Dual-Resource Constrained Distributed Flexible Scheduling for Aerospace Structural Components

doi:10.16182/j.issn1004731x.joss.24-0089

Abstract

Abstract:

A dual-resource constrained distributed flexible job-shop scheduling model was established by taking into account the worker constraints of the finishing process and the requirements of distributed multi-factory collaboration in the production of aerospace structural components. A hybrid grey wolf optimization algorithm based on the critical factory was proposed to solve this problem. The model contained four subproblems: factory selection, operation sequencing, machine selection, and worker selection. In view of these four sub-problems, a four-layer coding and a new decoding method were designed to avoid the use conflict of machines and workers. In addition, a new mechanism for hunting and searching for prey by wolf packs was developed to ensure population diversity and improve the global search ability of the algorithm while taking into account the constraints of factories and workers. A local search strategy based on critical factories was developed to enhance the local search capability of the algorithm in the context of distributed characteristics. The effectiveness of the algorithm in solving dual-resource constrained distributed flexible scheduling was verified by using extended standard examples and aerospace structural component examples.

Key words: aerospace structural components, distributed flexible job-shop scheduling, dual-resource constraint, critical factories, grey wolf optimization algorithm

CLC Number:

TP18

Wang Yufang, Zhang Dianqing, Hua Xiaolin, Yao Binbin, Chen Fan. Dual-Resource Constrained Distributed Flexible Scheduling for Aerospace Structural Components[J]. Journal of System Simulation, 2024, 36(11): 2722-2740.

Figures/Tables 20

Table 1

Symbol definition of DRCDFJSP model

符号	定义
$i, i'$	结构件序号
$h, h'$	工序序号
$v, v'$	精工序序号
$j, j'$	机器序号
$f, f'$	工厂序号
$g$	员工编号
$n$	结构件总数
$H i$	结构件 $i$ 包含的工序数
$N$	工厂总数
$U f$	第 $f$ 个工厂
$m f$	$U f$ 中的机器总数
$w f$	$U f$ 中的员工总数
$O i h$	结构件 $i$ 的第 $h$ 道工序
$O i v$	结构件 $i$ 的第 $v$ 道精工序
$M f j$	$U f$ 中的第 $j$ 台机器
$W f g$	$U f$ 中的第 $g$ 个员工
$t i h f j$	$O i h$ 在机器 $M f j$ 上的加工时间
$S i h f j$	$O i h$ 在机器 $M f j$ 上的开始加工时间
$C i h f j$	$O i h$ 在机器 $M f j$ 上的结束加工时间
$T f j g$	$W f g$ 操作机器 $M f j$ 的完工时间
$L$	一个足够大的正数
$C i$	结构件 $i$ 的完工时间
$Z i f$	0-1决策变量，如果结构件i选择在工厂f加工，则 $Z i f = 1$ ，否则 $Z i f = 0$
$X i h f j$	0-1决策变量，当 $O i h$ 选择在 $M f j$ 上加工，则 $X i h f j = 1$ ，否则 $X i h f j = 0$
$Y i h i' h' f j$	0-1决策变量，当 $O i h$ 在 $O i' h'$ 之前在 $M f j$ 加工时，则 $Y i h i' h' f j = 1$ ，否则 $Y i h i' h' f j = 0$
$δ i v f j g$	0-1决策变量，精工序 $O i v$ 由员工 $W f g$ 在机器 $M f j$ 上进行加工，则 $δ i v f j g = 1$ ，否则 $δ i v f j g = 0$
$τ f j j' g$	0-1决策变量，当 $M f j$ 为 $W f g$ 操作 $M f j'$ 的紧前机器，则 $τ f j j' g = 1$ ，否则 $τ f j j' g = 0$
$C m a x$	连续决策变量，表示最大完工时间

