We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight differs from the expected one. For this problem, we provide a dynamic programming algorithm and present techniques aimed at reducing its space and time complexities. Finally, we computationally compare the performances of the proposed algorithm with those of different exact algorithms presented so far in the literature for robust optimization problems.

中文翻译：

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鲁棒背包问题的精确解

我们考虑背包问题的一个不确定变体，其中物品的重量事先并不确切知道，但属于给定的区间，并且对重量与预期不同的物品数量施加了上限。对于这个问题，我们提供了一种动态规划算法，并提出了旨在降低其空间和时间复杂性的技术。最后，我们在计算上比较了所提出算法的性能与迄今为止文献中针对鲁棒优化问题提出的不同精确算法的性能。