Testcases and code.

The critical chain method is often used to improve robustness in single-project scheduling, but there are two challenges when applying it to multi-project scheduling. First, the existing robustness measure focuses on time elasticity within sub-projects but neglects elasticity across sub-projects, making it difficult to balance drum resource requirements. Second, the differential evolution (DE) algorithm is adopted to solve this problem, but continuous evolutionary operators have limited flexibility, leading to numerous transformations between the continuous solution space and the discrete problem space. Therefore, we adjust the critical chain multi-project scheduling model by incorporating the drum buffer and the capacity constraint buffer and propose a robustness measure that considers both time elasticity within and among sub-projects. Meanwhile, we design an enhanced discrete DE algorithm, which not only discretizes the encoding–decoding strategy and evolutionary operators but also uses a hill-climbing algorithm to enhance local search. Experiments are conducted to verify the effectiveness of the robustness measure and the algorithm. The results indicate that, averaged over the eight instances, the enhanced discrete DE algorithm achieves an improvement of more than 3.3% in robustness compared with the overall mean of the benchmark algorithms. Furthermore, our robustness measure strengthens the stability of the scheduling plan and reduces buffer consumption and overflow during multi-project scheduling.关键链法（critical chain method）常被用于提升单项目调度的鲁棒性，但将其应用于多项目调度时存在两项挑战。其一，现有鲁棒性度量仅聚焦于子项目内部的时间弹性，却忽视了跨子项目的弹性，致使难以平衡瓶颈资源（drum resource）的需求；其二，过往研究多采用差分进化（differential evolution, DE）算法求解该问题，但连续进化算子的灵活性有限，导致连续解空间与离散问题空间间需进行大量转换。为此，本文通过引入鼓缓冲（drum buffer）与容量约束缓冲（capacity constraint buffer），对关键链多项目调度模型进行了修正，并提出了同时兼顾子项目内部及跨子项目时间弹性的鲁棒性度量指标。同时，本文设计了一种增强型离散差分进化算法，该算法不仅对编解码策略与进化算子进行离散化处理，还引入爬山算法以强化局部搜索能力。为验证所提鲁棒性度量指标与算法的有效性，本文开展了仿真实验。实验结果表明，在8个测试实例的平均性能上，相较于基准算法的整体均值，增强型离散差分进化算法的鲁棒性提升幅度超过3.3%。此外，本文提出的鲁棒性度量指标可有效提升调度计划的稳定性，降低多项目调度过程中的缓冲消耗与溢出情况。