Combinatorial Optimization - Böcker

The author presents polyhedral results and exact solution methods for location problems encountered in telecommunications, but which also have applications in other areas, such as transportation and supply chain management.

The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.

Combinatorial optimization algorithms are used in many applications including the design, management, and operations of communication networks. The objective of this book is to advance and promote the theory and applications of combinatorial optimization in communication networks. Each chapter of the book is written by an expert dealing with theoretical, computational, or applied aspects of combinatorial optimization.Topics covered in the book include the combinatorial optimization problems arising in optical networks, wireless ad hoc networks, sensor networks, mobile communication systems, and satellite networks. A variety of problems are addressed using combinatorial optimization techniques, ranging from routing and resource allocation to QoS provisioning.

Written by reputable researchers, this book covers various important areas of study on Traveling Salesman Problem, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, thorough computational analysis of heuristic and metaheuristic algorithms, and more.

The quadratic assignment problem (QAP) is a classical combinatorial optimization problem with numerous applications in facility location, scheduling, manufacturing, VLSI design, and statistical data analysis. The QAP is a problem from both theoretical and practical points of view: the QAP is NP-hard to solve to optimality and to approximate within a constant approximation ratio; and QAP instances of size larger than 22 are still considered intractable. Hence, the QAP is in effect a problem that has yet to be solved. This volume presents a general overview of the most studied aspects of the QAP, as well as outlining a number of research directions which in the 1990s seem to be promising. The book gives a systematic presentation of various results scattered in the literature, such as: bounding techniques and exact solution methods, linearizations, heuristic approaches and computational complexity. Some more recent research directions discussed in detail in the book are the asymptotic behaviour of the QAP and restricted versions of the problem: in particular, polynomially solvable and provably hard cases of the QAP.This volume should be of interest to researchers and students interested in the quadratic assignment problem and to practitioners who face the QAP and wish to better understand this problem in its inherent complexity.

Combinatorial Engineering of Decomposable Systems presents a morphological approach to the combinatorial design/synthesis of decomposable systems. Applications involve the following: design (e.g., information systems; user's interfaces; educational courses); planning (e.g., problem-solving strategies; product life cycles; investment); metaheuristics for combinatorial optimization; information retrieval; etc.

This book is a revised and updated version of the INFORMS award winner for "best dissertation on Location Analysis of 1995". The book integrates two seemingly unrelated fields: location analysis and fractional programming. Location analysis deals with the problem of where to locate facilities in such a way as to optimize a particular criterion taking into account the existing clients. Fractional programming is a special field of nonlinear programming dealing with optimization problems where the objective function consists of a ratio of given functions. Although the application scope of fractional programming is vast, it has not been much related to specific operations-research problems, and in particular, to location analysis. This book bridges the gap by tackling several location models that require combined solution techniques and theoretical results from both fields. Included are results in discrete location, especially in two-level location models, and the theoretical and practical potential of fractional programming in location theory.The book should be of value to researchers in mathematics, operations research and management science interested in combinatorial optimization, fractional programming, and location theory.

This work focuses on three disciplines of applied mathematics: control theory, location science and computational geometry. The author shows how methods and tools from convex geometry in a wider sense can help solve various problems from these disciplines. More precisely they consider mainly the tent method (as an application of a generalized separation theory of convex cones) in nonclassical variational calculus, various median problems in Euclidean and other Minkowski spaces (including a detailed discussion of the Fermat-Torricelli problem) and different types of partitionings of topologically complicated polygonal domains into a minimum number of convex pieces. Figures are used extensively throughout and there is also a large collection of exercises.

The technique of randomization has become very prevalent since it offers superior performance and simplicity. Numerous researchers work in this area of vital importance. Parallel Computing is also very important since one can get excellent speedups using parallel computers. This book combines these two domains. It provides a summary of the state-of-the-art results and techniques in the area of randomized parallel computing. There are few texts in the area of randomized computing, and more surprisingly there is no text in the area of randomized parallel computing. Thus our book fills the void in this very important area. Audience: This is a reference book for researchers, educators, and students. It can also be used as a text for an advanced graduate course on randomized computing, parallel computing, or distributed computing.

Presenting a set of contributions by the most influential authors on the Steiner Tree problem, the authors of this text address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications. The book is intended for advanced undergraduates, graduates and research scientists in combinational optimization and computer science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.

Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly. This work provides major algorithmic aspects and applications of NAPs as contributed by international experts. The chapters included in this book are concerned with major applications and the latest algorithmic solution approaches for NAPs. Approximation algorithms, polyhedral methods, semidefinite programming approaches and heuristic procedures for NAPs are included, while applications of this problem class in the areas of multiple-target tracking in the context of military surveillance systems, of experimental high energy physics, and of parallel processing are presented. This work shoudl appeal to researchers and graduate students in the areas of combinatorial optimization, mathematical programming, operations research, physics, and computer science.

