The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects

Arnaud Fréville () and SaÏd Hanafi ()

Annals of Operations Research, 2005, vol. 139, issue 1, 195-227

Abstract: The multidimensional 0-1 knapsack problem (MKP) is a resource allocation model that is one of the most well-known integer programming problems. During the last few decades, an impressive amount of research on the 0-1 knapsack problem has been published in the literature, and efficient special-purpose methods have become available for solving very large-scale instances. However, the multidimensional case has received less attention from the operational research community. Although recent advances have made solving medium size instances possible, solving the NP-hard problem remains a very interesting challenge, especially when the number of constraints increases. This paper surveys the principal results published in the literature concerning both the problem's theoretical properties and its approximate or exact solutions. The paper focuses on the more recent results—for example, those relevant to surrogate and composite duality, new preprocessing approaches creating enhanced versions of leading commercial software, and efficient metaheuristic-based methods. Copyright Springer Science + Business Media, Inc. 2005

Keywords: multidimensional 0-1 knapsack problem; heuristics and metaheuristics; probabilistic and worst-case analysis; surrogate and composite duality; preprocessing; MIP solvers (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-005-3448-8 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:139:y:2005:i:1:p:195-227:10.1007/s10479-005-3448-8

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-005-3448-8

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().