Exact and Heuristic Methods in Combinatorial Optimization: A Study on the Linear Ordering and the Maximum Diversity Problem(175 Applied Mathematical Sciences)

In the last decades, algorithmic advances as well as hardware and software improvements have provided an excellent environment to create and develop solving methods to hard optimization problems. Modern exact and heuristic techniques are dramatically enhancing our ability to solve significant practical problems. This monograph sets out state-of-the-art methodologies for solving combinatorial optimization problems, illustrating them with two well-known problems. This second edition of the book extends the first one by adding to the ‘linear ordering problem’ (LOP), included in the first edition, the ‘maximum diversity problem’ (MDP). In this way, we provide the reader with the background, elements and strategies to tackle a wide range of different combinatorial optimization problems. 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 and the MDP 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. This monograph provides the basic principles and fundamental ideas that will enable students and practitioners to create valuable applications based on both exact and heuristic technologies. Specifically, it is aimed at engineers, scientists, operations researchers, and other applications specialists who are looking for the most appropriate and recent optimization tools to solve particular problems. The book provides a broad spectrum of advances in search strategies with a focus on its algorithmic and computational aspects.

Table of Contents:
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.

About the Author :
​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.

Review :
“The book is well suited for readers who want to learn how to solve real world combinatorial optimization problems as the methods are well explained and a lot of algorithms are given with pseudo-code. The authors explain all terms they use and the book is well understandable. … All in all this book can be recommended to anyone interested in combinatorial optimization who wants to get an overview of the classical solution approaches in this field.” (Isabel Beckenbach, zbMATH 1500.90001, 2023)