A dynamic programming heuristic for the quadratic knapsack problem

Djeumou Fomeni, Franklin and Letchford, Adam (2014) A dynamic programming heuristic for the quadratic knapsack problem. INFORMS Journal on Computing, 26 (1). pp. 173-182. ISSN 1526-5528

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It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it can be solved in pseudo-polynomial time. We show however that the dynamic programming approach to the linear knapsack problem can be modified to yield a highly effective constructive heuristic for the quadratic version. In our experiments, the lower bounds obtained by our heuristic were consistently within a fraction of a percent of optimal. Moreover, the addition of a simple local search step enabled us to obtain the optimal solution of all instances considered.

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Journal Article
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INFORMS Journal on Computing
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04 Mar 2013 14:10
Last Modified:
21 Nov 2022 23:17