'Exact' and 'heuristic' techniques are enhancing our ability to overcome intractable obstacles in the world of optimization. Using the linear ordering problem as an illustration, this text provides a toolkit for tackling a variety of combinatorial dilemmas.

Faced with the challenge of solving the hard optimization problems that abound in the real world, existing methods often encounter great difficulties. Important applications in business, engineering or economics cannot be tackled by the techniques that have formed the predominant focus of academic research throughout the past three decades. Exact and heuristic approaches are dramatically changing our ability to solve problems of practical significance and are extending the frontier of problems that can be handled effectively. This monograph details state-of-the-art optimization methods, both exact and heuristic, for the LOP. The authors employ the LOP to illustrate contemporary optimization technologies as well as how to design successful implementations of exact and heuristic procedures. Therefore, they do not limit the scope of this book to the LOP, but on the contrary, provide the reader with the background and practical strategies in optimization to tackle different combinatorial problems.

Self-contained monograph on algorithmic issues related to the linear ordering problem Comprehensive general introduction to algorithms for computing approximate and exact solutions of combinatorial optimization problems Accessible without deep mathematical background Includes supplementary material: sn.pub/extras

Autorentext

Rafael Martí is Professor of Statistics and Operations Research at the University of Valencia, Spain. He received a doctoral degree in Mathematics in 1994, and has done extensive research in metaheuristics for hard optimization problems. Dr Martí has about 200 publications, half of them in indexed journals (JCR). He authored several books in optimization, included the co-edited Handbook of Heuristics, a 3-volume reference in the area, published by Springer (2018). Prof. Martí has supervised 7 doctoral and 14 Master thesis, and has secured an American patent. Prof. Martí is currently area editor in the Journal of Heuristics, and associate editor in several journals, including the European Journal of Operational Research, and Math. Prog. Computation. He is Senior Research Associate of the private company OptTek Systems (USA), and has given more than 50 invited and plenary talks. Dr. Martí has been invited Professor in many universities, including the University of Colorado (USA), the University of Molde (Norway), the University of Wien (Austria), the University of Bretagne-Sud (France), or the University College of Dublin (Ireland). He coordinates the Spanish Network on Metaheuristics, funded by the Spanish government as a Network of excellence, and the doctoral program "Statistics and Optimization" at the Univerity of Valencia. Gerhard Reinelt is professor of Computer Science at Heidelberg University, Germany, since 1992. He received a doctoral degree in Mathematics in 1985 and habilitated in Computer Science in 1991, both at the University of Augsburg, Germany. His main research activities are concerned with the development, analysis and implementation of algorithms for the solution of large-scale combinatorial optimization and mixed-integer programming problems. This comprises the design of fast approximate heuristics as well as the development of algorithms for computing provably optimum solutions, where emphasis is laid on methods for cutting plane generation. Reinelt has supervised 21 doctoral students and published several books and co-edited volumes.

Klappentext
Complex optimization problems abound in the real world. In the face of these challenges, established methods often fall short of providing solutions. However, 'exact' and 'heuristic' techniques are dramatically enhancing our ability to solve significant practical problems in the world of optimization. They are changing the landscape in the field, broadening the frontiers of the possible, and allowing us to engage effectively with a whole new range of challenges. This monograph sets out state-of-the-art optimization methods for tackling the 'linear ordering problem' (LOP). Whereas important applications in business, engineering and economics lie beyond the reach of methodologies that have been the focus of academic research for three decades, the fresh approaches set out in this volume provide practical solutions to the LOP. The focus on the LOP does not limit the monograph's scope and applicability, however. The exact and heuristic techniques outlined in these pages can be put to use in any number of combinatorial optimization problems. While the authors employ the LOP to illustrate cutting-edge optimization technologies, the book is also a tutorial on how to design effective and successful implementations of exact and heuristic procedures alike. The information in these pages provides readers with a toolkit that can be employed in a variety of settings. As a result, the book will be of great interest to researchers and practitioners in a number of fields, including computer science, mathematics, operations research, management science, industrial engineering, and economics. It is also suitable for use as a textbook on issues of practical optimization in a masters course, or as a reference book for engineering optimization algorithms. The authors have sought to make the book accessible to as wide an audience as possible by providing the reader with basic definitions and concepts in optimization. In addition, the numerous tutorials aid speedy assimilation, while thecoverage given to the next generation of Flash software prepares readers for future developments.

Inhalt
1 Introduction.- 2 Heuristic Methods.- 3 Meta-Heuristics.- 4 Branch-and-Bound.- 5 Branch-and-Cut.- 6 The Linear Ordering Polytope.- 7 Further Aspects.- References.- Index.