Multi-objective workshop layout optimization based on adaptive genetic simulated annealing algorithm
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摘要: 良好的车间设施布局能有效改善制造工艺流程、降低加工设备间物流运输成本，进而增强制造企业精益化程度。基于FK公司制造车间实际情况设计布局约束条件，构造以最小化车间物流成本和缩短搬运时间为优化目标的车间布局数学模型，并提出改进的遗传模拟退火算法对模型进行优化求解。该算法一方面引入自适应遗传算子策略，实现算法求解过程中遗传算子的动态修正；另一方面借用模拟退火算法的概率突跳性避免算法过早收敛，提高其全局寻优能力，进一步增强算法求解性能。通过设计对比试验及实际应用案例验证分析了模型与算法的可行性、有效性，结果表明该算法具有良好的寻优能力，可以有效降低车间物流成本和缩短搬运时间，对实际车间布局具有良好的改进作用。Abstract: Good layout of workshop facilities can effectively improve the manufacturing process, reduce the cost of logistics and transportation between processing equipment, and then enhance the degree of lean manufacturing enterprises. Based on the actual situation of manufacturing workshop of FK company, this paper designed the layout constraint conditions, constructed the mathematical model of workshop layout to minimize the logistics cost and logistics time, and proposed an improved genetic simulated annealing algorithm to solve the model. On the one hand, the adaptive genetic operator strategy is introduced to realize the dynamic modification of genetic operator in the process of solving the algorithm. On the other hand, the probability jump of simulated annealing algorithm can avoid premature convergence, improve its global optimization ability and further enhance the performance of the algorithm. The feasibility and effectiveness of the model and algorithm are verified and analyzed by design comparison test and practical application case. The results show that the algorithm has good optimization ability, can effectively reduce the cost and time of workshop logistics, and has a good role in improving the actual workshop layout.
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表 1 作业单元尺寸表
序号 名称 长度/m 宽度/m 1 原材料区 6 2 2 3号车床区 4 3 3 2号铣床区 5 4 4 数控加工中心 4 3.5 5 3号磨床区 3 2 6 剪床区 4.5 1 7 2号车床区 4.5 3.5 8 1号铣床区 4 4 9 2号磨床区 4 3 10 1号车床区 4.5 3 11 钻床区 5 4 12 1号磨床区 4 3.5 13 产品储存区 5.5 3.8 
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表 2 作业单元间的单位费用
元/m 序号 1 2 3 4 5 6 7 8 9 10 11 12 13 1 3.5 5.4 4.8 2.8 6 2 3.1 5.5 7.3 3.4 3 7 4 2.8 5.6 5 8.3 6 5 6.5 9.6 7 9 0 9.3 5.6 6.8 8 0 7.5 9 0 6.1 10 6.1 12 6.3 11 5.8 5.3 7.3 8.7 12 6.4 13
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表 3 作业单元间的搬运频率
次/天 序号 1 2 3 4 5 6 7 8 9 10 11 12 13 1 68 53 5 74 30 2 15 26 14 21 3 60 11 4 36 26 5 38 6 47 15 42 7 8 9 18 8 10 9 12 10 4 5 4 11 3 5 4 12 5 13
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表 4 作业单元间的搬运速度
m/s 序号 1 2 3 4 5 6 7 8 9 10 11 12 13 1 5 5 5 5 5 5 5 5 5 5 5 5 2 3 2 3 2 1 1 1 2 2 2 1 1 3 1 1 2 3 2 3 2 1 1 2 1 2 4 1 1 2 1 1 1 1 1 2 1 3 1 5 1 1 1 2 1 2 1 1 3 1 1 2 6 2 2 2 1 1 2 1 2 1 1 1 2 7 2 1 2 2 3 1 2 1 1 2 1 2 8 2 2 1 4 1 2 3 1 1 2 3 2 9 1 2 1 2 1 2 1 2 1 1 1 2 10 2 2 3 1 1 1 1 2 1 2 1 1 11 1 3 1 1 1 2 2 1 1 2 1 2 12 2 1 2 1 1 2 1 2 1 1 2 1 13 5 5 5 5 5 5 5 5 5 5 5 5
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表 5 算法参数设定对比
参数 方案1 方案2 方案3 方案4 算法类型 GA GA GA GA-SA $ {\mathit{P}}_{\mathit{c}} $ 0.4 $ {P}_{c}=\left\{\begin{array}{l}0.4 ,g \leqslant \dfrac{2}{5}G\\ 0.2,\dfrac{2}{5}G < g \leqslant \dfrac{4}{5}G\\ 0.15,\dfrac{4}{5}G < g \leqslant G\end{array}\right. $ 自适应取值法（本文式（13）） 自适应取值法（本文式（13）） $ {\mathit{P}}_{\mathit{m}} $ 0.15 $ {P}_{m}=\left\{\begin{array}{l}0.15,g \leqslant \dfrac{2}{5}G\\ 0.25,\dfrac{2}{5}G\le g \leqslant \dfrac{4}{5}G\\ 0.3,\dfrac{4}{5}G\leqslant g \leqslant G\end{array}\right. $ 自适应取值法（本文式（14）） 自适应取值法（本文式（14）） $ \mathit{g}\mathit{e}\mathit{n} $ 500 500 500 500 $ \mathit{t} $ / / / 3 000 ${\mathit{T} }_{{\rm{end}} }$ / / / 1 000 λ / / / 0.8
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表 6 优化后作业单元位置坐标
序号 作业单元 横坐标 纵坐标 所属行数 1 原材料区 18.5 2.5 1 2 3号车床区 23.3 9 2 3 2号铣床区 7.8 10.5 2 4 数控加工中心 3 9.8 2 5 3号磨床区 3.3 3.5 1 6 剪床区 12 9 2 7 2号车床区 7.8 17 3 8 1号铣床区 29.5 10.5 1 9 2号磨床区 3 17 3 10 1号车床区 13.5 3.5 1 11 钻床区 23.8 2.8 1 12 1号磨床区 17.3 9 3 13 产品储存区 8.5 2.5 1
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