This monograph is concerned with network restoration problems to ensure telecommunication network survivability. More precisely, the author studies the problems of determining minimum cost link capacities in order to satisfy a given set of requirements, that is the network synthesis problem, restoration of which is a special application. The author illustrates the role that combinatorial optimization techniques can play in the solutions of various classes of synthesis problem encountered in telecommunication planning. The author presents a literature review, mathematical formulations, and a complexity analysis. Lower bounds, and exact solutions for some classes of this problem are provided. Furthermore, she develops a tabu search heuristic for finding good approximate solutions for real size instances. The monograph also provides an introduction to SDH/SONET telecommunication networks and to various survivability techniques.

Randomization techniques have been employed to solve numerous problems of computing both sequentially and in parallel. Examples of randomized algorithms that are asymptotically better than their deterministic counterparts in solving various fundamental problems abound. Randomized algorithms have the advantages of simplicity and better performance both in theory and often in practice. This two-volume handbook is a collection of articles covering a wide spectrum of issues in randomization. The handbook should be a valuable reference for all the important areas of algorithm design, including those essential to its applications in computer science and engineering.

This volume concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial--geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Researchers in network design, applied optimization, and design of algorithms should find this book useful.

This volume is a collection of 16 articles contributed by influential experts in the field of Steiner tree applications. The articles are designed to explore the impact on industries of the long-term theoretical development of Steiner tree problems. The authors address various Steiner tree problems originating from and applied to industry fields, such as the design of electronic circuits, telecommunication networks, computer networks, and computer biology. This book should be a good reference tool for scientists who depend on Steiner tree problems in some way.

This volume provides information on theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including: polyhedral theory for symmetric and asymmetric TSP; branch and bound, and branch and cut algorithms; probabilistic aspects of TSP; thorough computational analysis of heuristic and metaheuristic algorithms: theoretical analysis of approximation algorithms, including the emerging area of domination analysis of algorithms; and discussion of TSP software and variations of TSP such as bottleneck TSP, generalized TSP, prize collecting TSP, maximizing TSP, orienteering problem, and so on.

This comprehensive volume offers a collection of 28 state-of-the-art articles contributed by experts of pattern recognition, string matching, or both. It contains fundamental concepts and notations, as well as reports on contemporary research with respect to both methodology and applications. In particular, it includes string matching related techniques for structural pattern recognition. It also explores many applications of pattern recognition strategies to image segmentation, intrusion detection, handwriting recognition and others.

In the last few decades, multiscale algorithms have become a dominant trend in large-scale scientific computation. Researchers have successfully applied these methods to a wide range of simulation and optimization problems. This book gives a general overview of multiscale algorithms; applications to general combinatorial optimization problems such as graph partitioning and the traveling salesman problem; and VLSICAD applications, including circuit partitioning, placement, and VLSI routing. Additional chapters discuss optimization in reconfigurable computing, convergence in multilevel optimization, and model problems with PDE constraints.

This text on the discrete ordered median problem (DOMP) unifies many classical and new facility location problems. Several exact and heuristic approaches are developed in this book in order to solve the DOMP. It is suitable for researchers in location theory, and graduate students in combinatorial optimization.

Combinatorial optimization algorithms are used in many applications including the design, management, and operations of communication networks. The objective of this book is to advance and promote the theory and applications of combinatorial optimization in communication networks. Each chapter of the book is written by an expert dealing with theoretical, computational, or applied aspects of combinatorial optimization.Topics covered in the book include the combinatorial optimization problems arising in optical networks, wireless ad hoc networks, sensor networks, mobile communication systems, and satellite networks. A variety of problems are addressed using combinatorial optimization techniques, ranging from routing and resource allocation to QoS provisioning.

The quadratic assignment problem (QAP) is a classical combinatorial optimization problem with numerous applications in facility location, scheduling, manufacturing, VLSI design, statistical data analysis, etc. The QAP is an extremely hard problem from both theoretical and practical points of view: 1) The QAP is NP-hard to solve to optimality and to approximate within a constant approximation ratio, and 2) QAP instances of size larger than 22 are still considered intractable. Hence, the QAP is in effect a problem that has yet to be solved. This volume presents a general overview of the most studied aspects of the QAP, as well as outlining a number of research directions which currently seem to be promising. The book gives a systematic presentation of various results scattered in the literature, such as: bounding techniques and exact solution methods, linearisations, heuristic approaches and computational complexity. Some more recent research directions discussed in detail in the book are the asymptotic behaviour of the QAP and restricted versions of the problem: in particular, polynomially solvable and provably hard cases of the QAP.Audience: This volume will be of interest to researchers and students interested in the quadratic assignment problem and to practitioners who face the QAP and wish to better understand this problem in its inherent complexity.

This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications. Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.

Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly. The purpose of this book is to provide in a single volume, major algorithmic aspects and applications of NAPs as contributed by leading international experts. The chapters included in this book are concerned with major applications and the latest algorithmic solution approaches for NAPs. Approximation algorithms, polyhedral methods, semidefinite programming approaches and heuristic procedures for NAPs are included, while applications of this problem class in the areas of multiple-target tracking in the context of military surveillance systems, of experimental high energy physics, and of parallel processing are presented. Audience: Researchers and graduate students in the areas of combinatorial optimization, mathematical programming, operations research, physics, and computer science.

This monograph is concerned with network restoration problems to ensure telecommunication network survivability. More precisely, the author studies the problems of determining minimum cost link capacities in order to satisfy a given set of requirements, that is the network synthesis problem, restoration of which is a special application. In this monograph, the author illustrates the role that combinatorial optimization techniques can play in the solutions of various classes of synthesis problem encountered in telecommunication planning. The author presents a literature review, mathematical formulations, and a complexity analysis. Lower bounds, and exact solutions for some classes of this problem are provided. Furthermore, she develops a tabu search heuristic for finding good approximate solutions for real size instances. The monograph also provides an introduction to SDH/SONET telecommunication networks and to various survivability techniques. Audience: The book will be of interest to researchers and professionals working in mathematics, operations research, and engineering economics, particularly when related to the telecommunications industry.

Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms.

In the last few decades, multiscale algorithms have become a dominant trend in large-scale scientific computation. Researchers have successfully applied these methods to a wide range of simulation and optimization problems. This book gives a general overview of multiscale algorithms; applications to general combinatorial optimization problems such as graph partitioning and the traveling salesman problem; and VLSICAD applications, including circuit partitioning, placement, and VLSI routing. Additional chapters discuss optimization in reconfigurable computing, convergence in multilevel optimization, and model problems with PDE constraints. Audience: Written at the graduate level, the book is intended for engineers and mathematical and computational scientists studying large-scale optimization in electronic design automation.

The technique of randomization has been employed to solve numerous prob­ lems of computing both sequentially and in parallel. Examples of randomized algorithms that are asymptotically better than their deterministic counterparts in solving various fundamental problems abound. Randomized algorithms have the advantages of simplicity and better performance both in theory and often in practice. This book is a collection of articles written by renowned experts in the area of randomized parallel computing. A brief introduction to randomized algorithms In the aflalysis of algorithms, at least three different measures of performance can be used: the best case, the worst case, and the average case. Often, the average case run time of an algorithm is much smaller than the worst case. 2 For instance, the worst case run time of Hoare's quicksort is O(n ), whereas its average case run time is only O( n log n). The average case analysis is conducted with an assumption on the input space. The assumption made to arrive at the O( n log n) average run time for quicksort is that each input permutation is equally likely. Clearly, any average case analysis is only as good as how valid the assumption made on the input space is. Randomized algorithms achieve superior performances without making any assumptions on the inputs by making coin flips within the algorithm. Any analysis done of randomized algorithms will be valid for all p0:.sible inputs.

The technique of randomization has been employed to solve numerous prob­ lems of computing both sequentially and in parallel. Examples of randomized algorithms that are asymptotically better than their deterministic counterparts in solving various fundamental problems abound. Randomized algorithms have the advantages of simplicity and better performance both in theory and often is a collection of articles written by renowned experts in practice. This book in the area of randomized parallel computing. A brief introduction to randomized algorithms In the analysis of algorithms, at least three different measures of performance can be used: the best case, the worst case, and the average case. Often, the average case run time of an algorithm is much smaller than the worst case. 2 For instance, the worst case run time of Hoare's quicksort is O(n ), whereas its average case run time is only O(nlogn). The average case analysis is conducted with an assumption on the input space. The assumption made to arrive at the O(n logn) average run time for quicksort is that each input permutation is equally likely. Clearly, any average case analysis is only as good as how valid the assumption made on the input space is. Randomized algorithms achieve superior performances without making any assumptions on the inputs by making coin flips within the algorithm. Any analysis done of randomized algorithms will be valid for all possible inputs.

At first sight discrete and fractional programming techniques appear to be two com­ pletely unrelated fields in operations research. We will show how techniques in both fields can be applied separately and in a combined form to particular models in location analysis. Location analysis deals with the problem of deciding where to locate facilities, con­ sidering the clients to be served, in such a way that a certain criterion is optimized. The term "facilities" immediately suggests factories, warehouses, schools, etc. , while the term "clients" refers to depots, retail units, students, etc. Three basic classes can be identified in location analysis: continuous location, network location and dis­ crete location. The differences between these fields arise from the structure of the set of possible locations for the facilities. Hence, locating facilities in the plane or in another continuous space corresponds to a continuous location model while finding optimal facility locations on the edges or vertices of a network corresponds to a net­ work location model. Finally, if the possible set of locations is a finite set of points we have a discrete location model. Each of these fields has been actively studied, arousing intense discussion on the advantages and disadvantages of each of them. The usual requirement that every point in the plane or on the network must be a candidate location point, is one of the mostly used arguments "against" continuous and network location models.