采用多场景多目标鲁棒优化的矩阵式单元制造系统生产-物流联动调度

Production-Logistics Synchronized Scheduling in Matrix Cellular Manufacturing Systems Employing Multi-Scenario Multi-Objective Robust Optimization

摘要

针对矩阵式单元制造系统生产-物流联动调度中时空耦合关系复杂，以及设备故障、作业时间波动等不确定性扰动频发的问题，提出了一种多场景多目标鲁棒优化调度模型。首先，采用场景表示法刻画多源不确定性，构建了以最小化订单同步时间、生产-物流同步时间及最大完工时间的多目标鲁棒优化模型。其次，设计了基于多场景鲁棒优化的模拟退火算法（MRSA），结合自适应权重调整机制，动态平滑多目标间的量纲差异，通过监测种群在各目标维度上的归一化偏离度，实现对解空间的高效均衡搜索。不同规模的算例仿真实验表明：在低、中、高不确定性场景下，所提鲁棒调度模型相比标称确定性模型，其最大完工时间等核心指标的抗风险底线（CVaR）实现了45%以上的优化；相较于固定权重模拟退火算法（FW-MSA），MRSA算法在关键性能指标上实现了20%～40%的显著优化。研究结果证实了所提模型与自适应算法实现了生产效率与风险控制的双重优化。

Abstract

To address the complex spatio-temporal coupling relations and frequent multi-source uncertainties (e.g., equipment failures and processing time fluctuations) in the production-logistics synchronized scheduling of matrix cellular manufacturing systems, a multi-scenario multi-objective robust optimization approach was proposed. First, a scenario-based method was employed to characterize multi-source uncertainties, and a multi-objective robust optimization model was developed to minimize the order synchronization time, production-logistics synchronization time, and makespan. Second, a multi-scenario robust simulated annealing (MRSA) algorithm was designed, incorporating a self-adaptive weight adjustment mechanism to dynamically smooth dimensional differences among multiple objectives. By monitoring the normalized deviation of the population in each objective dimension, the algorithm achieves an efficient and balanced search of the solution space. Simulation experiments across various problem scales demonstrate that, compared to the nominal deterministic model, the proposed robust scheduling model improves the conditional value at risk (CVaR) of core indicators (e.g., makespan) by over 45% under low, medium, and high uncertainty scenarios. Furthermore, compared to the fixed-weight multi-scenario simulated annealing (FW-MSA) algorithm, MRSA achieves a significant 20%—40% improvement in key performance indicators (KPIs). The results confirm that the proposed model and self-adaptive algorithm effectively optimize both production efficiency and risk mitigation.

关键词

矩阵式单元制造系统 / 生产-物流联动 / 不确定性 / 多目标鲁棒优化

Key words

matrix-based cellular manufacturing system / production-logistics synchronization / uncertainty / multi-objective robust optimization / self-adaptive algorithm

参考文献

[1] Yetis Hasan, Karakose Mehmet, Baygin Nursena. Blockchain—based mass customization framework using optimized production management for industry 4.0 applications[J]. Engineering Science and Technology, an International Journal, 2022, 36: 101151.

[2] Wang Miao, Tong Yifei, Zhuang Cunbo, et al. Towards industry 5.0: a framework of reconfigurable matrix—structured manufacturing system[J]. Journal of Manufacturing Systems, 2025, 82: 114-36.

[3] Nielsen Christian P, Avhad Akshay, Schou Casper, et al. Control system architecture for matrix—structured manufacturing systems[J]. Computers in Industry, 2023, 146: 103851.

[4] Li Mingxing, Huang George Q. Production—intralogistics synchronization of industry 4.0 flexible assembly lines under graduation intelligent manufacturing system[J]. International Journal of Production Economics, 2021, 241: 108272.

[5] Li Mingxing, Guo Daqiang, Li Ming, et al. Operation twins: production—intralogistics synchronisation in Industry 4.0[J]. International Journal of Production Research, 2023, 61(15): 5193-211.

[6] 李明星, 张凯, 苏意芬, 等. 分布式柔性智能制造系统联动管控架构与方法研究进展及展望[J]. 西安交通大学学报, 2025, 59(12): 21-43.

[7] Li Mingxing, Zhang Kai, Su Yifen, et al. Synchronization architectures and methods for distributed flexible smart manufacturing systems: research progress and prospects[J]. Journal of Xi’an Jiaotong University, 2025, 59(12): 21-43.

[8] Zeng Junhai, Xie Wei, Pan Mi. A discrete moth—flame optimization algorithm for multiple automated guided vehicles scheduling problem in a matrix manufacturing workshop[J]. Applied Soft Computing, 2024, 163: 111846.

[9] Wang Xuewu, Zhang Jianing, Hua Yi, et al. Effective NSGA—Ⅱ algorithm for a limited AGV scheduling problem in matrix manufacturing workshops with undirected material flow[J]. Complex System Modeling and Simulation, 2025, 5(1): 68-85.

[10] Chi Hao, Sang Hong—Yan, Zhang Biao, et al. BDE—Jaya: A binary discrete enhanced Jaya algorithm for multiple automated guided vehicle scheduling problem in matrix manufacturing workshop[J]. Swarm and Evolutionary Computation, 2024, 89: 101651.

