of the main purposes of this paper is to provide the reader with a relevant classification of the area which will help him identify the fundamental structure of the problem (if any) he has to cope with, and relate it to already published work. In order to obtain a fairly good coverage of the matter, we have thus been led to identify three basic models aroung which the whole paper is organized: a general model using minimum cost multicommodity flows (Section 2); models in terms of tree-like networks (Section 3); models using nonsmultaneous single-commodity or multicommodity flows (Section 4). In each bcase the most important variants of the basic models have been surveyed with the purpose of providing as much information as possible concerning (a) the various contexts of applications from which the problem arose; (b) the main computational methods proposed in the literature for solving it, with emphasis on those techniques which appear at present, to be most efficient or promising.

Networks synthesis and optimum network design problems: Models, solution methods and applications

1.Generalites sur les graphes / 2.Le probleme du plus court chemin / 3. Les algebres de chemins / 4.Arbres et arborescences / 5. Flots et reseaux de transport / 6.Flots avec multiplicateurs.multiflots / 7.Couplages et b-couplages / 8.Parcours euleriens et hamiltoniens / 9.Matroides / 10.Les problemes"non polynomiaux"/ 11.Les algorithmes d'enumeration par separation et evaluations / 12.Les algorithmes approches / Annexes :Programmation lineaire - Programmation lineaire en nombres entiers - Relaxation lagrangienne et resolution du probleme dual - Programmation dynamique - Les problemes de ratio m minimumm

Graphes et algorithmes

Pre-Semirings, Semirings and Dioids.- Combinatorial Properties of (Pre)-Semirings.- Topology on Ordered Sets: Topological Dioids.- Solving Linear Systems in Dioids.- Linear Dependence and Independence in Semi-Modules and Moduloids.- Eigenvalues and Eigenvectors of Endomorphisms.- Dioids and Nonlinear Analysis.- Collected Examples of Monoids, (Pre)-Semirings and Dioids.

Graphs, dioids and semirings : new models and algorithms

A new approach for crew pairing problems by column generation with an application to air transportation

The origins of Graph Theory date back to Euler (1736) with the solution of the celebrated 'Koenigsberg Bridges Problem'; and to Hamilton with the famous 'Trip around the World' game (1859), stating for the first time a problem which, in its most recent version the 'Traveling Salesman Problem' -, is still the subject of active research. Yet, it has been during the last fifty years or sowith the rise of the electronic computersthat Graph theory has become an indispensable discipline in terms of the number and importance of its applications across the Applied Sciences. Graph theory has been especially central to Theoretical and Algorithmic Computer Science, and Automatic Control, Systems Optimization, Economy and Operations Research, Data Analysis in the Engineering Sciences. Close connections between graphs and algebraic structures have been widely used in the analysis and implementation of efficient algorithms for many problems, for example: transportation network optimization, telecommunication network optimization and planning, optimization in scheduling and production systems, etc. The primary objectives of GRAPHS, DIODS AND SEMIRINGS: New Models and Algorithms are to emphasize the deep relations existing between the semiring and diod structures with graphs and their combinatorial properties, while demonstrating the modeling and problem-solving capability and flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures, which either extend usual algebra (i.e., semirings), or correspond to a new branch of algebra (i.e., diods), apart from the classical structures of groups, rings, and fields.

Michel Minoux

Papers

Networks synthesis and optimum network design problems: Models, solution methods and applications

Graphes et algorithmes

Graphs, dioids and semirings : new models and algorithms

A new approach for crew pairing problems by column generation with an application to air transportation

Graphs, Dioids and Semirings: New Models and Algorithms (Operations Research/Computer Science Interfaces Series)