Quadratic bottleneck knapsack problems

Authors:
Ruonan Zhang;Abraham P. Punnen
Affiliations:
Department of Mathematics, Simon Fraser University Surrey, Surrey, Canada V3T 0A3;Department of Mathematics, Simon Fraser University Surrey, Surrey, Canada V3T 0A3
Venue:
Journal of Heuristics
Year:
2013

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Abstract

In this paper we study the quadratic bottleneck knapsack problem (QBKP) from an algorithmic point of view. QBKP is shown to be NP-hard and it does not admit polynomial time 驴-approximation algorithms for any 驴0 (unless P=NP). We then provide exact and heuristic algorithms to solve the problem and also identify polynomially solvable special cases. Results of extensive computational experiments are reported which show that our algorithms can solve QBKP of reasonably large size and produce good quality solutions very quickly. Several variations of QBKP are also discussed.