Multi-objective Optimization Algorithm for Non-linear Manufacturing Process Based on Three-tier Virtual Workflow Model
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摘要: 时间、生产质量和成本是加工制造中相互制约的重要参数, 平衡此参数使制造工艺最优是一个NP (Non-deterministic polynomial)难题, 对此出现了许多优秀的调度方法. 然而这些方法的优化对象均为线性工艺, 对于普遍存在的非线性工艺却无法调度优化. 针对此不足, 本文以非线性工艺为优化对象提出了三层虚拟工作流模型Three-VMG (Three-virtual model graph)及其优化算法Three-OVMG (Three-optimal virtual model graph). 该模型和算法首先建立非线性工作流, 采用虚拟技术寻找虚拟结点进行重构, 将其改造为虚拟线性工作流; 其次结合工艺特点对模型进行分段, 采用逆向分层串归约来实现段内最优解, 采用累积最优解来衔接各段间的值; 最后根据优化结果自顶向下完成各层资源的优化调度. 实验表明, 该过程较传统时间最小化优化调度算法具有显著的优化效果, 其性能及可操作性也能满足工程要求.Abstract: Time, production quality and cost are important parameters of mutual constraints in manufacturing. Balancing these parameters to make the manufacturing process more reasonable is an NP (non-deterministic polynomial) problem, and there are many excellent scheduling methods to solve this problem. However, the optimization objects of these methods are linear processes, so they can not be scheduled and optimized for the prevalent non-linear processes. To overcome the deficiency, a three-tier virtual workflow model, Three-VMG (three-virtual model graph), and its optimization algorithm, Three-OVMG (three-optimal virtual model graph), are proposed to optimize the non-linear processes in this paper. The model and algorithm first establish a non-linear workflow, using virtual technology to find virtual nodes for reconstruction, thus transforming it into virtual linear workflow. Secondly, according to the process characteristics, the model is segmented. Uses serial reduction strategy to calculate reverse hierarchical solution in each segment, and then cumulative values of solutions between segments. Finally, according to the optimization results, the optimal scheduling of resources at each level is top-down accomplished. Experiments show that the process has a significant optimization effect compared with the traditional time minimization optimal scheduling algorithms. In addition, the performance and operability of the algorithm can meet the engineering requirements.
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Key words:
- Workflow /
- manufacturing process /
- optimize scheduling /
- virtual technology /
- production quality
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表 1 冲压工艺质量检测结点集合P和T
Table 1 Node set P and T of stamping process quality inspection
结点 含义 p1 供应商 p2 采购部 p3 采购部质检 p4 冲压加工 p5 零件抽检部 p6 精修部 p7 质检部 pE 仓库 t1 备料 t2 采购就绪 t3 采购部质检就绪 t4 待冲压 t5 抽检质量就绪 t6 精修就绪 t7 质检就绪 tE 待入库 表 2 各部门服务的时间、质量和费用
Table 2 Time, quality and cost of departmental services
编号 时间 (天) 质量 (%) 费用 (万元) B1 30 95.1 10.5 B2 25 95.6 11.0 B3 20 94.2 10.2 C1 20 95.6 0.5 C2 18 97.0 0.6 S1 21 97.6 0.65 S2 20 96.8 0.63 D1 20 96.9 0.67 D2 19 96.7 0.65 D3 18 96.0 0.66 t2 15 99.8 0.45 t4 1 98.8 0.05 t6 7 99.9 0.2 tE 1 99.9 0.04 cp1 — 95.0 — cp2 — 97.5 — -
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