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| branch and bound travelling salesman problem: The Traveling Salesman Problem and Its Variations G. Gutin, A.P. Punnen, 2006-05-02 A brilliant treatment of a knotty problem in computing. This volume contains chapters written by reputable researchers and provides the state of the art in 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, and includes a thorough computational analysis of heuristic and metaheuristic algorithms. |
| branch and bound travelling salesman problem: The Traveling Salesman Problem David L. Applegate, Robert E. Bixby, Vašek Chvátal, William J. Cook, 2011-09-19 This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience. The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us. |
| branch and bound travelling salesman problem: In Pursuit of the Traveling Salesman William J. Cook, 2014-11-09 The story of one of the greatest unsolved problems in mathematics What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics—and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today’s state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets. In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem. |
| branch and bound travelling salesman problem: Computer Information Systems and Industrial Management Khalid Saeed, Władysław Homenda, 2016-09-09 This book constitutes the proceedings of the 15th IFIP TC8 International Conference on Computer Information Systems and Industrial Management, CISIM 2016, held in Vilnius, Lithuania, in September 2016. The 63 regular papers presented together with 1 inivted paper and 5 keynotes in this volume were carefully reviewed and selected from about 89 submissions. The main topics covered are rough set methods for big data analytics; images, visualization, classification; optimization, tuning; scheduling in manufacturing and other applications; algorithms; decisions; intelligent distributed systems; and biometrics, identification, security. |
| branch and bound travelling salesman problem: Research Advancements in Smart Technology, Optimization, and Renewable Energy Vasant, Pandian, Weber, Gerhard, Punurai, Wonsiri, 2020-08-07 As environmental issues remain at the forefront of energy research, renewable energy is now an all-important field of study. And as smart technology continues to grow and be refined, its applications broaden and increase in their potential to revolutionize sustainability studies. This potential can only be fully realized with a thorough understanding of the most recent breakthroughs in the field. Research Advancements in Smart Technology, Optimization, and Renewable Energy is a collection of innovative research that explores the recent steps forward for smart applications in sustainability. Featuring coverage on a wide range of topics including energy assessment, neural fuzzy control, and biogeography, this book is ideally designed for advocates, policymakers, engineers, software developers, academicians, researchers, and students. |
| branch and bound travelling salesman problem: Arc Routing Angel Corberan, Gilbert Laporte, 2015-01-01 This book provides a thorough and up-to-date discussion of arc routing by world-renowned researchers. Organized by problem type, the book offers a rigorous treatment of complexity issues, models, algorithms, and applications. Arc Routing: Problems, Methods, and Applications opens with a historical perspective of the field and is followed by three sections that cover complexity and the Chinese Postman and the Rural Postman problems; the Capacitated Arc Routing Problem and routing problems with min-max and profit maximization objectives; and important applications, including meter reading, snow removal, and waste collection. |
| branch and bound travelling salesman problem: The Traveling Salesman Problem D.B. Shmoys, J.K. Lenstra, A.H.G. Rinnooy Kan, E.L. Lawler, 1985 The Traveling Salesman Problem is central to the area of Combinatorial Optimization, and it is through this problem that many of the most important developments in the area have been made. This book focuses on essential ideas; through them it illustrates all the concepts and techniques of combinatorial optimization concisely but comprehensively. The extensive reference list and numerous exercises direct the reader towards related fields, and give results. Each of the twelve chapters in this volume is concerned with a specific aspect of the Traveling Salesman Problem, and is written by an authority on that aspect. It is hoped, that the book will serve as a state-of-the-art survey of the Traveling Salesman problem which will encourage further investigations, and that it will also be useful for its comprehensive coverage of the techniques of combinatorial optimization. |
| branch and bound travelling salesman problem: Ten Applications of Graph Theory Hansjoachim Walther, 2012-12-06 Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the tree of knowledge of mathematics and related fields does not grow only by putting forth new bran ches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-tri vially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as completely integrable systems, chaos, synergetics and large-scale order, which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathe matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific endeavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another. |
