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Assignment Problems
- ISBN-10 0898716632
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- Publisher Society for Industrial and Applied Mathematics
- Publication date March 19, 2009
- Language English
- Dimensions 7.25 x 0.75 x 10.25 inches
- Print length 395 pages
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The Quadratic Assignment Problem
Related Papers
Encyclopedia of Optimization
Panos Pardalos
Panos M Pardalos
Abstract This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior.
Güneş Erdoğan
The Quadratic Assignment Problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this dissertation, we analyze the binary structure of the QAP and present new IP formulations. We focus on “flow-based” formulations, strengthen the formulations with valid inequalities, and report computational experience with a branch-and-cut algorithm. Next, we present new classes of instances of the QAP that can be completely or partially reduced to the Linear Assignment Problem and give procedures to check whether or not an instance is an element of one of these classes. We also identify classes of instances of the Koopmans-Beckmann form of the QAP that are solvable in polynomial time. Lastly, we present a strong lower bound based on Bender’s decomposition.
Cesar Beltran-Royo
Pesquisa Operacional
Paulo Boaventura Netto
We investigate the classical Gilmore-Lawler lower bound for the quadratic assignment problem. We provide evidence of the difficulty of improving the Gilmore-Lawler bound and develop new bounds by means of optimal reduction schemes. Computational results are reported indicating that the new lower bounds have advantages over previous bounds and can be used in a branch-and-bound type algorithm for the quadratic assignment problem.
Computers & Operations Research
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Assignment Problems
- Institute of Discrete Mathematics (5050)
Research output : Book/Report › Book
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
- Application
- Theoretical
T1 - Assignment Problems
AU - Burkard, Rainer
AU - Dell'Amico, Mauro
AU - Martello, Silvano
N1 - 382 Seiten
SN - 978-0-898716-63-4
BT - Assignment Problems
PB - SIAM - Society of Industrial and Applied Mathematics
CY - Philadelphia
Location Science pp 345–363 Cite as
The Quadratic Assignment Problem
- Zvi Drezner 4
- First Online: 01 January 2015
4571 Accesses
9 Citations
The quadratic assignment problem is reviewed in this chapter. Weights between pairs of facilities and distances between the same number of locations are given. The problem is to find the assignment of facilities to locations that minimizes the weighted sum of distances. This problem is considered to be one of the most difficult combinatorial optimization problems. The construction of efficient solution algorithms (exact or heuristic) is challenging and has been extensively investigated by the communities working in Operations Research/Management Science, Industrial Engineering, or Computer Science. Examples of applications are given, the related layout problem is briefly described, exact and heuristic solution algorithms are reviewed, and a list of test problem instances and results are reported.
- Exact methods
- Metaheuristics
- Quadratic assignment
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Drezner, Z. (2015). The Quadratic Assignment Problem. In: Laporte, G., Nickel, S., Saldanha da Gama, F. (eds) Location Science. Springer, Cham. https://doi.org/10.1007/978-3-319-13111-5_13
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This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. 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 is a useful tool for researchers, practitioners, and graduate students. ... Rainer E. Burkard, Mauro Dell'Amico, Silvano Martello. Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2009 - Assignment problems (Programming) - 382 pages.
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 ...
Assignment Problems OT106_Burkard-DellAmicoFM-01-11-12.indd 1 1/31/2012 11:18:37 AM. Assignment Problems Rainer Burkard Graz University of Technology Graz, Austria Mauro Dell'Amico University of Modena and Reggio Emilia Reggio Emilia, Italy Silvano Martello University of Bologna
Assignment Problems is a useful tool for researchers, practitioners, and graduate students. It provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. The authors have organised the book into 10 self-contained chapters to ...
Linear Assignment Problems and Extensions ∗ Rainer E. Burkard † Eranda C¸ela † Abstract This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We
Assignment Problems is a useful tool for researchers, practitioners, and graduate students. It provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. ... Rainer Burkard is a Professor of Mathematics at Graz University of ...
