The disjunctively constrained knapsack problem consists in packing a subset of pairwisely compatible items in a capacity-constrained knapsack such that the total profit of the selected items is maximized while satisfying the knapsack capacity. DCKP has numerous applications and is however computationally challenging (NP-hard). In this work, we present a threshold search based memetic algorithm for solving the DCKP that combines the memetic framework with threshold search to find high quality solutions. Extensive computational assessments on two sets of 6340 benchmark instances in the literature demonstrate that the proposed algorithm is highly competitive compared to the state-of-the-art methods. In particular, we report 24 and 354 improved best-known results (new lower bounds) for Set I (100 instances) and for Set II (6240 instances), respectively. We analyze the key algorithmic components and shed lights on their roles for the performance of the algorithm. The code of our algorithm will be made publicly available.

中文翻译：

---

解取约束背包问题的基于阈值搜索的模因算法

析取约束背包问题在于将成对兼容项目的子集包装在容量受限的背包中，以使所选项目的总利润最大化，同时满足背包容量。DCKP具有许多应用程序，但是计算难度很大（NP困难）。在这项工作中，我们提出了一种基于阈值搜索的模因算法来解决DCKP，该算法将模因框架与阈值搜索相结合以找到高质量的解决方案。在文献中对两组6340个基准实例的大量计算评估表明，与最新方法相比，该算法具有很高的竞争力。特别是，我们报告了Set I（100个实例）和Set II（6240个实例）的24个和354个最佳已知结果（新的下界）的改进，分别。我们分析了关键算法组件，并阐明了它们在算法性能方面的作用。我们算法的代码将公开提供。