the traveling salesman problem a computational study princeton series in applied mathematics

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The Traveling Salesman Problem

Author : David L. Applegate
ISBN : 9781400841103
Genre : Mathematics
File Size : 20. 48 MB
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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.

In Pursuit Of The Traveling Salesman

Author : William Cook
ISBN : 9780691152707
Genre : Mathematics
File Size : 23. 73 MB
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Covers the history, applications, theory, and computation of the traveling salesman problem right up to state-of-the-art solution machinery.

Combinations Of Intelligent Methods And Applications

Author : Ioannis Hatzilygeroudis
ISBN : 9783319268606
Genre : Computers
File Size : 26. 24 MB
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This volume includes extended and revised versions of the papers presented at the 4th Workshop on “Combinations of Intelligent Methods and Applications” (CIMA 2014) which was intended to become a forum for exchanging experience and ideas among researchers and practitioners dealing with combinations of different intelligent methods in Artificial Intelligence. The aim is to create integrated or hybrid methods that benefit from each of their components. Some of the existing presented efforts combine soft computing methods (fuzzy logic, neural networks and genetic algorithms). Another stream of efforts integrates case-based reasoning or machine learning with soft-computing methods. Some of the combinations have been more widely explored, like neuro-symbolic methods, neuro-fuzzy methods and methods combining rule-based and case-based reasoning. CIMA 2014 was held in conjunction with the 26th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2014).

Experimental Algorithms

Author : Andrew V. Goldberg
ISBN : 9783319388519
Genre : Computers
File Size : 85. 83 MB
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This book constitutes the refereed proceedings of the 15th International Symposium on Experimental Algorithms, SEA 2016, held in St. Petersburg, Russia, in June 2016. The 25 revised full papers presented were carefully reviewed and selected from 54 submissions. The main theme of the symposium is the role of experimentation and of algorithm engineering techniques in the design and evaluation of algorithms and data structures. SEA covers a wide range of topics in experimental algorithmics, bringing together researchers from algorithm engineering, mathematical programming, and combinatorial optimization communities.

Operations Research Proceedings 2014

Author : Marco Lübbecke
ISBN : 9783319286976
Genre : Business & Economics
File Size : 25. 41 MB
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This book contains a selection of refereed papers presented at the "International Conference on Operations Research (OR 2014)", which took place at RWTH Aachen University, Germany, September 2-5, 2014. More than 800 scientists and students from 47 countries attended OR 2014 and presented more than 500 papers in parallel topical streams, as well as special award sessions. The theme of the conference and its proceedings is "Business Analytics and Optimization".

Covering Walks In Graphs

Author : Futaba Fujie
ISBN : 9781493903054
Genre : Mathematics
File Size : 74. 60 MB
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Covering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and Hamiltonian concepts are examined. Describes several variations of traceable numbers, which provide new frame works for several well-known Hamiltonian concepts and produce interesting new results.

Combinatorial Search From Algorithms To Systems

Author : Youssef Hamadi
ISBN : 9783642414824
Genre : Computers
File Size : 43. 36 MB
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Although they are believed to be unsolvable in general, tractability results suggest that some practical NP-hard problems can be efficiently solved. Combinatorial search algorithms are designed to efficiently explore the usually large solution space of these instances by reducing the search space to feasible regions and using heuristics to efficiently explore these regions. Various mathematical formalisms may be used to express and tackle combinatorial problems, among them the constraint satisfaction problem (CSP) and the propositional satisfiability problem (SAT). These algorithms, or constraint solvers, apply search space reduction through inference techniques, use activity-based heuristics to guide exploration, diversify the searches through frequent restarts, and often learn from their mistakes. In this book the author focuses on knowledge sharing in combinatorial search, the capacity to generate and exploit meaningful information, such as redundant constraints, heuristic hints, and performance measures, during search, which can dramatically improve the performance of a constraint solver. Information can be shared between multiple constraint solvers simultaneously working on the same instance, or information can help achieve good performance while solving a large set of related instances. In the first case, information sharing has to be performed at the expense of the underlying search effort, since a solver has to stop its main effort to prepare and commu nicate the information to other solvers; on the other hand, not sharing information can incur a cost for the whole system, with solvers potentially exploring unfeasible spaces discovered by other solvers. In the second case, sharing performance measures can be done with little overhead, and the goal is to be able to tune a constraint solver in relation to the characteristics of a new instance – this corresponds to the selection of the most suitable algorithm for solving a given instance. The book is suitable for researchers, practitioners, and graduate students working in the areas of optimization, search, constraints, and computational complexity.

Topics In Quaternion Linear Algebra

Author : Leiba Rodman
ISBN : 9781400852741
Genre : Mathematics
File Size : 44. 5 MB
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Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Matheuristics

Author : Vittorio Maniezzo
ISBN : 9781441913067
Genre : Business & Economics
File Size : 29. 29 MB
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Metaheuristics support managers in decision-making with robust tools that provide high-quality solutions to important applications in business, engineering, economics, and science in reasonable time frames, but finding exact solutions in these applications still poses a real challenge. However, because of advances in the fields of mathematical optimization and metaheuristics, major efforts have been made on their interface regarding efficient hybridization. This edited book will provide a survey of the state of the art in this field by providing some invited reviews by well-known specialists as well as refereed papers from the second Matheuristics workshop to be held in Bertinoro, Italy, June 2008. Papers will explore mathematical programming techniques in metaheuristics frameworks, and especially focus on the latest developments in Mixed Integer Programming in solving real-world problems.

Applied Integer Programming

Author : Der-San Chen
ISBN : 9781118210024
Genre : Mathematics
File Size : 68. 83 MB
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An accessible treatment of the modeling and solution of integerprogramming problems, featuring modern applications andsoftware In order to fully comprehend the algorithms associated withinteger programming, it is important to understand not onlyhow algorithms work, but also why they work.Applied Integer Programming features a unique emphasis onthis point, focusing on problem modeling and solution usingcommercial software. Taking an application-oriented approach, thisbook addresses the art and science of mathematical modeling relatedto the mixed integer programming (MIP) framework and discusses thealgorithms and associated practices that enable those models to besolved most efficiently. The book begins with coverage of successful applications,systematic modeling procedures, typical model types, transformationof non-MIP models, combinatorial optimization problem models, andautomatic preprocessing to obtain a better formulation. Subsequentchapters present algebraic and geometric basic concepts of linearprogramming theory and network flows needed for understandinginteger programming. Finally, the book concludes with classical andmodern solution approaches as well as the key components forbuilding an integrated software system capable of solvinglarge-scale integer programming and combinatorial optimizationproblems. Throughout the book, the authors demonstrate essential conceptsthrough numerous examples and figures. Each new concept oralgorithm is accompanied by a numerical example, and, whereapplicable, graphics are used to draw together diverse problems orapproaches into a unified whole. In addition, features of solutionapproaches found in today's commercial software are identifiedthroughout the book. Thoroughly classroom-tested, Applied Integer Programmingis an excellent book for integer programming courses at theupper-undergraduate and graduate levels. It also serves as awell-organized reference for professionals, software developers,and analysts who work in the fields of applied mathematics,computer science, operations research, management science, andengineering and use integer-programming techniques to model andsolve real-world optimization problems.

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