Table 1

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 2

Table 3

Table 4

Table 5

Comparison results of strategy effectiveness

算例	n × m× w	CFHGWO-4		CFHGWO-5		CFHGWO-6		CFHGWO
算例	n × m× w	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD
DMK01	10×6×5	25.00	21.88	14.29	14.38	20.00	18.03	20.00	17.49
DMK02	10×6×5	14.81	16.36	8.00	10.85	8.00	12.55	14.81	15.75
DMK03	15×8×7	9.93	8.13	7.30	6.14	10.56	9.47	11.19	10.34
DMK04	15×8×7	15.69	14.56	4.44	5.58	12.24	12.00	14.00	13.04
DMK05	15×4×4	9.40	10.08	4.50	3.60	7.83	8.78	7.83	8.78
DMK06	10×15×8	13.04	10.79	7.69	9.62	7.69	7.46	6.25	6.91
DMK07	20×5×4	14.16	15.02	9.35	9.01	14.16	14.14	11.82	12.85
DMK08	20×10×8	12.35	9.45	4.59	5.22	11.82	11.17	10.19	10.44
DMK09	20×10×8	12.74	9.92	2.59	4.36	12.74	10.88	13.41	10.88
DMK10	20×15×12	10.80	10.55	9.52	8.02	9.52	8.45	9.95	9.13
DLA01	10×5×4	14.67	15.59	0	0.60	9.43	16.06	12.13	15.90
DLA02	10×5×4	16.35	19.59	0	2.01	15.27	20.56	15.27	21.06
DLA03	10×5×4	29.92	29.71	0	4.02	24.95	32.56	26.99	31.88
DLA04	10×5×4	15.56	19.31	0	1.81	11.08	12.56	12.35	14.64
DLA05	10×5×4	0	5.35	0	0	0	4.28	0	4.52
DLA06	15×5×4	21.17	20.63	3.98	2.45	20.49	18.04	18.51	17.54
DLA07	15×5×4	25.13	25.02	3.14	2.22	21.17	22.19	22.16	23.21
DLA08	15×5×4	22.57	20.73	1.79	1.26	16.86	18.35	17.48	20.17
DLA09	15×5×4	25.61	25.14	3.19	2.34	21.90	23.81	23.26	23.76
DLA10	15×5×4	30.64	31.26	3.23	2.23	28.57	29.03	29.10	29.52
Mean		16.98	16.95	4.38	4.79	14.21	15.52	14.84	15.89
算例	n × m× w	CFHGWO-4		CFHGWO-5		CFHGWO-6		CFHGWO
算例	n × m× w	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD
DMK01	10×6×5	17.24	14.68	11.11	12.59	14.29	16.67	0	0
DMK02	10×6×5	0	0	0	6.50	17.86	17.86	0	0
DMK03	15×8×7	4.51	4.90	5.93	7.54	11.19	10.34	0	0
DMK04	15×8×7	0	2.22	0	4.97	8.51	10.20	2.27	0
DMK05	15×4×4	5.36	5.56	4.50	5.56	7.83	8.31	0	0
DMK06	10×15×8	6.25	4.62	4.76	7.46	9.09	8.28	0	0
DMK07	20×5×4	5.83	5.35	6.73	6.60	6.73	11.37	0	0
DMK08	20×10×8	0	4.63	4.28	4.63	11.01	10.44	0	0
DMK09	20×10×8	0.88	0.60	1.74	2.27	11.72	10.54	1.74	0
DMK10	20×15×12	5.47	4.55	7.32	6.70	9.95	7.89	0	0
DLA01	10×5×4	0	0.12	0	0.24	8.22	15.59	0	0
DLA02	10×5×4	0	1.62	0	1.82	11.86	19.59	0	0
DLA03	10×5×4	0	2.65	0	4.02	21.40	29.71	0	0
DLA04	10×5×4	0	0.81	0	0.94	9.34	12.35	0	0
DLA05	10×5×4	0	0	0	0	0	3.26	0	0
DLA06	15×5×4	1.93	1.60	2.55	1.06	17.33	17.36	0	0
DLA07	15×5×4	1.82	1.72	4.42	3.66	19.40	20.43	0	0
DLA08	15×5×4	1.79	1.00	0	0.58	15.25	14.92	0.45	0
DLA09	15×5×4	1.22	2.02	2.61	1.68	19.44	21.89	0	0
DLA10	15×5×4	0.83	1.32	2.04	1.82	25.93	25.79	0	0
Mean		2.66	3.00	2.90	4.03	12.82	14.64	0.22	0

