Discrete Diversity and Dispersion Maximization

This book demonstrates the metaheuristic methodologies that apply to maximum diversity problems to solve them. Maximum diversity problems arise in many practical settings from facility location to social network analysis and constitute an important class of NP-hard problems in combinatorial optimization. In fact, this volume presents a "missing link" in the combinatorial optimization-related literature. In providing the basic principles and fundamental ideas of the most successful methodologies for discrete optimization, this book allows readers to create their own applications for other discrete optimization problems. Additionally, the book is designed to be useful and accessible to researchers and practitioners in management science, industrial engineering, economics, and computer science, while also extending value to non-experts in combinatorial optimization. Owed to the tutorials presented in each chapter, this book may be used in a master course, a doctoral seminar, or as supplementary to a primary text in upper undergraduate courses.

The chapters are divided into three main sections. The first section describes a metaheuristic methodology in a tutorial style, offering generic descriptions that, when applied, create an implementation of the methodology for any optimization problem. The second section presents the customization of the methodology to a given diversity problem, showing how to go from theory to application in creating a heuristic. The final part of the chapters is devoted to experimentation, describing the results obtained with the heuristic when solving the diversity problem. Experiments in the book target the so-called MDPLIB set of instances as a benchmark to evaluate the performance of the methods.

Auteur

Rafael Martí is Professor of Statistics and Operations Research at the University of Valencia, Spain. He received a doctoral degree in Mathematics from the University of Valencia in 1994. He has done extensive research in metaheuristics for hard optimization problems. Dr Martí has about 200 publications, half of them in indexed journals (JCR),. His h-index is 54 according to Google scholar. He is the co-author of several monographic and edited books, such as "The Linear Ordering Problem" (Springer 2011) or "Metaheuristics for Business Analytics" (Springer 2018). Prof. Martí has recently co-edited the "Handbook of Heuristics", a 3-volume reference in the area, published by Springer, and has secured an American patent. Prof. Martí is currently Area Editor in the Journal of Heuristics, and Associate Editor in many journals of the area, such as EJOR, TOP, or Math. Prog. Comp. He is Senior Research Associate of OptTek Systems (USA), and has given about 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), and University of Bretagne-Sud (France), or the University College of Dublin (Ireland). He coordinates the Spanish Network on Metaheuristics, currently funded by the Spanish government. Anna Martínez-Gavara is Associate Professor of Statistics and Operations Research at the University of Valencia, Spain. She received a doctoral degree in Mathematics from the University of Valencia in 2008. She has done extensive research in metaheuristics for hard optimization problems. Prof. Martínez-Gavara has close to 200 cites according to Google scholar, and has been referee for the most important journals in optimization, such as EJOR, Computers and OR, or JOGO. Prof. Martínez-Gavara is co-author in 16 publications in journals indexed in JCR, most of them in the first quartile as EJOR, ESWA, or Information Sciences. In addition, she is co-author in more than 15 other publications including non-indexed journals, book chapters and publications in proceedings of both national and international congresses. He has made more than 30 presentations at conferences (national and international) and at universities, as well as various research stays at the universities of Marseille (France), l'École Polytechnique de Paris (France), Colorado (USA) and Nottingham (UK). Prof. Martínez-Gavara teaches courses such as Statistical and Optimization in Master's Degree in Data Science or Mathematical programming in the Degree in Mathematics, among others.