半导体晶圆节能分布式制造与预维护联合优化

doi:10.16182/j.issn1004731x.joss.21-0190

摘要/Abstract

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 $Ω$ 指标能够实现全部占优，对于解决该类问题具有显著的优势和竞争力。

关键词: 半导体晶圆, 节能分布式制造, 预维护, 联合优化

Abstract:

Aiming at the joint optimization problem of energy-saving distributed manufacturing and preventive maintenance for semiconductor wafers, a two-stage green scheduling model considering both the manufacturing stage and the inspection and repair stage is established to minimize the makespan, the total carbon emissions and the total preventive maintenance cost. An improved hybrid multi-objective grey wolf optimization (IHMGWO)algorithm is proposed. The decoding schemes of factory allocation strategy, machine allocation strategy and synchronous scheduling maintenance strategy considering the flexibility of maintenance workers are designed in IHMGWO. By designing the initial population fusion strategy, predation behavior search strategy, and sub-population mutation strategy, the optimization performance of the algorithm is improved. The comparative experiments of 360 test cases show that the IHMGWO algorithm proposed in this paper can achieve most dominance for SP indicator and all dominance for IGD and $Ω$ indicator, which has certain advantages and competitiveness for solving such problems.

Key words: semiconductor wafers, energy-saving distributed manufacturing, preventive maintenance, joint optimization

中图分类号:

TP301.6

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/表 15

图1

图2

图3

图4

表1

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	$Ω$ /%	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%
2064	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
2074	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
2084	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
2065	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
2075	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
2085	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
5064	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
5074	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
5084	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
5065	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
5075	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
5085	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
10064	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
10074	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
10084	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
10065	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
10075	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
10085	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2

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		$Ω$		SP		IGD		$Ω$
	P	Win	P	Win	P	Win	P	Win	P	Win	P	Win
2064	0.114	=	0.017	+	0.005	+	0.959	=	0.005	+	0.005	+
2074	0.203	=	0.009	+	0.005	+	0.285	=	0.013	+	0.005	+
2084	0.139	=	0.007	+	0.005	+	0.333	=	0.005	+	0.005	+
2065	0.203	=	0.009	+	0.008	+	0.241	=	0.007	+	0.005	+
2075	0.028	+	0.005	+	0.005	+	0.203	=	0.005	+	0.005	+
2085	0.333	=	0.005	+	0.005	+	0.575	=	0.017	+	0.012	+
5064	0.445	=	0.139	+	0.008	+	0.799	=	0.009	+	0.005	+
5074	0.445	=	0.028	+	0.007	+	0.203	=	0.005	+	0.014	+
5084	0.721	=	0.009	+	0.005	+	0.333	=	0.007	+	0.005	+
5065	0.445	=	0.005	+	0.008	+	0.721	=	0.007	+	0.005	+
5075	0.878	=	0.007	+	0.005	+	0.241	=	0.009	+	0.007	+
5085	0.114	=	0.028	+	0.016	+	0.009	+	0.008	+	0.005	+
10064	0.445	=	0.059	+	0.013	+	0.575	=	0.005	+	0.013	+
10074	0.575	=	0.007	+	0.005	+	0.241	=	0.017	+	0.008	+
10084	0.169	=	0.037	+	0.007	+	0.959	=	0.022	+	0.007	+
10065	0.074	=	0.005	+	0.005	+	0.047	+	0.059	+	0.005	+
10075	0.037	+	0.005	+	0.009	+	0.799	=	0.005	+	0.005	+
10085	0.285	=	0.007	+	0.008	+	0.241	=	0.022	+	0.013	+

表3

表4

4种算法实验结果对比(工厂数为2)

算例	IHMGWO			MOGWO			NSGA-III			IMOGWO
算例	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%
2064	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
2074	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
2084	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
2065	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
2075	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
2085	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
5064	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
5074	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
5084	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
5065	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
5075	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
5085	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
10064	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
10074	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
10084	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
10065	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
10075	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
10085	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4

表5

4种算法实验结果对比(工厂数为3)

算例	IHMGWO			MOGWO			NSGA-III			IMOGWO
算例	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%	SP	IGD	$Ω$ /%
2064	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
2074	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
2084	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
2065	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
2075	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
2085	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
5064	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
5074	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
5084	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
5065	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
5075	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
5085	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
10064	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
10074	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
10084	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
10065	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
10075	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
10085	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5

表6

图5

图6

图7

图8

表7

IHMGWO算法获得的Pareto最优解集(部分)

序号	$T C T$ /kgCO₂	$T$ cost(元)	$C m a x$ /min	调度方案
序号	$T C T$ /kgCO₂	$T$ cost(元)	$C m a x$ /min	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

表7

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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[4,6]
	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[10,20]
	每个工位上机器的加工功率/(kW·h^-1)	U[5,8]
	每个工位上机器的空转功率/(kW·h^-1)	U[1,5]
	设备预维护的固定成本(元)	U[10,15]
	加工层次	4/5
	每个工位上机器数(台)	U[2,5]
	设备预维护时间/min	U[3,11]
	工人预维护的单位工资(元)	U[2,7]
检测维修阶段	工件的检测修复时间/min	U[1-2]
	工位数/个	2
	每个工位上机器的加工功率/(kW·h^-1)	U[3,6]
	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[1,3]

指标	MOGWO		NSGA-III		IMOGWO
指标	P	Sig(P<0.05)	P	Sig(P<0.05)	P	Sig(P<0.05)
SP	0.002(0.002)	Y(Y)	0.000(0.002)	Y(Y)	0.002(0.003)	Y(Y)
GD	0.000(0.000)	Y(Y)	0.000(0.000)	Y(Y)	0.000(0.000)	Y(Y)
IGD	0.000(0.000)	Y(Y)	0.000(0.000)	Y(Y)	0.000(0.000)	Y(Y)