Tian Xiang, Kong Yang, Liu Xiyu
School of Health Management, Binzhou Medical University, Yantai, Shandong, China.
School of Business, Shandong Normal University, Jinan, Shandong, China.
PLoS One. 2025 Sep 3;20(9):e0330020. doi: 10.1371/journal.pone.0330020. eCollection 2025.
The hybrid flow-shop scheduling problem is widely present and applied in industries such as production, manufacturing, transportation, and aerospace. In recent years, due to the advantages of nonlinear access and fully parallel processing, the probe machine has shown powerful computing capabilities and promising applications in solving various combinatorial optimization problems. This work firstly proposes an Improved Probe Machine with Multi-Level Probe Operations (IPMMPO) and ingeniously designs general data libraries and probe libraries tailored for multi-scenario HFS problems, including HFS with identical parallel machines and HFS with unrelated parallel machines, no-wait scenario, and standard scenario. Secondly, based on the data libraries of the IPMMPO, two tuple sets suitable for constraint programming modeling are further designed as data preprocessing. Next, a CP model (IPMMPO-CP) applicable to multi-scenario HFS problems is proposed. Finally, based on a large number of instances and real cases, IPMMPO-CP is compared with 9 representative algorithms and 2 latest CP models. The results demonstrate that the proposed IPMMPO-CP outperforms the compared algorithms and models.
混合流水车间调度问题广泛存在于生产、制造、运输和航空航天等行业并得到应用。近年来，由于具有非线性访问和全并行处理的优势，探测机在解决各种组合优化问题方面展现出强大的计算能力和广阔的应用前景。这项工作首先提出了一种具有多级探测操作的改进型探测机（IPMMPO），并巧妙地设计了针对多场景混合流水车间调度问题定制的通用数据库和探测库，包括具有相同并行机的混合流水车间调度问题、具有非相关并行机的混合流水车间调度问题、无等待场景和标准场景。其次，基于IPMMPO的数据库，进一步设计了两个适用于约束编程建模的元组集作为数据预处理。接下来，提出了一种适用于多场景混合流水车间调度问题的约束编程模型（IPMMPO-CP）。最后，基于大量实例和实际案例，将IPMMPO-CP与9种代表性算法和2种最新的约束编程模型进行了比较。结果表明，所提出的IPMMPO-CP优于所比较的算法和模型。