| branch and bound travelling salesman problem: Operations Research Wayne L. Winston, 1987 |
| branch and bound travelling salesman problem: Neutrosophic Travelling Salesman Problem in Trapezoidal Fuzzy number using Branch and Bound Technique S. Subasri, K. Selvakumari, Travelling salesman problem is a well-known studied problem and intensely used in combinatorial optimization. In this article, we discuss a Neutrosophic fuzzy travelling salesman problem in which each element is considered as a Neutrosophic trapezoidal fuzzy numbers. Here, we provide the Branch and Bound technique is to find the optimal solution. The efficiency of this method is proved by solving a numerical example. |
| branch and bound travelling salesman problem: Integer and Combinatorial Optimization Laurence A. Wolsey, George L. Nemhauser, 2014-08-28 Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list.-Optima A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems.-Computing Reviews [This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners.-Mathematical Reviews This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization.-Bulletin of the London Mathematical Society This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments.-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp. |
| branch and bound travelling salesman problem: DESIGN AND ANALYSIS OF ALGORITHMS R. PANNEERSELVAM, 2007-12-18 This highly structured text provides comprehensive coverage of design techniques of algorithms. It traces the complete development of various algorithms in a stepwise approach followed by their pseudo-codes to build an understanding of their application in practice. With clear explanations, the book analyzes different kinds of algorithms such as distance-based network algorithms, search algorithms, sorting algorithms, probabilistic algorithms, and single as well as parallel processor scheduling algorithms. Besides, it discusses the importance of heuristics, benchmarking of algorithms, cryptography, and dynamic programming. Key Features : Offers in-depth treatment of basic and advanced topics. Includes numerous worked examples covering varied real-world situations to help students grasp the concepts easily. Provides chapter-end exercises to enable students to check their mastery of content. This text is especially designed for students of B.Tech and M.Tech (Computer Science and Engineering and Information Technology), MCA, and M.Sc. (Computer Science and Information Technology). It would also be useful to undergraduate students of electrical and electronics and other engineering disciplines where a course in algorithms is prescribed. |
| branch and bound travelling salesman problem: Combinatorial Optimization Alexander Schrijver, 2003-02-12 From the reviews: About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as the Lawler simply. I think that now, with this volume Springer has landed a coup: The Schrijver. The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency. OR-Spectrum |
| branch and bound travelling salesman problem: Novel Trends in the Traveling Salesman Problem Donald Davendra, Magdalena Bialic-Davendra, 2020-12-09 The Traveling Salesman Problem (TSP) is widely considered one of the most intensively studied problems in computational mathematics and operations research. Since its inception, it has become the poster child for computational complexity research. A number of problems have been transformed to a TSP problem and its application base now extends into scheduling, manufacturing, routing, and logistics. With the advent of high-performance computing and advanced meta-heuristics such as GPU programming and swarm-based algorithms, the TSP problem is positioned firmly as the go-to problem for the development of the next generation of high-performance intelligent heuristics. This book looks to leverage some of these new paradigms for both students and researchers in this field. |
| branch and bound travelling salesman problem: Intelligent Computational Optimization in Engineering Mario Köppen, Gerald Schaefer, Ajith Abraham, 2011-07-15 We often come across computational optimization virtually in all branches of engineering and industry. Many engineering problems involve heuristic search and optimization, and, once discretized, may become combinatorial in nature, which gives rise to certain difficulties in terms of solution procedure. Some of these problems have enormous search spaces, are NP-hard and hence require heuristic solution techniques. Another difficulty is the lack of ability of classical solution techniques to determine appropriate optima of non-convex problems. Under these conditions, recent advances in computational optimization techniques have been shown to be advantageous and successful compared to classical approaches. This Volume presents some of the latest developments with a focus on the design of algorithms for computational optimization and their applications in practice. Through the chapters of this book, researchers and practitioners share their experience and newest methodologies with regard to intelligent optimization and provide various case studies of the application of intelligent optimization techniques in real-world applications.This book can serve as an excellent reference for researchers and graduate students in computer science, various engineering disciplines and the industry. |
