Advances In Combinatorial Optimization: Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems PDF Download
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Author: Moustapha Diaby
Publisher: World Scientific
ISBN: 981470489X
Category : Mathematics
Languages : en
Pages : 218
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Book Description
Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes 'P' (polynomial time) and 'NP' (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.
Author: Moustapha Diaby
Publisher: World Scientific
ISBN: 981470489X
Category : Mathematics
Languages : en
Pages : 218
Get Book Here
Book Description
Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes 'P' (polynomial time) and 'NP' (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.
Author: András Frank
Publisher: OUP Oxford
ISBN: 0199205272
Category : Mathematics
Languages : en
Pages : 664
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Book Description
Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.
Author: Salvatore Greco
Publisher: Springer Nature
ISBN: 3030685209
Category : Technology & Engineering
Languages : en
Pages : 69
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Book Description
This book presents novel and original metaheuristics developed to solve the cost-balanced traveling salesman problem. This problem was taken into account for the Metaheuristics Competition proposed in MESS 2018, Metaheuristics Summer School, and the top 4 methodologies ranked are included in the book, together with a brief introduction to the traveling salesman problem and all its variants. The book is aimed particularly at all researchers in metaheuristics and combinatorial optimization areas. Key uses are metaheuristics; complex problem solving; combinatorial optimization; traveling salesman problem.
Author: Bernhard Korte
Publisher: Springer Science & Business Media
ISBN: 3540292977
Category : Mathematics
Languages : en
Pages : 596
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Book Description
This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.
Author: Frank Neumann
Publisher: Springer Science & Business Media
ISBN: 3642165443
Category : Mathematics
Languages : en
Pages : 215
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Book Description
Bioinspired computation methods such as evolutionary algorithms and ant colony optimization are being applied successfully to complex engineering problems and to problems from combinatorial optimization, and with this comes the requirement to more fully understand the computational complexity of these search heuristics. This is the first textbook covering the most important results achieved in this area. The authors study the computational complexity of bioinspired computation and show how runtime behavior can be analyzed in a rigorous way using some of the best-known combinatorial optimization problems -- minimum spanning trees, shortest paths, maximum matching, covering and scheduling problems. A feature of the book is the separate treatment of single- and multiobjective problems, the latter a domain where the development of the underlying theory seems to be lagging practical successes. This book will be very valuable for teaching courses on bioinspired computation and combinatorial optimization. Researchers will also benefit as the presentation of the theory covers the most important developments in the field over the last 10 years. Finally, with a focus on well-studied combinatorial optimization problems rather than toy problems, the book will also be very valuable for practitioners in this field.
Author: Alexander Schrijver
Publisher: Springer Science & Business Media
ISBN: 9783540443896
Category : Business & Economics
Languages : en
Pages : 2024
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Book Description
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
Author: Alexander K. Hartmann
Publisher: John Wiley & Sons
ISBN: 3527606866
Category : Science
Languages : en
Pages : 360
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Book Description
A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.
Author: Laurence A. Wolsey
Publisher: John Wiley & Sons
ISBN: 1118626869
Category : Mathematics
Languages : en
Pages : 782
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Book Description
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.
Author: Winfried Hochstättler
Publisher: Springer Science & Business Media
ISBN: 3642038220
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Graph algorithms are easy to visualize and indeed there already exists a variety of packages to animate the dynamics when solving problems from graph theory. Still it can be difficult to understand the ideas behind the algorithm from the dynamic display alone. CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. In the course book, intended for readers at advanced undergraduate or graduate level, computer exercises and examples replace the usual static pictures of algorithm dynamics. For this volume we have chosen solely algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows, weighted and unweighted matchings both for bipartite and non-bipartite graphs. Find more information at http://schliep.org/CATBox/.
Author: Bruce A. Reed
Publisher: Springer Science & Business Media
ISBN: 0387224440
Category : Mathematics
Languages : en
Pages : 357
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Book Description
Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research
