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The Quadratic Assignment Problem

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 879/5 ( reviews)

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Book Synopsis The Quadratic Assignment Problem by : E. Cela

Download or read book The Quadratic Assignment Problem written by E. Cela. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.

The Quadratic Assignment Problem

1997-12-31 Mathematics
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Release : 1997-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 788/5 ( reviews)

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Book Synopsis The Quadratic Assignment Problem by : E. Cela

Download or read book The Quadratic Assignment Problem written by E. Cela. This book was released on 1997-12-31. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.

Assignment Problems, Revised Reprint

2012-10-31 Mathematics
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Release : 2012-10-31
Genre : Mathematics
Kind : eBook
Book Rating : 221/5 ( reviews)

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Book Synopsis Assignment Problems, Revised Reprint by : Rainer Burkard

Download or read book Assignment Problems, Revised Reprint written by Rainer Burkard. This book was released on 2012-10-31. Available in PDF, EPUB and Kindle. Book excerpt: Assignment Problems is a useful tool for researchers, practitioners and graduate students. In 10 self-contained chapters, it provides a comprehensive treatment of assignment problems from their conceptual beginnings through present-day theoretical, algorithmic and practical developments. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems and many variations of these. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in areas related to discrete mathematics and combinatorial optimisation. The revised reprint provides details on a recent discovery related to one of Jacobi's results, new material on inverse assignment problems and quadratic assignment problems, and an updated bibliography.

Handbook of Combinatorial Optimization

2006-08-18 Business & Economics
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Release : 2006-08-18
Genre : Business & Economics
Kind : eBook
Book Rating : 301/5 ( reviews)

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Book Synopsis Handbook of Combinatorial Optimization by : Ding-Zhu Du

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du. This book was released on 2006-08-18. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.

The Traffic Assignment Problem

2015-01-19 Mathematics
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Release : 2015-01-19
Genre : Mathematics
Kind : eBook
Book Rating : 272/5 ( reviews)

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Book Synopsis The Traffic Assignment Problem by : Michael Patriksson

Download or read book The Traffic Assignment Problem written by Michael Patriksson. This book was released on 2015-01-19. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems. This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.

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