Table 5

Table 6

Fig. 6

Table 7

Table 8

Table 9

Table 10

Process information of structural components

结构件	工序1			工序2			工序3			工序4			工序5			工序6
结构件	名称	时间/机器		名称	时间/机器		名称	时间/机器		名称	时间/机器		名称	时间/机器		名称	时间/机器
J₁	数控车	3/M₁₄ 4/M₁₅	2/M₂₄ 4/M₂₅	车端面	5/M₁₁ 4/M₁₂ 4/M₁₃	6/M₂₁ 5/M₂₂ 4/M₂₃	车外圆	8/M₁₁ 6/M₁₂ 7/M₁₃	9/M₂₁ 7/M₂₂ 7/M₂₃	镗孔	5/M₁₈	5/M₂₈	钳	3/M₁₁₀	3/M₂₁₀	车槽	4/M₁₁ 5/M₁₂ 4/M₁₃	5/M₂₁ 6/M₂₂ 3/M₂₃
J₂	车端面	3/M₁₁ 4/M₁₂ 5/M₁₃	6/M₂₁ 4/M₂₂ 5/M₂₃	镗孔	4/M₁₈	4/M₂₈	钳	2/M₁₁₀	2/M₂₁₀	铣平面	3/M₁₆ 4/M₁₇	3/M₂₆ 4/M₂₇	数控车	3/M₁₄ 4/M₁₅	2/M₂₄ 4/M₂₅	车外圆	5/M₁₁ 5/M₁₂ 7/M₁₃	6/M₂₁ 7/M₂₂ 5/M₂₃
J₃	车外圆	8/M₁₁ 8/M₁₂ 9/M₁₃	9/M₂₁ 8/M₂₂ 9/M₂₃	车端面	4/M₁₁ 6/M₁₂ 4/M₁₃	5/M₂₁ 5/M₂₂ 4/M₂₃	检验	3/M₁₉	3/M₂₉	镗孔	4/M₁₈	4/M₂₈	数控车	5/M₁₄ 4/M₁₅	6/M₂₄ 4/M₂₅	铣平面	6/M₁₆ 4/M₁₇	5/M₂₆ 4/M₂₇
J₄	热处理	3/M₁₁₁	3/M₂₁₁	车槽	6/M₁₁ 6/M₁₂ 5/M₁₃	5/M₂₁ 6/M₂₂ 7/M₂₃	镗孔	5/M₁₈	4/M₂₈	钳	6/M₁₁₀	6/M₂₁₀	车外圆	3/M₁₁ 4/M₁₂ 5/M₁₃	4/M₂₁ 5/M₂₂ 6/M₂₃	车端面	8/M₁₁ 9/M₁₂ 8/M₁₃	7/M₂₁ 9/M₂₂ 7/M₂₃
J₅	车外圆	4/M₁₁ 5/M₁₂ 5/M₁₃	5/M₂₁ 7/M₂₂ 4/M₂₃	铣键槽	3/M₁₆ 3/M₁₇	4/M₂₆ 4/M₂₇	热处理	6/M₁₁₁	6/M₂₁₁	数控车	2/M₁₄ 3/M₁₅	2/M₂₄ 4/M₂₅	铣平面	5/M₁₆ 4/M₁₇	4/M₂₆ 5/M₂₇	车端面	6/M₁₁ 6/M₁₂ 5/M₁₃	6/M₂₁ 7/M₂₂ 5/M₂₃
J₆	车外圆	2/M₁₁ 3/M₁₂ 2/M₁₃	3/M₂₁ 2/M₂₂ 4/M₂₃	铣平面	6/M₁₆ 5/M₁₇	5/M₂₆ 5/M₂₇	数控车	5/M₁₄ 4/M₁₅	5/M₂₄ 4/M₂₅	镗孔	2/M₁₈	2/M₂₈	车槽	7/M₁₁ 6/M₁₂ 6/M₁₃	8/M₂₁ 6/M₂₂ 7/M₂₃	钳	6/M₁₁₀	6/M₂₁₀
