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IMA Journal of Management Mathematics Advance Access published online on April 15, 2008
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpn004
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A survey of effective heuristics and their application to a variety of knapsack problems

Christophe Wilbaut{dagger} and Said Hanafi{ddagger}

LAMIH UMR 8530, Université de Valenciennes, Le Mont Houy, 59313 Valenciennes Cedex 9, France

Said Salhi§

Centre for Heuristic Optimisation, Kent Business School, University of Kent, Canterbury, Kent, UK

{dagger} Email: christophe.wilbaut{at}univ-valenciennes.fr

{ddagger} Email: said.hanafi{at}univ-valenciennes.fr

§ Email: s.salhi{at}kent.ac.uk

Received on 27 March 2007. Accepted on 12 February 2008.

We present a family of knapsack problems (KPs) while highlighting their particular applications. Though most of the problems are derived from the classical KP, the differences arise in the addition or modification of the constraints or in the way the objective function is defined. Appropriate techniques that were found to be successful in solving these problems are briefly reviewed. Hybrid methods that combine the strengths of different methods such as exact and heuristics are also briefly discussed. Some research avenues that we believe to be useful and challenging are also pointed out.

Keywords: knapsack; heuristics; 0–1 variables


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