系统仿真学报 ›› 2022, Vol. 34 ›› Issue (3): 584-602.doi: 10.16182/j.issn1004731x.joss.21-0190
收稿日期:
2021-03-09
修回日期:
2021-05-06
出版日期:
2022-03-18
发布日期:
2022-03-22
通讯作者:
叶春明
E-mail:dj8519@163.com;yechm6464@163.com
作者简介:
董君(1985-),女,博士生,讲师,研究方向为智能算法、生产调度等。E-mail:基金资助:
Received:
2021-03-09
Revised:
2021-05-06
Online:
2022-03-18
Published:
2022-03-22
Contact:
Chunming Ye
E-mail:dj8519@163.com;yechm6464@163.com
摘要:
针对半导体晶圆节能分布式制造与预维护联合优化问题,构建了同时考虑制造阶段和检测修复阶段,以最小化最大完工时间、总碳排放和总预维护成本为优化目标的两阶段绿色调度模型,提出了改进的混合多目标灰狼优化(improved hybrid multi-objective grey wolf optimization,IHMGWO)算法,设计了工厂分配策略、机器分配策略以及考虑维修工人柔性的同步调度维护策略的解码方案。通过设计初始化种群融合策略、捕食行为搜索策略、子种群变异策略,提高了算法的寻优性能。360个测试算例的对比实验表明,所提出的IHMGWO算法针对SP指标能够实现大部分占优,针对IGD和
中图分类号:
董君, 叶春明. 半导体晶圆节能分布式制造与预维护联合优化[J]. 系统仿真学报, 2022, 34(3): 584-602.
Jun Dong, Chunming Ye. Research on Joint Optimization of Energy-Saving Distributed Manufacturing and Preventive Maintenance for Semiconductor Wafers[J]. Journal of System Simulation, 2022, 34(3): 584-602.
图4
小规模测试算例甘特图Algorithm 1 Mutation strategyInput:The population C1, individual dimension dim,Population size N/2Output:New population C2Step: Description1.For i=1:N/22.??X=huilang(i).Position3.??I=[1,2,3,...,dim]4.??For k=1:dim5.???rnum=rand(1)6.???I=I(randperm(numel(I)))7.???If rnum≥0.58.????newX(k)=I(1)9.???Else10.????k1=k+111.????If k1==dim+112.??????k1=113.????End14.????While ismember(X(k1),NewX)15.??????If k<dim16.???????k1=k1+117.??????End18.?????End19.?????NewX(k)=X(k1)20.???End21.????I(find(I==NewX(k)))=22.??End23.????C2(i,:)=NewX24.End
表1
数据集中主要参数及其取值
加工 阶段 | 参数名称 | 取值 |
---|---|---|
全阶段 | 工件数/个 | 20/50/100 |
工位数/个 | 6/7/8 | |
电能碳排放因子/(kgCO2·J-1) | 1.874 2×10-7 | |
机器遗忘因子 | U[0.1,0.3] | |
机器上润滑油的使用量/L | U[0.2,0.4] | |
机器上润滑油的有效使用期/h | U[ | |
润滑油碳排放因子/(kgCO2·J-1) | 469 | |
机器退化率 | 0.018 | |
制造 阶段 | 工件在各个工位的加工时间/min | U[ |
每个工位上机器的加工功率/(kW·h-1) | U[ | |
每个工位上机器的空转功率/(kW·h-1) | U[ | |
设备预维护的固定成本(元) | U[ | |
加工层次 | 4/5 | |
每个工位上机器数(台) | U[ | |
设备预维护时间/min | U[ | |
工人预维护的单位工资(元) | U[ | |
检测维修阶段 | 工件的检测修复时间/min | U[ |
工位数/个 | 2 | |
每个工位上机器的加工功率/(kW·h-1) | U[ | |
每个工位上的机器数(台) | 2 | |
加工层次 | 2 | |
每个工位上机器的空转功率/(kW·h-1) | U[ |
表2
初始化种群质量对比
算例 | 工厂数为2 | 工厂数为3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
初始化种群融合策略 | 初始化种群随机生成策略 | 初始化种群融合策略 | 初始化种群随机生成策略 | |||||||||
