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A Branch-and-Bound Algorithm to Solve Large Scale Integer Quadratic Multi-Knapsack Problems

Tolla, Pierre; Soutif, Eric; Quadri, Dominique (2007), A Branch-and-Bound Algorithm to Solve Large Scale Integer Quadratic Multi-Knapsack Problems, in Plasil, Frantisek; Sack, Harald; Meinel, Christoph; Van Der Hoek, Wiebe; Italiano, Giuseppe; Van Leeuwen, Jan, SOFSEM 2007: Theory and Practice of Computer Science, Springer : Berlin, p. 456-464. http://dx.doi.org/10.1007/978-3-540-69507-3_39

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Type
Communication / Conférence
Date
2007
Conference title
SOFSEM 2007: 33rd Conference on Current Trends in Theory and Practice of Computer Science
Conference date
2007-01
Conference city
Harrachov
Conference country
République tchèque
Book title
SOFSEM 2007: Theory and Practice of Computer Science
Book author
Plasil, Frantisek; Sack, Harald; Meinel, Christoph; Van Der Hoek, Wiebe; Italiano, Giuseppe; Van Leeuwen, Jan
Publisher
Springer
Series title
Lecture Notes in Computer Science
Series number
4362
Published in
Berlin
ISBN
978-3-540-69506-6
Pages
456-464
Publication identifier
http://dx.doi.org/10.1007/978-3-540-69507-3_39
Metadata
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Author(s)
Tolla, Pierre
Soutif, Eric
Quadri, Dominique
Abstract (EN)
The separable quadratic multi-knapsack problem (QMKP) consists in maximizing a concave separable quadratic integer (non pure binary) function subject to m linear capacity constraints. In this paper we develop a branch-and-bound algorithm to solve (QMKP) to optimality. This method is based on the computation of a tight upper bound for (QMKP) which is derived from a linearization and a surrogate relaxation. Our branch-and-bound also incorporates pre-processing procedures. The computational performance of our branch-and-bound is compared to that of three exact methods: a branch-and-bound algorithm developed by Djerdjour et al. (1988), a 0-1 linearization method originally applied to the separable quadratic knapsack problem with a single constraint that we extend to the case of m constraints, a standard branch-and-bound algorithm (Cplex9.0 quadratic optimization). Our branch-and-bound clearly outperforms other methods for large instances (up to 2000 variables and constraints).
Subjects / Keywords
Surrogate relaxation; Linearization; Separable quadratic function; Integer programming; Branch-and-bound

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