| branch and bound travelling salesman problem: Algorithm Engineering and Experimentation Adam Louis Buchsbaum, 2001-09-12 •DIMACSSpecialFocusonNextGenerationNetworks •TheHopkinsCenterforAlgorithmEngineering •NECResearchInstitute Thefollowingprovidedin-kindsupport,facilitatingtheworkshop. •AT&T •SIAM,theSocietyforIndustrialandAppliedMathematics •SIGACT,theACMSIGonAlgorithmsandComputationTheory ALENEX2001ProgramCommittee NinaAmenta,(UniversityofTexas,Austin) AdamBuchsbaum,(AT&TLabs–Research;Co-chair) RudolfFleischer,(HongKongUniversityofScience&Technology) LyleMcGeoch,(AmherstCollege) S. |
| branch and bound travelling salesman problem: Heuristic Search Stefan Edelkamp, Stefan Schroedl, 2011-05-31 Search has been vital to artificial intelligence from the very beginning as a core technique in problem solving. The authors present a thorough overview of heuristic search with a balance of discussion between theoretical analysis and efficient implementation and application to real-world problems. Current developments in search such as pattern databases and search with efficient use of external memory and parallel processing units on main boards and graphics cards are detailed. Heuristic search as a problem solving tool is demonstrated in applications for puzzle solving, game playing, constraint satisfaction and machine learning. While no previous familiarity with heuristic search is necessary the reader should have a basic knowledge of algorithms, data structures, and calculus. Real-world case studies and chapter ending exercises help to create a full and realized picture of how search fits into the world of artificial intelligence and the one around us. - Provides real-world success stories and case studies for heuristic search algorithms - Includes many AI developments not yet covered in textbooks such as pattern databases, symbolic search, and parallel processing units |
| branch and bound travelling salesman problem: Ant Colony Optimization Marco Dorigo, Thomas Stutzle, 2004-06-04 An overview of the rapidly growing field of ant colony optimization that describes theoretical findings, the major algorithms, and current applications. The complex social behaviors of ants have been much studied by science, and computer scientists are now finding that these behavior patterns can provide models for solving difficult combinatorial optimization problems. The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic technique based on ant behavior. This book presents an overview of this rapidly growing field, from its theoretical inception to practical applications, including descriptions of many available ACO algorithms and their uses. The book first describes the translation of observed ant behavior into working optimization algorithms. The ant colony metaheuristic is then introduced and viewed in the general context of combinatorial optimization. This is followed by a detailed description and guide to all major ACO algorithms and a report on current theoretical findings. The book surveys ACO applications now in use, including routing, assignment, scheduling, subset, machine learning, and bioinformatics problems. AntNet, an ACO algorithm designed for the network routing problem, is described in detail. The authors conclude by summarizing the progress in the field and outlining future research directions. Each chapter ends with bibliographic material, bullet points setting out important ideas covered in the chapter, and exercises. Ant Colony Optimization will be of interest to academic and industry researchers, graduate students, and practitioners who wish to learn how to implement ACO algorithms. |
| branch and bound travelling salesman problem: Nature-Inspired Computation and Swarm Intelligence Xin-She Yang, 2020-04-10 Nature-inspired computation and swarm intelligence have become popular and effective tools for solving problems in optimization, computational intelligence, soft computing and data science. Recently, the literature in the field has expanded rapidly, with new algorithms and applications emerging. Nature-Inspired Computation and Swarm Intelligence: Algorithms, Theory and Applications is a timely reference giving a comprehensive review of relevant state-of-the-art developments in algorithms, theory and applications of nature-inspired algorithms and swarm intelligence. It reviews and documents the new developments, focusing on nature-inspired algorithms and their theoretical analysis, as well as providing a guide to their implementation. The book includes case studies of diverse real-world applications, balancing explanation of the theory with practical implementation. Nature-Inspired Computation and Swarm Intelligence: Algorithms, Theory and Applications is suitable for researchers and graduate students in computer science, engineering, data science, and management science, who want a comprehensive review of algorithms, theory and implementation within the fields of nature inspired computation and swarm intelligence. |
