Abstract: As an important branch of flexible manufacturing, the virtual manufacturing cell (hereafter referred to as “virtual cell”) has attracted much attention in recent years. The virtual cell refers to the formation of a logical production cell by selecting the required equipment from alternative equipment resources based on the similarity of production tasks and considering the production conditions or constraints, and forming a logically interrelated virtual dynamic production entity by connecting the logistics system without changing the physical layout of equipment and resources, which has the advantages of reducing production preparation time and work-in-process inventory and improving equipment utilization. The virtual cell is mostly used in the production of large and complex products, whose production and logistics organization are complex, and the transportation of workpieces is mostly done with large transportation equipment such as flatbed transporters, traveling cranes and forklifts. It can be seen that the effective implementation of the virtual cell depends on the effective flow of the production logistics system, and the transportation organization has an important impact on the effective development and implementation of the scheduling scheme. Existing studies related to virtual cells ignore the influence of factors such as intra- and inter-transport capacity and non-load transport time, and the heterogeneity of parallel machines is not considered sufficient. These factors affect the recycling and availability of transportation equipment, which affects the continuity of production logistics and utilization of processing equipment. Consequently, the scheduling scheme often departs substantially from the actual production organization process or even is not even feasible.
In summary, this paper constructs a joint decision model of transportation organization and heterogeneous parallel machine scheduling under the constrained transportation capacity the intra- and inter-virtual cell, non-load transportation time and heterogeneous parallel machines, with the objectives of minimizing the maximum completion time and minimizing the total transportation time. Moreover, an improved NSGA-II algorithm is proposed to solve the model. The proposed algorithm is used to combine the crossover and mutation processes of particle swarm optimization and the genetic algorithm to improve the convergence speed of the algorithm. The evolution mechanism of the simulated annealing algorithm is applied to the mutation process of the genetic algorithm, which leads to an increase in population diversity and prevented the problem of the genetic algorithm from being easy to fall into local optimum. The simulations of examples with small, medium, and large dimension indicate that C-metric, diversity metric, Inverted Generational Distance (IGD), and computation time are better than standard NSGA-II. These findings reveal that the proposed algorithm presents more advantages than standard NSGA-II for solution quality, diversity, robustness, and convergence.
In actual production, there may be some variability in the transportation time of different workpieces at the same transportation distance, and the priority of each workpiece processing and transportation task may be different. In future research, the solving capability of the algorithm can be further improved, while the variability of transportation organization of different workpieces and the priority of each workpiece processing and transportation task can be incorporated into the joint decision problem of transportation organization inside and outside the virtual cell and scheduling of heterogeneous parallel machines for consideration.

Key words: virtual manufacturing cell, scheduling, production logistics, heterogeneous parallel machines, NSGA-II

摘要： 针对以往虚拟单元调度相关研究忽略了单元内外运输能力的限制、空载运输时间,以及对并行机的异质性考虑不够充分等问题,本研究以最大完工时间最小和总运输时间最短为目标,构建了虚拟单元运输组织与异质并行机调度联合决策模型,并提出了改进的NSGA-II算法对模型进行求解。所提算法将粒子群算法与NSGA-II的交叉、变异过程相融合,提高了算法的收敛速度。并将模拟退火算法的进化机制应用于NSGA-II的变异过程,避免了NSGA-II容易陷入局部最优的问题。通过小、中、大规模算例的仿真实验发现,所提算法与标准的NSGA-II相比,算法的鲁棒性、收敛性和解集的质量、多样性等方面表现出较高的优势。

关键词: 虚拟制造单元, 调度, 生产物流, 异质并行机, NSGA-II