The multiple-choice knapsack problem (MCKP) is a classic NP-hard combinatorial optimization problem. Motivated by several significant real-world applications, this work investigates a novel variant of MCKP called chance-constrained multiple-choice knapsack problem (CCMCKP), where the item weights are random variables. In particular, we focus on the practical scenario of CCMCKP, where the probability distributions of random weights are unknown but only sample data is available. We first present the problem formulation of CCMCKP and then establish two benchmark sets. The first set contains synthetic instances and the second set is devised to simulate a real-world application scenario of a certain telecommunication company. To solve CCMCKP, we propose a data-driven adaptive local search (DDALS) algorithm. The main novelty of DDALS lies in its data-driven solution evaluation approach that can effectively handle unknown probability distributions of item weights. Moreover, in cases with unknown distributions, high intensity of chance constraints, limited amount of sample data and large-scale problems, it still exhibits good performance. Experimental results demonstrate the superiority of DDALS over other baselines on the two benchmarks. Additionally, ablation studies confirm the effectiveness of each component of the algorithm. Finally, DDALS can serve as the baseline for future research, and the benchmark sets are open-sourced to further promote research on this challenging problem.

翻译：多选背包问题（MCKP）是一类经典的NP难组合优化问题。受若干重要实际应用的驱动，本文研究了一种名为机会约束多选背包问题（CCMCKP）的新型MCKP变体，其中物品重量为随机变量。特别地，我们聚焦于CCMCKP的实际场景：随机重量的概率分布未知，仅有样本数据可用。我们首先给出了CCMCKP的问题形式化描述，并构建了两个基准测试集：第一个包含合成实例，第二个则针对某电信公司的实际应用场景设计。为求解CCMCKP，本文提出了一种数据驱动的自适应局部搜索（DDALS）算法。DDALS的主要创新在于其数据驱动的解评价方法，可有效处理物品重量的未知概率分布。此外，在分布未知、机会约束强度高、样本数据有限及大规模问题等场景下，该算法仍表现出良好的性能。实验结果表明，DDALS在两个基准测试集上均优于其他基线方法。消融研究进一步验证了算法各组成部分的有效性。最后，DDALS可作为未来研究的基线方法，而基准测试集将开源以推动该挑战性问题的深入研究。