| branch and bound travelling salesman problem: Optimization Techniques and Applications with Examples Xin-She Yang, 2018-09-19 A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniques in optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The author—a noted expert in the field—covers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming. In addition, the book discusses artificial neural network, clustering and classifications, constraint-handling, queueing theory, support vector machine and multi-objective optimization, evolutionary computation, nature-inspired algorithms and many other topics. Designed as a practical resource, all topics are explained in detail with step-by-step examples to show how each method works. The book’s exercises test the acquired knowledge that can be potentially applied to real problem solving. By taking an informal approach to the subject, the author helps readers to rapidly acquire the basic knowledge in optimization, operational research, and applied data mining. This important resource: Offers an accessible and state-of-the-art introduction to the main optimization techniques Contains both traditional optimization techniques and the most current algorithms and swarm intelligence-based techniques Presents a balance of theory, algorithms, and implementation Includes more than 100 worked examples with step-by-step explanations Written for upper undergraduates and graduates in a standard course on optimization, operations research and data mining, Optimization Techniques and Applications with Examples is a highly accessible guide to understanding the fundamentals of all the commonly used techniques in optimization. |
| branch and bound travelling salesman problem: Network Models Michael O. Ball, 1995 Hardbound. The set of papers in this Handbook reflect the rich theory and wide range of applications of network models. Two of the most vibrant applications areas of network models are telecommunications and transportation. Several chapters explicitly model issues arising in these problem domains. Research on network models has been closely aligned with the field of computer science both in developing data structures for efficiently implementing network algorithms and in analyzing the complexity of network problems and algorithms. The basic structure underlying all network problems is a graph. Thus, historically, there have been strong ties between network models and graph theory. A companion volume in the Handbook series, entitled Network Routing, examines problems related to the movement of commodities over a network. The problems treated arise in several application areas including logistics, telecommunications, facility location, VLSI desi |
| branch and bound travelling salesman problem: Vehicle Routing Paolo Toth, Daniele Vigo, 2014-12-05 Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Operations researchers have made significant developments in the algorithms for their solution, and Vehicle Routing: Problems, Methods, and Applications, Second Edition reflects these advances. The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area; it emphasizes methodology related to specific classes of vehicle routing problems and, since vehicle routing is used as a benchmark for all new solution techniques, contains a complete overview of current solutions to combinatorial optimization problems. It also includes several chapters on important and emerging applications, such as disaster relief and green vehicle routing. |
| branch and bound travelling salesman problem: Algorithms Sanjoy Dasgupta, Christos H. Papadimitriou, Umesh Virkumar Vazirani, 2006 This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include:The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text DasGupta also offers a Solutions Manual which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel it is a joy to read. Tim Roughgarden Stanford University |
| branch and bound travelling salesman problem: DESIGN METHODS AND ANALYSIS OF ALGORITHMS S. K. BASU, 2005-01-01 The design of correct and efficient algorithms for problem solving lies at the heart of computer science. This concise text, without being highly specialized, teaches the skills needed to master the essentials of this subject. With clear explanations and engaging writing style, the book places increased emphasis on algorithm design techniques rather than programming in order to develop in the reader the problem-solving skills. The treatment throughout the book is primarily tailored to the curriculum needs of B.Tech students in computer science and engineering, B.Sc. (Hons.) and M.Sc. students in computer science, and MCA students. The book focuses on the standard algorithm design methods and the concepts are illustrated through representative examples to offer a reader-friendly text. Elementary analysis of time complexities is provided for each example-algorithm. A varied collection of exercises at the end of each chapter serves to reinforce the principles/methods involved. |
