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goerigk m introduction robust combinatorial optimization 2024

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Textbook in PDF format 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. Preface Contents Symbols Introduction A Robust Decision-Making Problem Purpose and Structure of This Book References Basic Concepts Complexity Big-O Notation Polynomial-Time Complexity NP-Hardness Approximation Algorithms Linear and Integer Linear Programming Graph Structures Combinatorial Problems The Knapsack Problem The Selection Problem The Shortest Path Problem The Minimum Spanning Tree Problem The Assignment Problem The Traveling Salesperson Problem Scheduling Problems The Matroid Optimization Problem Further Reading Exercises Solutions References Robust Problems Robust Decision Criteria Uncertainty Sets Comparing Criteria Relationships to Multi-Criteria Optimization Further Reading Exercises Solutions References General Reformulation Results Convexity of Uncertainty Sets Interval Uncertainty Min-Max Problems Two-Stage and Recoverable Problems Min-Max Regret Problems Discrete Uncertainty Min-Max Problems Two-Stage and Recoverable Problems Min-Max Regret Problems Polytopal Uncertainty Min-Max Problems Two-Stage and Recoverable Problems Min-Max Regret Problems Budgeted Uncertainty Min-Max Problems Two-Stage and Recoverable Problems Min-Max Regret Problems Relationships Between Uncertainty Sets Further Reading Exercises Solutions References General Solution Methods Scenario Generation Abstract Method Scenario Generation for Min-Max Problems Scenario Generation for Min-Max Regret Problems Scenario Generation for Two-Stage and Recoverable Problems Approximation Methods Reducing Discrete Uncertainty Sets Norm-Based Approximation for Discrete Uncertainty Sets Reducing Interval Uncertainty Sets Pseudopolynomial Methods and Approximation Schemes Further Reading Exercises Solutions References Robust Selection Problems Min-Max Selection Min-Max Regret Selection Discrete Uncertainty Interval Uncertainty Budgeted Uncertainty Two-Stage Selection Discrete Uncertainty Polytopal Uncertainty Continuous Budgeted Uncertainty Discrete Budgeted Uncertainty Recoverable Selection Discrete Uncertainty Interval Uncertainty Continuous Budgeted Uncertainty Discrete Budgeted Uncertainty Further Reading Exercises Solutions References Robust Shortest Path Problems Min-Max Shortest Path Min-Max Regret Shortest Path Discrete Uncertainty Interval Uncertainty Two-Stage Shortest Path Discrete Uncertainty Discrete Budgeted Uncertainty Recoverable Shortest Path Discrete Uncertainty Interval Uncertainty Further Reading Exercises Solutions References Robust Spanning Tree Problems Min-Max Spanning Tree Min-Max Regret Spanning Tree Discrete Uncertainty Interval Uncertainty Two-Stage Spanning Tree Recoverable Spanning Tree Discrete Uncertainty Interval Uncertainty Discrete Budgeted Uncertainty Further Reading Exercises Solutions References Other Combinatorial Problems Robust Assignment Problems Robust Knapsack Problems Robust Traveling Salesperson Problems Robust Scheduling Problems Further Reading Exercises Solutions References Other Models for Robust Optimization Ordered Weighted Averaging Ellipsoidal Uncertainty K-Adaptability and Min-Max-Min Decision-Dependent Uncertainty Further Reading Exercises Solutions References Open Problems A Problem Definitions Alphabetical Index

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goerigk m introduction robust combinatorial optimization 2024