SP | IGD | SP | IGD | SP | IGD | SP | IGD | |||||
20*6*4 | 0.180 6 | 0.092 1 | 80 | 0.241 1 | 0.262 2 | 20 | 0.184 4 | 0.102 3 | 76 | 0.171 9 | 0.267 8 | 24 |
20*7*4 | 0.188 6 | 0.107 5 | 78 | 0.220 0 | 02 258 | 22 | 0.165 2 | 0.104 2 | 75 | 0.207 7 | 0.188 0 | 25 |
20*8*4 | 0.163 7 | 0.109 1 | 77 | 0.232 4 | 0.229 0 | 23 | 0.161 5 | 0.062 9 | 80 | 0.182 3 | 0.184 8 | 20 |
20*6*5 | 0.233 1 | 0.110 4 | 69 | 0.302 6 | 0.271 6 | 31 | 0.162 3 | 0.100 6 | 72 | 0.194 7 | 0.202 3 | 28 |
20*7*5 | 0.158 1 | 0.091 8 | 80 | 0.243 4 | 0.257 6 | 20 | 0.164 0 | 0.068 6 | 84 | 0.211 2 | 0.208 2 | 16 |
20*8*5 | 0.154 5 | 0.080 7 | 78 | 0.168 0 | 0.174 0 | 22 | 0.164 2 | 0.081 7 | 78 | 0.191 4 | 0.183 8 | 22 |
50*6*4 | 0.338 3 | 0.241 9 | 73 | 0.352 3 | 0.335 1 | 27 | 0.325 2 | 0.095 7 | 85 | 0.330 5 | 0.346 7 | 15 |
50*7*4 | 0.229 7 | 0.149 7 | 76 | 0.186 9 | 0.339 3 | 24 | 0.282 6 | 0.154 0 | 72 | 0.236 4 | 0.372 4 | 28 |
50*8*4 | 0.227 8 | 0.100 9 | 78 | 0.239 4 | 0.241 6 | 22 | 0.296 9 | 0.165 6 | 76 | 0.208 0 | 0.354 4 | 24 |
50*6*5 | 0.286 8 | 0.120 4 | 76 | 0.353 7 | 0.358 4 | 24 | 0.314 5 | 0.119 1 | 82 | 0.307 2 | 0.378 7 | 18 |
50*7*5 | 0.258 2 | 0.117 1 | 77 | 0.226 7 | 0.394 4 | 23 | 0.240 4 | 0.139 9 | 76 | 0.379 6 | 0.335 7 | 24 |
50*8*5 | 0.203 4 | 0.112 1 | 68 | 0.387 5 | 0.260 5 | 31 | 0.204 2 | 0.137 1 | 85 | 0.425 8 | 0.398 0 | 15 |
100*6*4 | 0.204 9 | 0.124 1 | 72 | 0.262 5 | 0.273 4 | 28 | 0.314 8 | 0.139 7 | 67 | 0.274 1 | 0.304 4 | 33 |
100*7*4 | 0.193 9 | 0.158 9 | 79 | 0.176 9 | 0.304 1 | 21 | 0.336 5 | 0.200 2 | 72 | 0.243 8 | 0.335 4 | 28 |
100*8*4 | 0.244 1 | 0.159 0 | 64 | 0.377 9 | 0.310 3 | 36 | 0.269 9 | 0.172 4 | 67 | 0.264 7 | 0.295 6 | 33 |
100*6*5 | 0.201 5 | 0.114 2 | 80 | 0.256 5 | 0.307 2 | 20 | 0.224 0 | 0.134 3 | 75 | 0.309 0 | 0.269 3 | 25 |
100*7*5 | 0.208 5 | 0.114 9 | 76 | 0.345 1 | 0.360 2 | 24 | 0.258 0 | 0.153 9 | 80 | 0.292 5 | 0.365 2 | 20 |
100*8*5 | 0.226 3 | 0.127 6 | 77 | 0.315 0 | 0.296 6 | 23 | 0.204 9 | 0.146 3 | 72 | 0.285 3 | 0.282 7 | 28 |
表3
初始种群质量Wilcoxon符号秩检验结果
算例 | 工厂数为2 | 工厂数为3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
SP | IGD | SP | IGD | |||||||||
P | Win | P | Win | P | Win | P | Win | P | Win | P | Win | |