| branch and bound travelling salesman problem: Decision Diagrams for Optimization David Bergman, Andre A. Cire, Willem-Jan van Hoeve, John Hooker, 2016-11-01 This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world. [Pascal Van Hentenryck] |
| branch and bound travelling salesman problem: Encyclopedia of Operations Research and Management Science Saul I. Gass, Carl M. Harris, 2012-12-06 Operations Research: 1934-1941, 35, 1, 143-152; British The goal of the Encyclopedia of Operations Research and Operational Research in World War II, 35, 3, 453-470; Management Science is to provide to decision makers and U. S. Operations Research in World War II, 35, 6, 910-925; problem solvers in business, industry, government and and the 1984 article by Harold Lardner that appeared in academia a comprehensive overview of the wide range of Operations Research: The Origin of Operational Research, ideas, methodologies, and synergistic forces that combine to 32, 2, 465-475. form the preeminent decision-aiding fields of operations re search and management science (OR/MS). To this end, we The Encyclopedia contains no entries that define the fields enlisted a distinguished international group of academics of operations research and management science. OR and MS and practitioners to contribute articles on subjects for are often equated to one another. If one defines them by the which they are renowned. methodologies they employ, the equation would probably The editors, working with the Encyclopedia's Editorial stand inspection. If one defines them by their historical Advisory Board, surveyed and divided OR/MS into specific developments and the classes of problems they encompass, topics that collectively encompass the foundations, applica the equation becomes fuzzy. The formalism OR grew out of tions, and emerging elements of this ever-changing field. We the operational problems of the British and U. s. military also wanted to establish the close associations that OR/MS efforts in World War II. |
| branch and bound travelling salesman problem: An Introduction to Linear Programming and Game Theory Paul R. Thie, Gerard E. Keough, 2011-09-15 Praise for the Second Edition: This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications. —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science. |
| branch and bound travelling salesman problem: Surveys in Combinatorial Optimization S. Martello, M. Minoux, C. Ribeiro, Gilbert Laporte, 2011-09-22 A collection of papers surveying recent progress in the field of Combinatorial Optimization.Topics examined include theoretical and computational aspects (Boolean Programming, Probabilistic Analysis of Algorithms, Parallel Computer Models and Combinatorial Algorithms), well-known combinatorial problems (such as the Linear Assignment Problem, the Quadratic Assignment Problem, the Knapsack Problem and Steiner Problems in Graphs) and more applied problems (such as Network Synthesis and Dynamic Network Optimization, Single Facility Location Problems on Networks, the Vehicle Routing Problem and Scheduling Problems). |
| branch and bound travelling salesman problem: Encyclopedia of Optimization Christodoulos A. Floudas, Panos M. Pardalos, 2008-09-04 The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as Algorithms for Genomics, Optimization and Radiotherapy Treatment Design, and Crew Scheduling. |
| branch and bound travelling salesman problem: Parallel Programming with MPI Peter Pacheco, 1997 Mathematics of Computing -- Parallelism. |
| branch and bound travelling salesman problem: Integer Programming Laurence A. Wolsey, 2020-10-20 A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition. The revised second edition: Contains new developments on column generation Offers a new chapter on Benders’ algorithm Includes expanded information on preprocessing, heuristics, and branch-and-cut Presents several basic and extended formulations, for example for fixed cost network flows Also touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field. |
| branch and bound travelling salesman problem: OPERATIONS RESEARCH : PRINCIPLES AND APPLICATIONS SRINIVASAN, G., 2017-06-01 This text, now in the Third Edition, aims to provide students with a clear, well-structured and comprehensive treatment of the theory and applications of operations research. The methodology used is to first introduce the students to the fundamental concepts through numerical illustrations and then explain the underlying theory, wherever required. Inclusion of case studies in the existing chapters makes learning easier and more effective. The book introduces the readers to various models of Operations Research (OR), such as transportation model, assignment model, inventory models, queueing theory and integer programming models. Various techniques to solve OR problems’ faced by managers are also discussed. Separate chapters are devoted to Linear Programming, Dynamic Programming and Quadratic Programming which