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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (6): 1097-1106    DOI: 10.3785/j.issn.1008-973X.2022.06.006
智能机器人     
第II类机器人混流装配线的平衡与排序联合决策
孙宝凤1(),张新康1,李根道2,*(),刘娇娇1
1. 吉林大学 交通学院，吉林 长春 130022
2. 长春理工大学 经济管理学院，吉林 长春 130012
Joint decision-making of balancing and sequencing for type-II robotic mixed-model assembly line
Bao-feng SUN1(),Xin-kang ZHANG1,Gen-dao LI2,*(),Jiao-jiao LIU1
1. College of Transportation, Jilin University, Changchun 130022, China
2. School of Economics and Management, Changchun University of Science and Technology, Changchun 130012, China
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摘要：

为了提高第II类机器人混流装配线系统能效，界定工业机器人5种工作状态，量化不同状态下的机器人能源消耗值，引入关停策略和考虑产品切换，以最小化最大工作时间和能源消耗为目标，构建平衡与排序联合决策双目标优化模型. 设计改进的非支配排序遗传算法II，通过同类算法对比分析，验证改进算法的有效性. 结合算例，揭示关停策略和产品切换准备作业对机器人混流装配线系统的技术影响。关停策略能够减少能耗，在装配线平衡性下降时的效果愈加明显，最大能耗节约率达到16.68%；考虑产品切换准备作业的影响，有利于机器人混流装配线作业效率和能源消耗的整体优化.
关键词： 机器人混流装配线系统;  能源消耗;  关停策略;  产品切换;  平衡与排序优化;  改进的分支配排序遗传算法II    
Abstract:

In order to optimize the energy and efficiency of the type-II robotic mixed-model assembly line system, firstly, five working states of industrial robots was defined to measure the robot energy consumption in state. A dual-objective optimization model of joint decision-making of balancing and sequencing was proposed in consideration of shutdown strategies and product switching. Its objectives were taken as minimizing the maximum working time and energy consumption. Next, the improved non-dominated sorting genetic algorithm II (NSGA-II) was designed and its validation was also verified by comparing with a similarly algorithm. Finally, the technical impact of shutdown strategy and product switching on the robotic mixed-model assembly line system was shown by example analysis. The shutdown strategy was able to bring energy savings to a certain extent, and the benefits become more obvious when the balance of the assembly line decreases, and the maximum energy saving rate reached 16.68%; the product switching in consideration was beneficial both to the operation efficiency and energy efficiency for the robotic mixed-model assembly line.
Key words: type-II robotic mixed-model assembly line system    energy consumption    shutdown strategy    product switching    balancing and sequencing optimization    improved non-dominated sorting genetic algorithm II
收稿日期: 2021-09-12 出版日期: 2022-06-30
CLC:  TP 278  
基金资助: 国家自然科学基金资助项目（61873109)；吉林省自然科学基金资助项目（20210101055JC）；一汽股份技术创新资助项目（KF2020-20006）
通讯作者: 李根道     E-mail: sunbf@jlu.edu.cn;gendaoli@cust.edu.cn
作者简介: 孙宝凤（1970—），女，教授，博士，从事智能物流系统规划与设计研究. orcid.org/0000-0002-9030-5523，E-mail： sunbf@jlu.edu.cn
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引用本文:

孙宝凤,张新康,李根道,刘娇娇. 第II类机器人混流装配线的平衡与排序联合决策[J]. 浙江大学学报(工学版), 2022, 56(6): 1097-1106.

Bao-feng SUN,Xin-kang ZHANG,Gen-dao LI,Jiao-jiao LIU. Joint decision-making of balancing and sequencing for type-II robotic mixed-model assembly line. Journal of ZheJiang University (Engineering Science), 2022, 56(6): 1097-1106.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.06.006    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I6/1097

