In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on the idea of relaxing MKP to a Bounded Sequential Multiple Knapsack Problem, i.e., a multiple knapsack problem in which item sizes are divisible. Such a relaxation, called sequential relaxation, is obtained by suitably replacing the items of a MKP instance with items with divisible sizes. Experimental results on benchmark instances show that the upper bound is effective, in terms of quality, when the ratio between the number of items and the number of knapsacks is small.

中文翻译：

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多背包问题的新上限

本文基于将MKP放宽到有界顺序多重背包问题（即物品大小可分割的多重背包问题）的思想，提出了多重背包问题（MKP）的新上限。通过用大小可分割的项目适当替换MKP实例的项目，可以获得这种松弛（称为顺序松弛）。在基准实例上的实验结果表明，当物品数量与背包数量之间的比率较小时，就质量而言，上限是有效的。