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About: Quadratic knapsack problem     Goto   Sponge   NotDistinct   Permalink

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The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective function: Given a set of items, each with a weight, a value, and an extra profit that can be earned if two items are selected, determine the number of items to include in a collection without exceeding capacity of the knapsack, so as to maximize the overall profit. Usually, quadratic knapsack problems come with a restriction on the number of copies of each kind of item: either 0, or 1. This special type of QKP forms the 0-1 quadratic knapsack problem, which was first discussed by Gallo et al.The 0-1 quadratic knapsack problem is a variation of knapsack problems, combining the features of unbounded knapsack problem, 0-1 knapsack problem