This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution. The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams. It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming. On the practical side, it explains how LBBD has been applied to a rapidly growing variety of problem domains. After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand. In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.
Introduction.- Inference Duality.- The Basic Logic-based Benders
Method.- Classical Benders Decomposition.- Combinatorial Benders
Cuts.- Stochastic and Robust Optimization.- LBBD and Decision Diagrams.- LBBD
and Heuristic Methods.- Task Assignment and Scheduling.- .Vehicle
Routing.- Shop, Factory, and Employee Scheduling.- Other Scheduling and
Logistics Problems; Health-related Applications.- Network Design.- Other
Applications.
John Hooker is Professor of Operations Research and T. Jerome Holleran Professor of Business Ethics and Social Responsibility at Carnegie Mellon University. He has published 200+ articles, 9 books, and 6 edited volumes in operations research, constraint programming, AI, formal logic, business ethics, ethics of AI, cross-cultural management, philosophy, and music theory. He is a Fellow of the Institute for Operations Research and the Management Sciences (INFORMS) as well as recipient of the INFORMS Computing Society Prize and the INFORMS Khachiyan Prize for lifetime achievements in optimization. He is equally active in the constraint programming community, where he has chaired conferences and workshops, served on the Executive Committee of the Association for Constraint Programming (ACP), and was recognized with the ACP Research Excellence Award. Dr. Hooker is a pioneer in the integration of optimization and constraint programming technologies, having written the first book and co-chaired the first conference on the subject. OR/CP integration now an important element of state-of-the-art optimization software. He also introduced logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method. It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems. He was the first to observe the phase transition phenomenon in satisfiability problems. He and T. Hadi introduced decision diagrams as an optimization method, and several investigators are now pursuing this line of research. In recent research, he draws on his dual background in ethics and operations research to develop optimization models for fairness and distributive justice.
