Journal of Heuristics

, Volume 19, Issue 4, pp 573–589

Quadratic bottleneck knapsack problems


  • Ruonan Zhang
    • Department of MathematicsSimon Fraser University Surrey
    • Department of MathematicsSimon Fraser University Surrey

DOI: 10.1007/s10732-011-9175-1

Cite this article as:
Zhang, R. & Punnen, A.P. J Heuristics (2013) 19: 573. doi:10.1007/s10732-011-9175-1


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 ϵ-approximation algorithms for any ϵ>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.


Quadratic Knapsack problem Bottleneck Quadratic threshold Semi-greedy

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© Springer Science+Business Media, LLC 2011