The multiple-choice knapsack problem (MCKP) is a classic combinatorial optimization with wide practical applications. This paper investigates a significant yet underexplored extension of MCKP: the multi-objective chance-constrained MCKP (MO-CCMCKP) under implicit probability distributions. The goal of the problem is to simultaneously minimize the total cost and maximize the confidence level of satisfying the capacity constraint, capturing essential trade-offs in domains like 5G network configuration. To address the computational challenge of evaluating chance constraints under implicit distributions, we first propose an order-preserving efficient resource allocation Monte Carlo (OPERA-MC) method. This approach adaptively allocates sampling resources to preserve dominance relationships while reducing evaluation time significantly. Further, we develop NHILS, a hybrid evolutionary algorithm that integrates specialized initialization and local search into NSGA-II to navigate sparse feasible regions. Experiments on synthetic benchmarks and real-world 5G network configuration benchmarks demonstrate that NHILS consistently outperforms several state-of-the-art multi-objective optimizers in convergence, diversity, and feasibility. The benchmark instances and source code will be made publicly available to facilitate research in this area.

翻译：多选择背包问题（MCKP）是经典的组合优化问题，具有广泛的实际应用。本文研究了MCKP一个重要但尚未充分探索的扩展：隐式概率分布下的多目标机会约束MCKP（MO-CCMCKP）。该问题的目标是在最小化总成本的同时最大化满足容量约束的置信水平，从而捕捉如5G网络配置等领域中的关键权衡关系。针对隐式分布下机会约束评估的计算挑战，我们首先提出了一种保序高效资源分配蒙特卡洛（OPERA-MC）方法。该方法通过自适应分配采样资源来保持支配关系，同时显著减少评估时间。进一步，我们开发了NHILS算法——一种将专用初始化和局部搜索集成到NSGA-II中的混合进化算法，用于在稀疏可行域中进行搜索。在合成基准测试和实际5G网络配置基准测试上的实验表明，NHILS在收敛性、多样性和可行性方面持续优于多种先进的多目标优化器。基准测试实例和源代码将公开提供，以促进该领域的研究。