zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Using a mixed integer programming tool for solving the 0-1 quadratic knapsack problem. (English) Zbl 1239.90075
Summary: We will consider the 0-1 quadratic knapsack problem (QKP). Our purpose is to show that using a linear reformulation of this problem and a standard mixed integer programming tool, it is possible to solve the QKP efficiently in terms of computation time and the size of problems considered, in comparison to existing methods. Considering a problem involving $n$ variables, the linearization technique we propose has the advantage of adding only $(n - 1)$ real variables and $2(n - 1)$ constraints. We present extensive computational results on randomly generated instances and on structured problems coming from applications. For example, the method allows us to solve randomly generated QKP instances exactly with up to 140 variables.

90C09Boolean programming
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C20Quadratic programming
Full Text: DOI