Purpose

The set-union knapsack problem is one of the most significant generalizations of the Non-deterministic Polynomial (NP)-hard 0-1 knapsack problem in combinatorial optimization, which has rich application scenarios. Although some researchers performed effective algorithms on normal-sized instances, the authors found these methods deteriorated rapidly as the scale became larger. Therefore, the authors design an efficient yet effective algorithm to solve this large-scale optimization problem, making it applicable to real-world cases under the era of big data.

Design/methodology/approach

The authors develop three targeted strategies and adjust them into the adaptive tabu search framework. Specifically, the dynamic item scoring tries to select proper items into the knapsack dynamically to enhance the intensification, while the age-guided perturbation places more emphasis on the diversification of the algorithm. The lightweight neighborhood updating simplifies the neighborhood operators to reduce the algorithm complexity distinctly as well as maintains potential solutions. The authors conduct comparative experiments against currently best solvers to show the performance of the proposed algorithm.

Findings

Statistical experiments show that the proposed algorithm can find 18 out of 24 better solutions than other algorithms. For the remaining six instances on which the competitor also achieves the same solutions, ours performs more stably due to its narrow gap between best and mean value. Besides, the convergence time is also verified efficiency against other algorithms.

Originality/value

The authors present the first implementation of heuristic algorithm for solving large-scale set-union knapsack problem and achieve the best results. Also, the authors provide the benchmarks on the website for the first time.

中文翻译：

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有效的本地搜索大型集结背包问题

目的

集组合背包问题是组合优化中非确定性多项式（NP）-硬0-1背包问题的最重要概括之一，它具有丰富的应用场景。尽管一些研究人员在正常大小的实例上执行了有效的算法，但作者发现，随着方法规模的扩大，这些方法迅速恶化。因此，作者设计了一种有效而有效的算法来解决这一大规模优化问题，使其适用于大数据时代下的实际案例。

设计/方法/方法

作者开发了三种有针对性的策略，并将其调整为自适应禁忌搜索框架。具体而言，动态项目评分会尝试动态地从背包中选择合适的项目以增强强度，而年龄引导的扰动则更加注重算法的多样性。轻量级的邻域更新简化了邻域运算符，从而显着降低了算法复杂度并维护​​了潜在的解决方案。作者针对目前最好的求解器进行了比较实验，以证明所提出算法的性能。

发现

统计实验表明，与其他算法相比，该算法可在24个更好的解决方案中找到18个。对于其余六个竞争对手也能达到相同解决方案的情况，由于最佳值和平均值之间的差距很小，我们的表现更加稳定。此外，收敛时间也证明了其相对于其他算法的效率。

创意/价值

作者提出了启发式算法的第一个实现，用于解决大规模集联盟背包问题并获得最佳结果。此外，作者首次在网站上提供了基准。