Audience: Assignment Problems is a useful tool for researchers, practitioners, and graduate students. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its many variations. ... R. Burkard, M. dell'Amico, Silvano Martello;
Abstract. Assignment problems deal with the question how to assign n items (e.g. jobs) to n machines (or workers) in the best possible way. They consist of two components: the assignment as underlying combinatorial structure and an objective function modeling the "best way".
The solution of QAP (F, D) produced by an ǫ-approximation algorithm is called an ǫ-approximate solution. Theorem 3.2 (Sahni and Gonzalez [164], 1976) The quadratic assignment problem is strongly NP-hard. For an arbitrary ǫ > 0, the existence of a polynomial time ǫ-approximation algorithm for the QAP implies P = N P.
Assignment Problems. Revised reprint. Rainer Burkard, Mauro Dell'Amico, Silvano Martello. Institute of Discrete Mathematics (5050) Research output: Book/Report › Book. Overview. Original language. English. Place of Publication.
Quadratic Assignment Problems. Rainer E. Burkard, Ulrich Derigs; Pages 99-119. QAP Heuristic 1: The method of increasing degree of freedom. Rainer E. Burkard, Ulrich Derigs; Pages 120-126. QAP Heuristic 2: Cutting plane and exchange method. Rainer E. Burkard, Ulrich Derigs; Pages 127-145.
A heuristic for quadratic Boolean programs with applications to quadratic assignment problems. R. Burkard Tilmann Bönniger. Mathematics, Computer Science. 1983; 146. Save. An algorithm for the quadratic assignment problem using Bender's decomposition. L. Kaufman F. Broeckx. Mathematics, Computer Science.
Welcome to the QAPLIB Home Page, the online version of QAPLIB - A Quadratic Assignment Problem Library by R.E. Burkard, S.E. Karisch and F. Rendl, (Journal of Global Optimization 10:391-403, 1997.) We appreciate any comments and contributions to QAPLIB and hope that this site continues to be a valuable source for research on the quadratic ...
This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. 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.
The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. ... R. E. Burkard and U. Derigs, Assignment and matching problems: Solution methods with Fortran programs, Lecture Notes in Economics and Mathematical Systems184 ...
Assignment Problems. / Burkard, Rainer; Dell'Amico, Mauro; Martello, Silvano. 1 ed. Philadelphia: SIAM - Society of Industrial and Applied Mathematics, 2009. Research ...
The Quadratic Assignment Problem ∗ Rainer E. Burkard ... The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the
Rainer E. Burkard. University of Cologne Federal Republic of Germany. Search for more papers by this author. Karl-Heinz Stratmann, Karl-Heinz Stratmann. ... This paper contains a comparative study of the numerical behavior of different algorithms for solving quadratic assignment problems. After the formulation of the problem, branch and bound ...
The quadratic assignment problem (QAP) (Burkard, Dell'Amico, Martello, 2009, Cela, 1998, Koopmans, Beckmann, 1957, Lawler, 1963, Pardalos, Rendl, Wolkowicz, 1994, Pitsoulis, Pardalos, 2008) is well studied in the combinatorial optimization literature. The original application that initiated the study of this versatile model comes from the ...
hence the name "Quadratic Assignment Problem". The constraints are identical to those of the linear assignment problem (Burkard and Cela 1999) but the objective function is quadratic rather than linear. The QAP was proven to be NP-hard by Sahni and Gonzalez ().Even obtaining an ε-approximation for a given ε > 0 cannot be done in polynomial time unless P = NP.
This chapter discusses the quadratic assignment problems (QAPs). The benefit or cost resulting from an economic activity at some location is dependent on the locations of other facilities. ... 386, 1983. R.E. Burkard and U. Derigs, Assignment andMatchingProblems: Solution Methods with FORTRAN-prOgmms, Springer, Berlin, 1980. R.E. Burkard and J ...
The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a ...