20*6*4 | 0.114 | = | 0.017 | + | 0.005 | + | 0.959 | = | 0.005 | + | 0.005 | + |
20*7*4 | 0.203 | = | 0.009 | + | 0.005 | + | 0.285 | = | 0.013 | + | 0.005 | + |
20*8*4 | 0.139 | = | 0.007 | + | 0.005 | + | 0.333 | = | 0.005 | + | 0.005 | + |
20*6*5 | 0.203 | = | 0.009 | + | 0.008 | + | 0.241 | = | 0.007 | + | 0.005 | + |
20*7*5 | 0.028 | + | 0.005 | + | 0.005 | + | 0.203 | = | 0.005 | + | 0.005 | + |
20*8*5 | 0.333 | = | 0.005 | + | 0.005 | + | 0.575 | = | 0.017 | + | 0.012 | + |
50*6*4 | 0.445 | = | 0.139 | + | 0.008 | + | 0.799 | = | 0.009 | + | 0.005 | + |
50*7*4 | 0.445 | = | 0.028 | + | 0.007 | + | 0.203 | = | 0.005 | + | 0.014 | + |
50*8*4 | 0.721 | = | 0.009 | + | 0.005 | + | 0.333 | = | 0.007 | + | 0.005 | + |
50*6*5 | 0.445 | = | 0.005 | + | 0.008 | + | 0.721 | = | 0.007 | + | 0.005 | + |
50*7*5 | 0.878 | = | 0.007 | + | 0.005 | + | 0.241 | = | 0.009 | + | 0.007 | + |
50*8*5 | 0.114 | = | 0.028 | + | 0.016 | + | 0.009 | + | 0.008 | + | 0.005 | + |
100*6*4 | 0.445 | = | 0.059 | + | 0.013 | + | 0.575 | = | 0.005 | + | 0.013 | + |
100*7*4 | 0.575 | = | 0.007 | + | 0.005 | + | 0.241 | = | 0.017 | + | 0.008 | + |
100*8*4 | 0.169 | = | 0.037 | + | 0.007 | + | 0.959 | = | 0.022 | + | 0.007 | + |
100*6*5 | 0.074 | = | 0.005 | + | 0.005 | + | 0.047 | + | 0.059 | + | 0.005 | + |
100*7*5 | 0.037 | + | 0.005 | + | 0.009 | + | 0.799 | = | 0.005 | + | 0.005 | + |
100*8*5 | 0.285 | = | 0.007 | + | 0.008 | + | 0.241 | = | 0.022 | + | 0.013 | + |
表4
4种算法实验结果对比(工厂数为2)
算例 | IHMGWO | MOGWO | NSGA-III | IMOGWO | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
SP | IGD | SP | IGD | SP | IGD | SP | IGD | |||||
20*6*4 | 0.115 9 | 0.052 4 | 90 | 0.225 5 | 0.270 9 | 1 | 0.263 0 | 0.221 0 | 6 | 0.177 8 | 0.171 3 | 3 |
20*7*4 | 0.160 4 | 0.081 7 | 90 | 0.186 7 | 0.310 4 | 4 | 0.388 8 | 0.242 9 | 1 | 0.150 9 | 0.215 8 | 5 |
20*8*4 | 0.114 1 | 0.048 7 | 87 | 0.198 0 | 0.323 5 | 6 | 0.206 0 | 0.174 0 | 4 | 0.199 8 | 0.146 8 | 3 |
20*6*5 | 0.088 9 | 0.017 2 | 86 | 0.163 4 | 0.187 7 | 3 | 0.179 3 | 0.172 5 | 4 | 0.231 3 | 0.249 4 | 7 |
20*7*5 | 0.204 3 | 0.078 5 | 85 | 0.153 8 | 0.197 7 | 5 | 0.409 5 | 0.224 8 | 3 | 0.189 6 | 0.168 3 | 7 |
20*8*5 | 0.135 8 | 0.040 0 | 90 | 0.131 3 | 0.206 1 | 3 | 0.212 8 | 0.199 8 | 2 | 0.137 9 | 0.189 1 | 5 |