greatly help in the decision-making process. The text facilitates easy comprehension of topics by the students due to inclusion of: • Examples and situations from the Indian context. • Numerous exercise problems arranged in a graded manner. • A large number of illustrative examples. The text is primarily intended for the postgraduate students of management, computer applications, commerce, mathematics and statistics. Besides, the undergraduate students of mechanical engineering and industrial engineering will find this book extremely useful. In addition, this text can also be used as a reference by OR analysts and operations managers. NEW TO THE THIRD EDITION • Includes two new chapters: – Chapter 14: Project Management—PERT and CPM – Chapter 15: Miscellaneous Topics (Game Theory, Sequencing and Scheduling, Simulation, and Replacement Models) • Incorporates more examples in the existing chapters to illustrate new models, algorithms and concepts • Provides short questions and additional numerical problems for practice in each chapter |
| branch and bound travelling salesman problem: The Logic of Logistics David Simchi-Levi, Xin Chen, Julien Bramel, 2007-07-03 Fierce competition in today's global market provides a powerful motivation for developing ever more sophisticated logistics systems. This book, written for the logistics manager and researcher, presents a survey of the modern theory and application of logistics. The goal of the book is to present the state-of-the-art in the science of logistics management. As a result, the authors have written a timely and authoritative survey of this field that many practitioners and researchers will find makes an invaluable companion to their work. |
| branch and bound travelling salesman problem: Model Rules of Professional Conduct American Bar Association. House of Delegates, Center for Professional Responsibility (American Bar Association), 2007 The Model Rules of Professional Conduct provides an up-to-date resource for information on legal ethics. Federal, state and local courts in all jurisdictions look to the Rules for guidance in solving lawyer malpractice cases, disciplinary actions, disqualification issues, sanctions questions and much more. In this volume, black-letter Rules of Professional Conduct are followed by numbered Comments that explain each Rule's purpose and provide suggestions for its practical application. The Rules will help you identify proper conduct in a variety of given situations, review those instances where discretionary action is possible, and define the nature of the relationship between you and your clients, colleagues and the courts. |
| branch and bound travelling salesman problem: The Vehicle Routing Problem Paolo Toth, 2002 |
| branch and bound travelling salesman problem: Computational Intelligence and Informatics Imre J. Rudas, János Fodor, Janusz Kacprzyk, 2010-10 This volume contains a careful selection of papers that are based on and are extensions of corresponding lectures presented at the jubilee conference. The main subject area called Computational Intelligence includes diverse topics. Therefore, we offer snapshots rather than a full coverage of a small particular subject to the interested reader. This principle is also supported by the common national root of the authors. |
| branch and bound travelling salesman problem: Stochastic Local Search Holger H. Hoos, Thomas Stützle, 2005 Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application. |
| branch and bound travelling salesman problem: Exact Exponential Algorithms Fedor V. Fomin, Dieter Kratsch, 2010-10-26 For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING. |
| branch and bound travelling salesman problem: Applied Integer Programming Der-San Chen, Robert G. Batson, Yu Dang, 2010-01-12 An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems. |
| branch and bound travelling salesman problem: Computational Complexity Sanjeev Arora, Boaz Barak, 2009-04-20 New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students. |
Solving Traveling Salesman Problems Using Branch and Bound Methods
Department of Production and Operations, University Tun Hussein Onn Malaysia, Johor, Malaysia talibon@gmail.com See more
Travelling Salesman Problem Using Branch And Bound …
The traveling salesman problem (TSP) is an algorithmic problem when focused on optimization; TSP is often used in computer science to find the most efficient route for data to travel …
The Traveling Salesman problem - Indiana State University
The Traveling Salesman Problem, deals with creating the ideal path that a salesman would take while traveling between cities. The solution to any given TSP would be the Shortest way to …
Branch and Bound Methods for the Traveling Salesman …
for the traveling salesman problem (TSP). The introduction (Section 1) discusses the main ingredients of branch and bound methods for the TSP. Sections 2, 3 and 4 discuss classes of …
Fast Branch and Bound Algorithm for the Travelling …
Branch and bound (B&B, BnB, branch & bound) is an approach advised for de- signing exact algorithms solving NP-hard combinatorial optimization and dis- crete problems.
