Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hyperplane location combining analytical and geometrical methods. The major portion of the text presents new results on this topic, including the extension of some special cases to all distances derived from norms and a discussion of restricted problems in the plane. Almost all results are proven in the text and most of them are illustrated by examples. Furthermore, relations to classical facility location and to problems in computational geometry are pointed out. Audience: The book is suitable for researchers, lecturers, and graduate students working in the fields of location theory or computational geometry.

In this thesis, we consider the location of median lines when there is a restriction on the slope of the line to locate as well as the more general location of median hyperplanes when there is a restriction on the slope vector of the hyperplane to locate. We are given a set of existing facilities in R^2 or R^n and we are searching for a new facility that is a line or a hyperplane, respectively, minimizing the sum of distances between the existing facilities and the new facility while satisfying a restriction on its slope. We investigate this problem in the plane R^2 using different distance ...

This comprehensive and clearly structured book presents essential information on modern Location Science. The book is divided into three parts: basic concepts, advanced concepts and applications. Written by the most respected specialists in the field and thoroughly reviewed by the editors, it first lays out the fundamental problems in Location Science and provides the reader with basic background information on location theory. Part II covers advanced models and concepts, broadening and expanding on the content presented in Part I. It provides the reader with important tools to help them understand and solve real-world location problems. Part III is dedicated to linking Location Science with other areas like GIS, telecommunications, healthcare, rapid transit networks, districting problems and disaster events, presenting a wide range of applications. This part enables the reader to understand the role of facility location in such areas, as well as to learn how to handle realistic location problems. The book is intended for researchers working on theory and applications involving location problems and models. It is also suitable as a textbook for graduate courses on facility location.

VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.

This book is a volume in honor of Zvi Drezner’s 75th birthday. Professor Drezner is a leading scholar in location science. He received his BSc degree in Mathematics in 1965 and his PhD. in Computer Science ten years later, both from the Technion in Haifa, Israel. Since 1978 he has published in excess of 300 papers in refereed journals and books. He has received many honors, among them the University Outstanding Professor in 2005-6, the Outstanding Research Award (both from Cal State-Fullerton), the Location Analysis Lifetime Achievement Award from the Society for Location Analysis, and was named a Lifetime Fellow in INFORMS.Zvi has worked in a variety of fields, but most prominently in continuous location models. His main contributions include a 1982 paper on competitive location analysis, which was the first contribution to formally use the von Stackelberg “leader-follower” concept in the plane, contributions in 1989 (along with many others) on the Weber problem, and work with Oded Berman on the p-median under uncertainty in 2008. He has also enriched the literature by many contributions that devise genetic algorithms and tabu search techniques (both heuristic algorithms), as well as global optimization techniques, such as the “big-triangle-small-triangle” method, applied to location problems.The chapters of the book have been chosen to provide readers with a large variety of topics in the field of location science, which normally are available only in many different specialist journals. In addition to easily approachable surveys, the contributions, written by the top specialists in the field, present the latest results as well.

This book presents a self-contained introduction to the theory of minisum hyperspheres. This specialized research area within the larger field of geometric optimization is full of interesting and open problems. This work provides an overview of the history of minisum hyperspheres as well as describes the best techniques for developing and solving minisum hypersphere problems. Various related areas of geometric and nonlinear optimization are also discussed. As the first publication devoted to this area of research, this work will be of great interest to graduate-level researchers studying minisum hypersphere problems as well as mathematicians interested geometric optimization.

This book constitutes the refereed proceedings of the Third International Conference on Swarm, Evolutionary, and Memetic Computing, SEMCCO 2012, held in Bhubaneswar, India, in December 2012. The 96 revised full papers presented were carefully reviewed and selected from 310 initial submissions. The papers cover a wide range of topics in swarm, evolutionary, memetic and other intelligent computing algorithms and their real world applications in problems selected from diverse domains of science and engineering.