An Introduction to Robust Combinatorial Optimization Concepts, Models and Algorithms for Decision Making under Uncertainty

This book offers a self-contained introduction to the world of robust combinatorial optimization. It explores decision-making using the min-max and min-max regret criteria, while also delving into the two-stage and recoverable robust optimization paradigms. It begins by introducing readers to general results for interval, discrete, and budgeted uncertainty sets, and subsequently provides a comprehensive examination of specific combinatorial problems, including the selection, shortest path, spanning tree, assignment, knapsack, and traveling salesperson problems.

The book equips both students and newcomers to the field with a grasp of the fundamental questions and ongoing advancements in robust optimization. Based on the authors’ years of teaching and refining numerous courses, it not only offers essential tools but also highlights the open questions that define this subject area.

1. Introduction.- 2. Basic Concepts.- 3. Robust Problems.- 4. General Reformulation Results.- 5. General Solution Methods.- 6. Robust  election Problems.- 7. Robust Shortest Path Problems.- 8. Robust Spanning Tree Problems.- 9. Other Combinatorial Problems.- 10. Other Models for Robust Optimization.- 11. Open Problems.

Marc Goerigk is a Professor and Chair of Business Decisions and Data Science at the University of Passau, Germany. He has previously held positions at the Universities of Siegen, Lancaster (UK), Kaiserslautern, and Göttingen, where he pursued his studies in mathematics. Marc has a keen interest in optimization under uncertainty.

Michael Hartisch currently serves as a temporary professor of Analytics & Mixed-Integer Optimization at Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany. Prior to this role, he was acting chair of Network and Data Science Management at the University of Siegen, Germany. His academic journey began with studies in mathematics at Friedrich Schiller University Jena, Germany. Michael’s primary focus is on optimization under uncertainty.