Branch-and-bound algorithm for the traveling salesman problem
The branch-and-bound algorithm for the traveling salesman problem uses a branch-and-bound tree, like the branch-and-bound algorithms for the knapsack problem and for solving integer …
SOLVING THE TRAVELLING SALESMAN PROBLEM …
In this paper we have shown a way to solve the Travelling Salesman Problem by using data tables and the branch and bound method which have given the correct solution to the problem …
Branch-and-Bound for the Travelling Salesman Problem
The Branch-and-Bound algorithm explicitly explores a large search space by recursively branching on disjunctions of possible values assigned to various decisions.
Travelling salesman problem using reduced algorithmic …
There were several algorithms existing to solve the travelling salesman problem using branch and bound technique. Here a reduced branch and bound (RBB) algorithm is proposed which uses …
Branch and Bound Method for Assignment Problem - Springer
In this paper, we propose to solve assignment problem using branch and bound (BB) method. The assignment problem is first transformed to travel-ling salesman problem (TSP) problem and …
The New Approach to Traveling Salesman Problem using …
goal of this research is to optimize the delivery of packages to appointed addresses in Jaipur. The delivery man has to deliver packages using the most efficient and shortest route moving from …
A Proposed Solution to Travelling Salesman Problem using …
The method we are proposing to solve the problem is Branch and Bound Method. The term branch and bound refers to all state space search methods in which all the children of E-node …
Branch and Bound Methods for the Traveling Salesman …
The introduction (Section 1) discusses the main ingredients of branch and bound methods for the TSP. Sections 2, 3 and 4 discuss classes of methods based on three different re- laxations of …
Traveling salesman problem
This paper also shows how the prize collecting traveling salesman problem (Balas, 2002) and the orienteering problem (Golden, Levy and Vohra, 1987; Fischetti, Salazar and Toth, 2002) are …
Branch And Bound Algorithm For Travelling Salesman Problem
In this article, we discuss a Neutrosophic fuzzy travelling salesman problem in which each element is considered as a Neutrosophic trapezoidal fuzzy numbers. Here, we provide the …
Branch-and-Bound Algorithm for Symmetric Travelling …
In this paper a branch-and-bound algorithm for the Symmet-ric Travelling Salesman Problem (STSP) is presented. The algorithm is based on the 1-tree Lagrangian relaxation. A new …
A Branch and Bound Algorithm to Solve Travelling Salesman …
Mar 30, 2022 · In this paper, we deployed branch and bound algorithm to obtain the optimal route in Intuitionistic fuzzy Travelling Salesman Problem. This algorithm is efficient and easily …
The New Approach to Traveling Salesman Problem using …
Key Words:-Branch and Bound technique, Two optimality, Cost matrix, Hungrerian method.
Fast Branch and Bound Algorithm for the Travelling …
Branch and Bound (Branch and Bound, BnB, branch & bound) is an approach advised for designing exact algorithms solving NP-hard combinatorial optimiza-tion and discrete problems.
