工程科学学报.第43卷，第11期：1491-1498.2021年11月 Chinese Journal of Engineering,Vol.43,No.11:1491-1498,November 2021 https://doi.org/10.13374/j.issn2095-9389.2020.02.26.002;http://cje.ustb.edu.cn 带有限缓冲区的混合流水车间多目标调度 袁庆欣四，董绍华 北京科技大学机械工程学院.北京100083 ☒通信作者，E-mail:15522625919@163.com 摘要研究对象是带有限缓冲区混合流水车间中的多目标调度问题.以各机器前置后置缓冲区容积有限、工件以批量形 式运输、运载设备的运载能力有限等作为资源限制因素，以最小化完工时间、最小化物料运输时间、最小化并行机前置缓冲 区空间占用率均衡指数为目标，建立调度模型.分别采用NSGA-Ⅱ、NSGA-Ⅲ算法求解该模型.并对比两者之间的差别：设置 不同的缓冲区容积.探究不同缓冲区容积对生产目标的影响.寻找最优缓冲区容积：建立不同模型.探究以最小化并行机前置 缓冲区空间占用率均衡指数为目标的意义，最后以某船用管类生产企业的实际生产案例作为对象，通过对比优化结果与实际 生产数据，验证了算法有效性. 关键词混合流水车间：多目标：缓冲区均衡：多约束：NSGA-Ⅲ 分类号U673.2 Optimizing multi-objective scheduling problem of hybrid flow shop with limited buffer YUAN Qing-xin,DONG Shao-hua School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:15522625919@163.com ABSTRACT Buffer zones in a production company are set before and after each processing equipment based on various factors such as workshop space in the hybrid-flow workshop,transportation capacity of the carrying equipment,ease of handling of the machine, machine productivity at various stages,and production cycle time.The objective of this paper was to optimizing the multi-objective scheduling problem in hybrid flow shop with limited buffer.As there was limited space(capacity)at front and rear buffers of each machine,transportation of workpieces in batches,limited carrying capacity of carrier equipment,differences in workability between parallel machines,and process determination,etc.,were considered as resource limiting factors,and based upon these factors two- objective scheduling model was established with the goal of minimizing completion time and minimizing material transportation time. The two-objective scheduling model was added with minimization parallel machine front buffer space occupancy rate equilibrium index as a new goal,and established a three-objective scheduling model.In this article,NSGA-II and NSGA-III algorithms were used to solve the three-objective scheduling model,and the crossover and mutation parts of the algorithm were redesigned according to the model established.The actual production data of a marine pipe production enterprise was taken as an example and optimization results were compared with the actual production data.Thus the effectiveness of the algorithm was verified,and the difference between the two algorithms when processing the three-target scheduling model was compared,and it is concluded that NSGA-III has better convergence effect when processing the three-objective model.To explore the impact of different buffer volumes on production,target values under different buffer volumes were compared,and finally optimal buffer volume for each target was found out;then the two-objective model and the three-objective model were compared under different buffer volumes.The optimization results of these indicators prove the practical importance of adding the minimization of the parallel machine front buffer space occupancy rate balance index. 收稿日期：2020-02-26 基金项目：国家自然科学基金资助项目(71301008)带有限缓冲区的混合流水车间多目标调度 袁庆欣苣，董绍华 北京科技大学机械工程学院，北京 100083 苣通信作者， E-mail：15522625919@163.com 摘    要    研究对象是带有限缓冲区混合流水车间中的多目标调度问题. 以各机器前置后置缓冲区容积有限、工件以批量形 式运输、运载设备的运载能力有限等作为资源限制因素，以最小化完工时间、最小化物料运输时间、最小化并行机前置缓冲 区空间占用率均衡指数为目标，建立调度模型. 分别采用 NSGA-II、NSGA-III 算法求解该模型，并对比两者之间的差别；设置 不同的缓冲区容积，探究不同缓冲区容积对生产目标的影响，寻找最优缓冲区容积；建立不同模型，探究以最小化并行机前置 缓冲区空间占用率均衡指数为目标的意义，最后以某船用管类生产企业的实际生产案例作为对象，通过对比优化结果与实际 生产数据，验证了算法有效性. 关键词    混合流水车间；多目标；缓冲区均衡；多约束；NSGA-III 分类号    U673.2 Optimizing multi-objective scheduling problem of hybrid flow shop with limited buffer YUAN Qing-xin苣 ，DONG Shao-hua School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China 苣 Corresponding author, E-mail: 15522625919@163.com ABSTRACT    Buffer zones in a production company are set before and after each processing equipment based on various factors such as workshop space in the hybrid-flow workshop, transportation capacity of the carrying equipment, ease of handling of the machine, machine productivity at various stages, and production cycle time. The objective of this paper was to optimizing the multi-objective scheduling problem in hybrid flow shop with limited buffer. As there was limited space (capacity) at front and rear buffers of each machine, transportation of workpieces in batches, limited carrying capacity of carrier equipment, differences in workability between parallel machines, and process determination, etc., were considered as resource limiting factors, and based upon these factors two￾objective scheduling model was established with the goal of minimizing completion time and minimizing material transportation time. The two-objective scheduling model was added with minimization parallel machine front buffer space occupancy rate equilibrium index as a new goal, and established a three-objective scheduling model. In this article, NSGA-II and NSGA-III algorithms were used to solve the three-objective scheduling model, and the crossover and mutation parts of the algorithm were redesigned according to the model established. The actual production data of a marine pipe production enterprise was taken as an example and optimization results were compared with the actual production data. Thus the effectiveness of the algorithm was verified, and the difference between the two algorithms when processing the three-target scheduling model was compared, and it is concluded that NSGA-III has better convergence effect when processing the three-objective model. To explore the impact of different buffer volumes on production, target values under different buffer volumes were compared, and finally optimal buffer volume for each target was found out; then the two-objective model and the three-objective model were compared under different buffer volumes. The optimization results of these indicators prove the practical importance of adding the minimization of the parallel machine front buffer space occupancy rate balance index. 收稿日期: 2020−02−26 基金项目: 国家自然科学基金资助项目（71301008） 工程科学学报，第 43 卷，第 11 期：1491−1498，2021 年 11 月 Chinese Journal of Engineering, Vol. 43, No. 11: 1491−1498, November 2021 https://doi.org/10.13374/j.issn2095-9389.2020.02.26.002; http://cje.ustb.edu.cn