50*6*4 | 0.117 5 | 0.058 3 | 80 | 0.171 1 | 0.281 5 | 10 | 0.218 7 | 0.226 9 | 8 | 0.203 0 | 0.211 0 | 2 |
50*7*4 | 0.108 6 | 0.056 7 | 82 | 0.185 9 | 0.216 0 | 2 | 0.147 1 | 0.200 8 | 9 | 0.509 8 | 0.305 6 | 7 |
50*8*4 | 0.132 3 | 0.089 0 | 73 | 0.182 0 | 0.259 4 | 5 | 0.349 3 | 0.184 8 | 20 | 0.141 2 | 0.226 2 | 2 |
50*6*5 | 0.191 6 | 0.116 0 | 74 | 0.211 7 | 0.332 6 | 4 | 0.241 5 | 0.267 2 | 5 | 0.263 4 | 0.227 1 | 17 |
50*7*5 | 0.239 6 | 0.178 1 | 77 | 0.255 5 | 0.428 1 | 8 | 0.309 4 | 0.256 6 | 6 | 0.302 4 | 0.400 5 | 9 |
50*8*5 | 0.131 1 | 0.084 7 | 79 | 0.198 7 | 0.253 6 | 7 | 0.253 2 | 0.169 7 | 12 | 0.156 4 | 0.202 7 | 2 |
100*6*4 | 0.225 1 | 0.133 6 | 82 | 0.206 9 | 0.262 2 | 9 | 0.221 1 | 0.326 7 | 3 | 0.227 3 | 0.296 4 | 6 |
100*7*4 | 0.139 9 | 0.122 7 | 75 | 0.179 7 | 0.306 6 | 7 | 0.410 6 | 0.234 8 | 13 | 0.136 1 | 0.268 4 | 5 |
100*8*4 | 0.076 7 | 0.173 0 | 74 | 0.180 5 | 0.262 8 | 15 | 0.201 9 | 0.312 0 | 6 | 0.233 6 | 0.221 8 | 5 |
100*6*5 | 0.133 6 | 0.131 4 | 75 | 0.174 9 | 0.274 8 | 15 | 0.183 5 | 0.191 7 | 8 | 0.205 5 | 0.224 5 | 2 |
100*7*5 | 0.161 6 | 0.079 2 | 77 | 0.172 2 | 0.340 1 | 10 | 0.428 1 | 0.237 2 | 12 | 0.269 3 | 0.250 9 | 1 |
100*8*5 | 0.103 4 | 0.006 7 | 94 | 0.143 6 | 0.237 6 | 3 | 0.201 5 | 0.173 8 | 3 | 0.135 0 | 0.235 8 | 0 |
表5
4种算法实验结果对比(工厂数为3)
算例 | IHMGWO | MOGWO | NSGA-III | IMOGWO | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
SP | IGD | SP | IGD | SP | IGD | SP | IGD | |||||
20*6*4 | 0.122 6 | 0.035 6 | 94 | 0.155 9 | 0.198 6 | 0 | 0.252 7 | 0.196 9 | 3 | 0.200 9 | 0.163 6 | 3 |
20*7*4 | 0.091 3 | 0.006 5 | 98 | 0.170 6 | 0.210 0 | 1 | 0.178 4 | 0.206 5 | 1 | 0.136 6 | 0.151 4 | 0 |
20*8*4 | 0.084 1 | 0.074 1 | 95 | 0.121 8 | 0.174 2 | 0 | 0.216 9 | 0.194 6 | 3 | 0.156 7 | 0.157 7 | 2 |
20*6*5 | 0.084 4 | 0.080 2 | 92 | 0.183 4 | 0.200 5 | 2 | 0.277 9 | 0.201 0 | 2 | 0.189 5 | 0.181 6 | 4 |
20*7*5 | 0.102 7 | 0.057 5 | 86 | 0.144 7 | 0.218 7 | 1 | 0.310 1 | 0.238 0 | 6 | 0.181 5 | 0.155 0 | 7 |
20*8*5 | 0.095 5 | 0.057 5 | 93 | 0.155 6 | 0.223 7 | 1 | 0.227 7 | 0.176 8 | 4 | 0.141 8 | 0.189 6 | 2 |
50*6*4 | 0.122 1 | 0.143 7 | 82 | 0.237 0 | 0.267 1 | 4 | 0.289 9 | 0.201 6 | 7 | 0.138 6 | 0.188 3 | 6 |
