集并背包问题和简化最大覆盖问题的高效局部搜索
Efficient and Effective Local Search for the Set-Union Knapsack Problem and Budgeted Maximum Coverage Problem
摘要：
集并背包问题（SUKP）和最大覆盖问题（BMCP）是背包问题的两个密切相关的变体问题。给定一组加权元素和一组具有非负值的项目，其中每个项目涵盖几个不同的元素，这两个问题的目标都是找到一个子集的项目，最大化的目标函数，同时满足背包容量（预算）约束。针对这两个问题，我们提出了一种高效的局部搜索算法E2LS。据我们所知，这是第一次，一个算法已经提出了这两个。E2LS通过应用所提出的新算子ADD $^*$来遍历细化的搜索区域，从而折衷了搜索区域和搜索效率。这种折衷机制允许E2LS广泛而快速地探索解决方案空间。在E2LS算法中还引入了禁忌搜索方法，以避免陷入局部最优。在168个不同规模的公共实例上进行的大量实验表明，该算法对SUKP和BMCP都具有良好的性能。
英文摘要：
The Set-Union Knapsack Problem (SUKP) and Budgeted Maximum Coverage Problem (BMCP) are two closely related variant problems of the popular knapsack problem. Given a set of weighted elements and a set of items with nonnegative values, where each item covers several distinct elements, these two problems both aim to find a subset of items that maximizes an objective function while satisfying a knapsack capacity (budget) constraint. We propose an efficient and effective local search algorithm called E2LS for these two problems. To our knowledge, this is the first time that an algorithm has been proposed for both of them. E2LS trade-offs the search region and search efficiency by applying a proposed novel operator ADD$^*$ to traverse the refined search region. Such a trade-off mechanism allows E2LS to explore the solution space widely and quickly. The tabu search method is also applied in E2LS to help the algorithm escape from local optima. Extensive experiments on a total of 168 public instances with various scales demonstrate the excellent performance of the proposed algorithm for both the SUKP and BMCP.
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