Lagrangian heuristics for the Quadratic Knapsack Problem

Jesus Cunha (), Luidi Simonetti () and Abilio Lucena ()

Computational Optimization and Applications, 2016, vol. 63, issue 1, 97-120

Abstract: This paper investigates two Lagrangian heuristics for the Quadratic Knapsack Problem. They originate from distinct linear reformulations of the problem and follow the traditional approach of generating Lagrangian dual bounds and then using their corresponding solutions as an input to a primal heuristic. One Lagrangian heuristic, in particular, is a Non-Delayed Relax-and-Cut algorithm. Accordingly, it differs from the other heuristic in that it dualizes valid inequalities on-the-fly, as they become necessary. The algorithms are computationally compared here with two additional heuristics, taken from the literature. Comparisons being carried out over problem instances up to twice as large as those previously used. Three out of the four algorithms, including the Lagrangian heuristics, are CPU time intensive and typically return very good quality feasible solutions. A certificate of that being given by the equally good Lagrangian dual bounds we generate. Finally, this paper is intended as a contribution towards the investigation of more elaborated heuristics to the problem, an area that has been barely investigated so far. Copyright Springer Science+Business Media New York 2016

Keywords: Quadratic Knapsack Problem; Lagrangian heuristics; Relax-and-Cut; Lower and upper bounds (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-015-9763-3 (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:coopap:v:63:y:2016:i:1:p:97-120

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9763-3

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().