50*7*4 | 0.118 0 | 0.017 7 | 87 | 0.125 1 | 0.254 5 | 5 | 0.216 9 | 0.179 4 | 7 | 0.247 6 | 0.263 4 | 1 |
50*8*4 | 0.336 7 | 0.222 9 | 63 | 0.277 5 | 0.471 6 | 7 | 0.163 8 | 0.477 4 | 23 | 0.559 3 | 0.241 7 | 7 |
50*6*5 | 0.103 4 | 0.053 9 | 77 | 0.318 6 | 0.184 7 | 7 | 0.165 8 | 0.227 3 | 10 | 0.131 6 | 0.167 1 | 6 |
50*7*5 | 0.116 2 | 0.099 1 | 71 | 0.178 0 | 0.211 5 | 10 | 0.212 7 | 0.168 8 | 12 | 0.175 5 | 0.217 7 | 7 |
50*8*5 | 0.169 0 | 0.115 7 | 62 | 0.296 8 | 0.320 9 | 7 | 0.341 9 | 0.197 1 | 14 | 0.310 4 | 0.393 6 | 17 |
100*6*4 | 0.171 1 | 0.116 3 | 78 | 0.191 9 | 0.190 9 | 6 | 0.289 1 | 0.189 7 | 14 | 0.119 2 | 0.370 0 | 2 |
100*7*4 | 0.193 7 | 0.090 6 | 83 | 0.200 1 | 0.272 8 | 7 | 0.239 4 | 0.204 0 | 5 | 0.211 6 | 0.197 8 | 5 |
100*8*4 | 0.214 8 | 0.109 0 | 77 | 0.253 8 | 0.215 1 | 10 | 0.235 3 | 0.186 4 | 6 | 0.151 3 | 0.122 9 | 7 |
100*6*5 | 0.196 9 | 0.091 8 | 89 | 0.174 1 | 0.307 2 | 7 | 0.360 6 | 0.245 5 | 2 | 0.196 6 | 0.262 7 | 2 |
100*7*5 | 0.118 9 | 0.073 7 | 74 | 0.144 9 | 0.195 5 | 5 | 0.316 8 | 0.181 9 | 20 | 0.177 0 | 0.167 8 | 1 |
100*8*5 | 0.099 6 | 0.107 3 | 82 | 0.206 3 | 0.210 1 | 6 | 0.203 5 | 0.231 0 | 8 | 0.302 2 | 0.226 1 | 4 |
表7
IHMGWO算法获得的Pareto最优解集(部分)
序号 | 调度方案 | ||||
---|---|---|---|---|---|
工厂1 | 工厂2 | ||||
1 | 14.5(19.6) | 17 956(0) | 687(807) | 15-16-17-11-7-19-3-6-8-1 | 14-13-10-18-20-2-5-4-9-12 |
2 | 14.1(20.0) | 18 039(0) | 687(807) | 15-16-17-11-7-19-3-6-8-1 | 14-13-10-18-4-20-5-2-9-12 |
3 | 14.4(19.7) | 17 393(0) | 697(821) | 11-17-6-7-8-1-16-3-15-19 | 4-10-20-18-9-12-14-5-2-13 |
4 | 14.3(20.6) | 19 372(0) | 664(850) | 17-1-3-7-16-6-19-15-8-11 | 5-4-10-9-14-12-2-18-13-20 |
5 | 16.0(19.8) | 17 325(0) | 719(856) | 15-3-17-11-6-8-1-19-16-7 | 9-18-20-14-12-10-5-4-2-13 |
6 | 15.0(18.9) | 17 389(0) | 701(839) | 8-15-1-3-17-6-16-11-7 | 12-2-19-4-18-5-20-13-9-14-10 |
7 | 14.1(20.6) | 17 565(0) | 696(833) | 17-8-7-11-3-1-15-6-16 | 12-18-19-9-13-14-2-10-20-5-4 |
8 | 14.6(21.2) | 18 143(0) | 671(859) | 17-11-7-3-6-16-8-1-15 | 13-12-18-19-2-14-5-10-9-20-4 |
9 | 15.3(20.3) | 17 588(0) | 680(863) | 11-17-6-7-1-3-8-15-16 | 14-4-10-2-9-18-19-13-5-20-12 |
10 | 14.0(19.8) | 17 620(0) | 682(861) | 8-17-1-11-7-15-6-16-3 | 13-10-18-5-4-19-2-9-12-14-20 |
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