Accelerating Benders decomposition for network design

Network design problems arise in many different application areas such as air freight, highway traffic and communications systems. This thesis concerns the development, analysis and testing of new techniques for solving network design problems. We study the application of Benders decomposition to solve mixed integer programming formulations of the network design problem. A new methodology for accelerating the convergence of Benders decomposition for network design is introduced. These acceleration techniques are also applicable to a much broader class of algorithms that includes Benders decomposition for general mixed integer programs, Dantzig-Wolfe decomposition for linear and nonlinear programs and other related procedures. These methods are specialized to network problems by the development of very efficient algorithms that exploit the underlying structure of these models. Computational experience demonstrating the value of these techniques is given. Another important issue in improving the computational performance of Benders decomposition for network design and other mixed integer programming models is the selection of a "good" mixed integer programming problem formulation. We give a criteria for choosing between two mathematical formulations of the same problem in the context of Benders decomposition. Since good heuristic methods are important in generating initial starting points for Benders decomposition, we study the accuracy of heuristic solution procedures for a particular type of network design problem. Worstcase performance measures of heuristic network design procedures are presented. For a restricted version of the network design model, we describe a procedure whose maximum percentage of error is bounded by a constant. For a more general version of the problem, we give results concerning the complexity of finding efficient (polynomially time bounded) heuristics for the network design problem. THESIS SUPERVISOR: Thomas L. Magnanti TITLE: Associate Professor of Operations Research and Management