The quadratic knapsack problem—a survey
The binary quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and challenging difficulty it has been studied intensively during the last two decades. The present paper gives a survey of upper bounds presented in th...
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| Published in | Discrete Applied Mathematics Vol. 155; no. 5; pp. 623 - 648 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Lausanne
Elsevier B.V
15.03.2007
Amsterdam Elsevier New York, NY |
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| Online Access | Get full text |
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| Abstract | The binary
quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and challenging difficulty it has been studied intensively during the last two decades. The present paper gives a survey of upper bounds presented in the literature, and show the relative tightness of several of the bounds. Techniques for deriving the bounds include relaxation from upper planes, linearization, reformulation, Lagrangian relaxation, Lagrangian decomposition, and semidefinite programming. A short overview of heuristics, reduction techniques, branch-and-bound algorithms and approximation results is given, followed by an overview of valid inequalities for the quadratic knapsack polytope. The paper is concluded by an experimental study where the upper bounds presented are compared with respect to strength and computational effort. |
|---|---|
| AbstractList | The binary
quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and challenging difficulty it has been studied intensively during the last two decades. The present paper gives a survey of upper bounds presented in the literature, and show the relative tightness of several of the bounds. Techniques for deriving the bounds include relaxation from upper planes, linearization, reformulation, Lagrangian relaxation, Lagrangian decomposition, and semidefinite programming. A short overview of heuristics, reduction techniques, branch-and-bound algorithms and approximation results is given, followed by an overview of valid inequalities for the quadratic knapsack polytope. The paper is concluded by an experimental study where the upper bounds presented are compared with respect to strength and computational effort. |
| Author | Pisinger, David |
| Author_xml | – sequence: 1 givenname: David surname: Pisinger fullname: Pisinger, David email: pisinger@diku.dk organization: Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark |
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| Keywords | Approximation algorithms Semidefinite programming Valid inequalities Upper bounds Quadratic knapsack problem Polytope Lagrangian Computer theory Decomposition method Semi definite programming Approximation algorithm Experimental study Constrained optimization Knapsack problem Relaxation Upper bound Objective function Combinatorics Quadratic function |
| Language | English |
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quadratic knapsack problem maximizes a quadratic objective function subject to a linear capacity constraint. Due to its simple structure and... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Approximation algorithms Computer science; control theory; systems Exact sciences and technology Mathematical programming Operational research and scientific management Operational research. Management science Quadratic knapsack problem Semidefinite programming Theoretical computing Upper bounds Valid inequalities |
| Title | The quadratic knapsack problem—a survey |
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