[11] 赵梓安, 周泓, 雷颖健. 基于改进狼群算法与仿真的单元调度优化[J]. 系统仿真学报, 2022, 34(2): 201-11.

[12] Zhao Zi′an, Zhou Hong, Lei Yingjian. Modeling and optimization for manufacturing cell scheduling based on improved wolf pack algorithm and simulation[J]. Journal of System Simulation, 2022, 34(2): 201-11.

[13] Schmidtke N, Rettmann A, Behrendt F. Matrix production systems—requirements and influences on logistics planning for decentralized production structures[C]//Proceedings of the 54th Hawaii International Conference on System Sciences. Honolulu: University of Hawai㊣i at Mānoa Hamilton Library, 2021: 7155-7164.

[14] 蔡磊, 李文锋, 罗云. 个性化定制车间生产—物流协同调度框架与算法研究[J]. 机械工程学报, 2022, 58(7): 214-26.

[15] Cai Lei, Li Wenfeng, Luo Yun. Framework and algorithm of customized workshop production—logistics collaborative scheduling[J]. Journal of Mechanical Engineering, 2022, 58(7): 214-226.

[16] Qi Q, Tao F, Hu T. Digital twin—driven smart manufacturing: connotation reference model and applications[J]. IEEE Transactions on Industrial Informatics, 2021, 17(3): 2129-2138.

[17] Ding Kai, Chan F T S, Zhang Xudong, et al. Defining a digital twin—based cyber—physical production system for autonomous manufacturing in smart shop floors[J]. International Journal of Production Research, 2019, 57(20): 6315-6334.

[18] 蒋红飞, 屈挺, 张凯, 等. 基于数字孪生的高动态生产系统联动决策方法[J]. 工业工程, 2021, 24(2): 57-67.

[19] Jiang Hongfei, Qu Ting, Zhang Kai, et al. A synchronized decision—making method for highly dynamic production system based on digital—twin[J]. Industrial Engineering Journal, 2021, 24(2): 57-67.

[20] 李明星, 屈挺, 李明, 等. 基于乱序执行的智造系统生产—物流指令化管控方法[J]. 工业工程, 2025, 28(3): 28-41.

[21] Li Mingxing, Qu Ting, Li Ming, et al. An out—of—order execution—based method of instruction control for production—logistics in smart manufacturing[J]. Industrial Engineering Journal, 2025, 28(3): 28-41.

[22] Guo Jun, Liu Wenjun, Peng Zhao, et al. Integrated scheduling of distributed production and distribution in group manufacturing with uncertain travel time[J]. Complex & Intelligent Systems, 2023, 9(2): 1871-89.

[23] Himmiche Sara, Marangé Pascale, Aubry Alexis, et al. Robustness evaluation process for scheduling under uncertainties[J]. Processes, 2023, 11(2): 371.

[24] 刘晶, 唐震, 王晓茜, 等. 基于元学习的设备故障知识图谱构建及推理方法[J]. 计算机集成制造系统, 2023, 29(11): 3600-3613.

[25] Liu Jing, Tang Zhen, Wang Xiaoxi, et al. Equipment fault knowledge graph and inference method based on meta—learning[J]. Computer Integrated Manufacturing Systems, 2023, 29(11): 3600-3613.

[26] Shavazipour Babooshka, Kwakkel Jan H, Miettinen Kaisa. Multi—scenario multi—objective robust optimization under deep uncertainty: a posteriori approach[J]. Environmental Modelling & Software, 2021, 144: 105134.

[27] Botte Marco, Schöbel Anita. Dominance for multi—objective robust optimization concepts[J]. European Journal of Operational Research, 2019, 273(2): 430—40.

[28] 贾峰, 李世豪, 沈建军, 等. 采用深度迁移学习与自适应加权的滚动轴承故障诊断[J]. 西安交通大学学报, 2022, 56(8): 1-10.

[29] Jia Feng, Li Shihao, Shen Jianjun, et al. Fault diagnosis of rolling bearings using deep transfer learning and adaptive weighting[J]. Journal of Xi’an Jiaotong University, 2022, 56(8): 1-10.

[30] Wang Zhiyuan, Pan Quanke, Gao Liang, et al. A cooperative iterated greedy algorithm for the distributed flowshop group robust scheduling problem with uncertain processing times[J]. Swarm and Evolutionary Computation, 2023, 79: 101320.

[31] Li Wanling, Murata T, Fauadi M H F B M. Robust scheduling for flexible job—shop problems with uncertain processing times[J]. IEEJ Transactions on Electronics, Information and Systems, 2015, 135(6): 713-720.

[32] Meloni C, Pranzo M, Samà M. Evaluation of VaR and CVaR for the makespan in interval valued blocking job shops[J]. International Journal of Production Economics, 2022, 247: 108455.

基金资助

国家自然科学基金资助项目(52405548)

国家自然科学基金资助项目(52375498)

广东省基础与应用基础研究基金资助项目(2026A1515011558)