An Exact Two-Matching Based Branch and Bound Algorithm …
We describe an algorithm for the symmetric traveling salesman problem (TSP) based on a bipartite two-matching lower bounding technique. The lower bound is strengthened by using …
Solving Traveling Salesman Problems Using Branch and …
Therefore, in this study we will examine the search for solving TSP problem using branch and bound methods. Keywords: Traveling Salesman Problem, The Greedy heuristic, Branch and …
Travelling Salesman Problem Using Branch And Bound …
The traveling salesman problem (TSP) is an algorithmic problem when focused on optimization; TSP is often used in computer science to find the most efficient route for data to travel …
The Traveling Salesman problem - Indiana State University
The Traveling Salesman Problem, deals with creating the ideal path that a salesman would take while traveling between cities. The solution to any given TSP would be the Shortest way to …
Branch and Bound Methods for the Traveling Salesman …
for the traveling salesman problem (TSP). The introduction (Section 1) discusses the main ingredients of branch and bound methods for the TSP. Sections 2, 3 and 4 discuss classes of …
Fast Branch and Bound Algorithm for the Travelling …
Branch and bound (B&B, BnB, branch & bound) is an approach advised for de- signing exact algorithms solving NP-hard combinatorial optimization and dis- crete problems.
Branch-and-bound algorithm for the traveling salesman …
The branch-and-bound algorithm for the traveling salesman problem uses a branch-and-bound tree, like the branch-and-bound algorithms for the knapsack problem and for solving integer …
SOLVING THE TRAVELLING SALESMAN PROBLEM USING …
In this paper we have shown a way to solve the Travelling Salesman Problem by using data tables and the branch and bound method which have given the correct solution to the problem …
Branch-and-Bound for the Travelling Salesman Problem
The Branch-and-Bound algorithm explicitly explores a large search space by recursively branching on disjunctions of possible values assigned to various decisions.
Travelling salesman problem using reduced algorithmic …
There were several algorithms existing to solve the travelling salesman problem using branch and bound technique. Here a reduced branch and bound (RBB) algorithm is proposed which uses …
Branch and Bound Method for Assignment Problem - Springer
In this paper, we propose to solve assignment problem using branch and bound (BB) method. The assignment problem is first transformed to travel-ling salesman problem (TSP) problem and …
The New Approach to Traveling Salesman Problem using …
goal of this research is to optimize the delivery of packages to appointed addresses in Jaipur. The delivery man has to deliver packages using the most efficient and shortest route moving from …
A Proposed Solution to Travelling Salesman Problem using …
The method we are proposing to solve the problem is Branch and Bound Method. The term branch and bound refers to all state space search methods in which all the children of E-node …
Branch and Bound Methods for the Traveling Salesman …
The introduction (Section 1) discusses the main ingredients of branch and bound methods for the TSP. Sections 2, 3 and 4 discuss classes of methods based on three different re- laxations of …
Traveling salesman problem
This paper also shows how the prize collecting traveling salesman problem (Balas, 2002) and the orienteering problem (Golden, Levy and Vohra, 1987; Fischetti, Salazar and Toth, 2002) are …
Branch And Bound Algorithm For Travelling Salesman …
In this article, we discuss a Neutrosophic fuzzy travelling salesman problem in which each element is considered as a Neutrosophic trapezoidal fuzzy numbers. Here, we provide the …
Branch-and-Bound Algorithm for Symmetric Travelling …
In this paper a branch-and-bound algorithm for the Symmet-ric Travelling Salesman Problem (STSP) is presented. The algorithm is based on the 1-tree Lagrangian relaxation. A new …
A Branch and Bound Algorithm to Solve Travelling …
Mar 30, 2022 · In this paper, we deployed branch and bound algorithm to obtain the optimal route in Intuitionistic fuzzy Travelling Salesman Problem. This algorithm is efficient and easily …
The New Approach to Traveling Salesman Problem using …
Key Words:-Branch and Bound technique, Two optimality, Cost matrix, Hungrerian method.
Fast Branch and Bound Algorithm for the Travelling …
Branch and Bound (Branch and Bound, BnB, branch & bound) is an approach advised for designing exact algorithms solving NP-hard combinatorial optimiza-tion and discrete problems.
An Exact Two-Matching Based Branch and Bound Algorithm …
We describe an algorithm for the symmetric traveling salesman problem (TSP) based on a bipartite two-matching lower bounding technique. The lower bound is strengthened by using …