图 1  综合装配顺序图
图 2  工序排序向量、分配向量和工作站的关系
图 3  编码向量与解码结果
图 4  基于FRC的工序排序向量交叉
图 5  基于OX的机器人分配、MPS产品投产顺序向量交叉
图 6  工序排序向量的变异
图 7  工序排序向量的邻域搜索
$ \eta $ $ N $ $ D $ $ M $ $ H $
1 19 3 3 1,1,1
2 19 3 3 3,2,1
3 19 3 4 1,1,1
4 19 3 4 3,2,1
5 61 4 5 1,1,1,1
6 61 4 5 1,3,4,5
7 61 4 7 1,1,1,1
8 61 4 7 1,3,4,5
9 61 4 10 1,1,1,1
10 61 4 10 1,3,4,5
11 111 5 9 1,1,1,1,1
12 111 5 9 1,2,4,5,8
13 111 5 9 5,3,2,1,1
14 111 5 9 1,4,8,3,1
15 111 5 13 1,1,1,1,1
16 111 5 13 1,2,4,5,8
17 111 5 13 5,3,2,1,1
18 111 5 13 1,4,8,3,1
19 111 5 15 1,1,1,1,1
20 111 5 15 1,2,4,5,8
表 1  基准算例数据表（部分）
水平 $ {s_{\text{p}}} $ $ {n_{\max }} $ $ {p_{\text{c}}} $ $ {p_{\text{m}}} $
1 0.04 0.45 0.22 1.09
2 0.49 0.74 0.69 0.65
3 0.20 0.80 0.78 0.25
4 1.76 0.51 0.80 0.51
$ {R_{\text{V}}} $极差 1.72 0.36 0.58 0.85
$ {R_{\text{V}}} $等级 1.00 4.00 3.00 2.00
表 2  响应变量均值和显著性等级排序
$\eta $ $ \overline {{N_{\text{m}}}} $ $ \overline C $ $ \overline S $ $ \overline T /s $
HPSA NSGA-II (HPSA, NSGA-II) (NSGA-II, HPSA) HPSA NSGA-II HPSA NSGA-II
1 13.50 13.20 0.46 0.37 0.25 0.27 46.29 19.09
2 7.40 3.70 0.56 0.29 1.41 1.53 53.09 26.87
3 3.20 2.90 0.63 0.19 0.24 0.03 42.51 26.23
4 14.80 13.70 0.51 0.30 1.24 0.56 42.32 27.56
5 11.20 15.80 0.23 0.42 3.72 3.54 90.45 48.91
6 45.00 55.80 0.17 0.59 12.85 9.35 89.65 47.45
7 35.30 54.40 0.21 0.56 3.62 2.99 98.87 47.19
8 31.80 61.40 0.13 0.65 12.01 11.15 99.74 48.34
9 15.60 15.10 0.28 0.44 2.90 5.99 118.65 57.62
10 23.80 29.00 0.20 0.45 16.84 15.62 119.83 56.50
11 32.90 50.40 0.21 0.58 10.99 6.51 205.42 119.77
12 31.70 63.90 0.10 0.55 39.93 27.88 186.05 123.80
13 39.10 76.10 0.13 0.63 26.95 16.22 183.14 120.85
14 34.50 79.50 0.12 0.57 30.55 18.55 184.47 122.53
15 22.40 21.60 0.24 0.34 10.79 8.69 196.36 130.17
16 24.80 42.60 0.15 0.58 38.35 27.07 202.19 130.60
17 27.20 34.80 0.07 0.67 21.25 18.09 199.51 127.65
18 25.60 53.50 0.15 0.65 32.87 25.56 202.00 129.96
19 18.70 22.30 0.16 0.43 8.75 11.78 202.06 132.87
20 21.50 42.50 0.25 0.45 44.03 35.24 211.06 133.63
表 3  基准算例下NSGA-II、HPSA性能指标均值
图 8  基准算例下算法求得的平均非支配解数量
图 9  基准算例下算法的平均覆盖率
图 10  基准算例下算法的平均空间分布
图 11  基准算例下算法的平均运行时间
图 12  有无关停策略的Pareto解的分布
图 13  有无关停策略的能耗节约率对比
P A 方案1 方案2 $ R $/%
F 1 F 2 F 1 F 2 F 1 F 2
1 20.30 141.53 16.68 131.67 17.83 6.97
2 — — 16.72 131.61 17.63 7.01
3 — — 16.90 131.38 16.74 7.17
4 — — 16.92 130.81 16.64 7.57
5 — — 17.05 130.22 16.00 7.99
平均值 20.30 141.53 16.86 131.14 16.97 7.34
表 4  有无产品切换的能效优化对比
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