This book offers as exploration into the emerging field of Inverse Combinatorial Optimization Problems (ICOPs), a transformative area within operations research. As traditional optimization focuses on maximizing or minimizing objectives under constraints, ICOPs reverse this process, allowing for the inference of hidden parameters from observed outcomes. This monograph provides a comprehensive framework for understanding and applying ICOPs across various domains. Key concepts such as inverse shortest path, spanning tree, and center location problems are meticulously examined, offering theoretical insights and algorithmic solutions. The authors present a structured approach to these complex problems, making this work an essential resource for both academic and practical applications. By addressing critical questions and providing algorithmic tools, this book is a must-read for those seeking to enhance network design, logistics, and strategic planning. Researchers, academics, and practitioners in operations research and management science will find this monograph invaluable. It not only contributes to academic discourse but also equips professionals with the knowledge to tackle real-world challenges. This book is a vital addition to any library supporting advanced studies in optimization and decision-making processes.

It provides a comprehensive review of the rapidly expanding field of inverse combinatorial optimization problems It includes in-depth discussions on a framework to integrate these problems and clarify their intricate relationship It covers a vast array of special topics, open problems and applications illustrating the wide use of these problems

Autorentext

Xiucui Guan obtained her Ph.D. at City University of Hong Kong on 2005 majoring in combinatorial optimization. After graduation, she worked as a lecturer from May 2005 to April 2007 and an associate professor from May 2007 to April 2018 at School of Mathematics, Southeast University, China. She has been employed as a professor of School of Mathematics since May 2018. I had visited Prof. Panos M. Pardalos at Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida for one year since February 2013. Her research interest includes discrete optimization, inverse combinatorial optimization, linear programming, algorithm design and analysis, etc. She has published more than 40 papers on combinatorial optimization, including more than 20 SCI indexed papers. I have been supported by 6 projects and 3 of them were supported by National Natural Science Foundation of China. I have cultivated 17 graduate students to obtain their masters’ degree at Mathematics and 3 Ph.D. students. I mainly study on Inverse Combinatorial Optimization Problems (ICOP) including inverse linear programming problems, inverse minimum/max+sum spanning tree problems, inverse center/median location problems, shortest path improvement/interdiction problems, etc. We built mathematical models for these ICOPs, analyzed their properties and designed efficient algorithms to solve them. There are many applications of ICOPs in the field of transportation networks, communication networks, geophysical sciences, electricity markets, medical decision-making areas, etc. Researches on the ICOPs can help solve their corresponding problems in applications.

Inhalt

Preface.- Part I. An Introduction to Inverse Combinatorial Optimization Problems.- An Outline of Inverse Combinatorial Optimization Problems.- Generalized Inverse Bottleneck Optimization Problems.- Generalized Inverse Maximum Capacity Path Problems.- Some General Methods to Solve Inverse Linear Programming Problem under Weighted 𝑙1 Norm.- Part II. Generalized Inverse Shortest Path Problems.- Shortest Path Improvement Problems.- Shortest Path Interdiction Problems on Trees.- Sum of Root-leaf Distance Interdiction Problems on Trees.- Restricted Inverse Optimal Value Problem on Shortest Path under Weighted 𝑙1 Norm on Trees.- Part III. Generalized Inverse Spanning Tree Problems.- Inverse Minimum Spanning Tree Problems.- Inverse Max+Sum Spanning Tree Problems.- Restricted Inverse Optimal Value Problem on Minimum Spanning Tree.- Partial Inverse Minimum Spanning Tree Problems.- Part IV. Generalized Inverse Center Location Problems.- Inverse vertex obnoxious 1-center location problems.- Inverse Quickest 1-Center Location Problem on Trees.- References.