Research on Joint Optimization of Energy-Saving Distributed Manufacturing and Preventive Maintenance for Semiconductor Wafers

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

Abstract

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

CLC Number:

TP301.6

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.

Figures/Tables 15

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

Table 2

Initial population quality comparisons

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

Table 2

Table 3

Wilcoxon signed rank test results of initial population quality

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	+

Table 3

Table 4

Experiment results comparisons of four algorithms (2 factories)

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

Table 4

Table 5

Experiment results comparisons of four algorithms (3 factories)

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

Table 5

Table 6

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 7

Pareto optimal solution set obtained by IHMGWO algorithm (part)

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

Table 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)

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