A Column Generation Algorithm For Optimal Traffic Assignment

"This unique monograph, a classic in its field, provides an account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas. The text further demonstrates the scope and limits of current models. Some familiarity with nonlinear programming theory and techniques is assumed. 1994 edition"--

The increasing power of computer technologies, the evolution of software en- neering and the advent of the intelligent transport systems has prompted traf c simulation to become one of the most used approaches for traf c analysis in s- port of the design and evaluation of traf c systems. The ability of traf c simulation to emulate the time variability of traf c phenomena makes it a unique tool for capturing the complexity of traf c systems. In recent years, traf c simulation – and namely microscopic traf c simulation – has moved from the academic to the professional world. A wide variety of traf- c simulation software is currently available on the market and it is utilized by thousands of users, consultants, researchers and public agencies. Microscopic traf c simulation based on the emulation of traf c ows from the dynamics of individual vehicles is becoming one the most attractive approaches. However, traf c simulation still lacks a uni ed treatment. Dozens of papers on theory and applications are published in scienti c journals every year. A search of simulation-related papers and workshops through the proceedings of the last annual TRB meetings would support this assertion, as would a review of the minutes from speci cally dedicated meetings such as the International Symposiums on Traf c Simulation (Yokohama, 2002; Lausanne, 2006; Brisbane, 2008) or the International Workshops on Traf c Modeling and Simulation (Tucson, 2001; Barcelona, 2003; Sedona, 2005; Graz 2008). Yet, the only comprehensive treatment of the subject to be found so far is in the user’s manuals of various software products.

This book combines the research activities of the authors, both of whom are researchers at Ecole Nationale de l’Aviation Civile (French National School of Civil Aviation), and presents their findings from the last 15 years. Their work uses air transport as its focal point, within the realm of mathematical optimization, looking at real life problems and theoretical models in tandem, and the challenges that accompany studying both approaches. The authors’ research is linked with the attempt to reduce air space congestion in Western Europe, USA and, increasingly, Asia. They do this through studying stochastic optimization (particularly artificial evolution), the sectorization of airspace, route distribution and takeoff slots, and by modeling airspace congestion. Finally, the authors discuss their short, medium and long term research goals. They hope that their work, although related to air transport, will be applied to other fields, such is the transferable nature of mathematical optimization. At the same time, they intend to use other areas of research, such as approximation and statistics to complement their continued inquiry in their own field. Contents 1. Introduction. Part 1. Optimization and Artificial Evolution 2. Optimization: State of the Art. 3. Genetic Algorithms and Improvements. 4. A new concept for Genetic Algorithms based on Order Statistics. Part 2. Applications to Air Traffic Control 5. Air Traffic Control. 6. Contributions to Airspace Sectorization. 7. Contribution to Traffic Assignment. 8. Airspace Congestion Metrics. 9. Conclusion and Future Perspectives. About the Authors Daniel Delahaye works for Ecole Nationale de l’Aviation Civile (French National School of Civil Aviation) in France. Stéphane Puechmorel works for Ecole Nationale de l’Aviation Civile (French National School of Civil Aviation) in France.

Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).

This volume investigates developments in, and management of, transportation systems, future trends and what effects these will have on society. The book studies transportation systems planning; traffic problems and the issue of conservation; the use of logistics, and the role of computers and robotics in traffic control.

This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems. This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.

This book contains eleven chapters describing some of the most recent methodological operations research developments in transportation. It is structured around the main transportation modes, and each chapter is written by a group of well-recognized researchers. Because of the major impact of operations research methods in the field of air transportation over the past forty years, it is befitting to open the book with a chapter on airline operations management. This book will prove useful to researchers, students, and practitioners in transportation and will stimulate further research in this rich and fascinating area. Volume 14 examines transport and its relationship with operations and management science 11 chapters cover the most recent research developments in transportation Focuses on main transportation modes-air travel, automobile, public transit, maritime transport, and more