The multiple-choice knapsack problem (MCKP) is a classic NP-hard combinatorial optimization problem. Motivated by several significant practical applications, this work investigates a novel variant of MCKP called data-driven chance-constrained multiple-choice knapsack problem (DDCCMCKP), where the item weight is a random variable with unknown probability distribution. We first present the problem formulation of DDCCMCKP, 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 DDCCMCKP, we propose a data-driven adaptive local search (DDALS) algorithm. The main merit of DDALS lies in evaluating solutions with chance constraints by data-driven methods, under the condition of unknown distributions and only historical sample data being available. The experimental results demonstrate the effectiveness of the proposed algorithm and show that it is superior to other baselines. Additionally, ablation experiments confirm the necessity of each component in the algorithm. Our proposed algorithm can serve as the baseline for future research, and the code and benchmark sets will be 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场景的启发，本文研究了一种名为数据驱动机会约束多选背包问题（DDCCMCKP）的新型MCKP变体，其中物品重量为概率分布未知的随机变量。我们首先给出了DDCCMCKP的问题建模，随后构建了两类基准测试集：第一类包含合成实例，第二类则针对某电信公司的真实应用场景进行模拟设计。为解决DDCCMCKP，我们提出了数据驱动自适应局部搜索（DDALS）算法。该算法的主要优势在于：在分布未知且仅拥有历史样本数据的条件下，能够通过数据驱动方法评估带有机会约束的可行解。实验结果表明，所提算法具有有效性，且性能优于其他基准方法。此外，消融实验证实了算法各关键组件的必要性。本文算法可作为未来研究的基准方法，相关代码与基准测试集将开源，以进一步推动这一挑战性问题的研究。