求解折扣0-1背包问题的启发式精确定位方法
Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem
摘要：
在本文中，我们考虑折扣0-1背包问题（DKP），这是一个经典的背包问题，其中一组项目被分解成三个项目的组的扩展。每组最多只能选择一个物品，目标是在遵守背包容量约束的情况下，最大化所选物品的总利润。在文献中，DKP是一个相对较新的问题。在本文中，我们提出了一个两阶段的方法，在该方法中，通过应用精确和/或启发式固定规则，可以被视为预处理阶段的第一阶段，减少了问题。剩下的问题可以通过动态规划来解决。在文献中的可用实例上进行的实验表明，固定技术是非常有用的，以解决这些情况。实际上，预处理阶段大大减少了这些实例的大小，从而显著减少了动态规划提供最优解所需的时间。
英文摘要：
In this paper we consider the discounted 0-1 knapsack problem (DKP), which is an extension of the classical knapsack problem where a set of items is decomposed into groups of three items. At most one item can be chosen from each group and the aim is to maximize the total profit of the selected items while respecting the knapsack capacity constraint. The DKP is a relatively recent problem in the literature. In this paper we propose a two-phase approach in which the problem is reduced by applying exact and / or heuristic fixation rules in a first phase that can be viewed as a preprocessing phase. The remaining problem can then be solved by dynamic programming. Experiments performed on available instances in the literature show that the fixation techniques are very useful to solve these instances. Indeed, the preprocessing phase greatly reduces the size of these instances, leading to a significant reduction in the time required for dynamic programming to provide an optimal solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