J₇	车外圆	7/M₁₁ 8/M₁₂ 8/M₁₃	8/M₂₁ 7/M₂₂ 9/M₂₃	检验	6/M₁₉	6/M₂₉	镗孔	4/M₁₈	4/M₂₈	铣平面	7/M₁₆ 6/M₁₇	8/M₂₆ 6/M₂₇	铣键槽	5/M₁₆ 6/M₁₇	6/M₂₆ 4/M₂₇	数控车	8/M₁₄ 8/M₁₅	8/M₂₄ 9/M₂₅
J₈	钳	3/M₁₁₀	3/M₂₁₀	数控车	4/M₁₄ 5/M₁₅	3/M₂₄ 4/M₂₅	车槽	8/M₁₁ 9/M₁₂ 8/M₁₃	9/M₂₁ 7/M₂₂ 9/M₂₃	铣键槽	8/M₁₆ 7/M₁₇	7/M₂₆ 8/M₂₇	车端面	7/M₁₁ 5/M₁₂ 6/M₁₃	6/M₂₁ 7/M₂₂ 4/M₂₃	铣平面	5/M₁₆ 6/M₁₇	7/M₂₆ 6/M₂₇
J₉	车槽	6/M₁₁ 8/M₁₂ 8/M₁₃	6/M₂₁ 8/M₂₂ 7/M₂₃	车外圆	5/M₁₁ 4/M₁₂ 5/M₁₃	5/M₂₁ 6/M₂₂ 4/M₂₃	镗孔	3/M₁₈	3/M₂₈	数控车	7/M₁₄ 6/M₁₅	8/M₂₄ 6/M₂₅	检验	5/M₁₉	6/M₂₉	车端面	6/M₁₁ 5/M₁₂ 4/M₁₃	6/M₂₁ 7/M₂₂ 4/M₂₃
J₁₀	车端面	8/M₁₁ 5/M₁₂ 6/M₁₃	5/M₂₁ 7/M₂₂ 6/M₂₃	铣平面	6/M₁₆ 7/M₁₇	7/M₂₆ 7/M₂₇	钳	2/M₁₁₀	3/M₂₁₀	车外圆	7/M₁₁ 8/M₁₂ 6/M₁₃	8/M₂₁ 7/M₂₂ 5/M₂₃	车槽	5/M₁₁ 4/M₁₂ 5/M₁₃	5/M₂₁ 4/M₂₂ 6/M₂₃	检验	4/M₁₉	3/M₂₉
J₁₁	数控车	8/M₁₄ 7/M₁₅	8/M₂₄ 6/M₂₅	铣平面	5/M₁₆ 6/M₁₇	8/M₂₆ 5/M₂₇	车槽	8/M₁₁ 8/M₁₂ 6/M₁₃	8/M₂₁ 8/M₂₂ 5/M₂₃	车外圆	7/M₁₁ 7/M₁₂ 6/M₁₃	7/M₂₁ 7/M₂₂ 5/M₂₃	热处理	3/M₁₁₁	3/M₂₁₁	车端面	5/M₁₁ 5/M₁₂ 6/M₁₃	5/M₂₁ 6/M₂₂ 5/M₂₃
J₁₂	铣平面	6/M₁₆ 7/M₁₇	6/M₂₆ 8/M₂₇	车端面	9/M₁₁ 8/M₁₂ 8/M₁₃	8/M₂₁ 9/M₂₂ 7/M₂₃	镗孔	2/M₁₈	3/M₂₈	车外圆	4/M₁₁ 4/M₁₂ 6/M₁₃	5/M₂₁ 6/M₂₂ 5/M₂₃	铣键槽	4/M₁₆ 5/M₁₇	5/M₂₆ 6/M₂₇	车槽	8/M₁₁ 8/M₁₂ 9/M₁₃	9/M₂₁ 7/M₂₂ 8/M₂₃
J₁₃	热处理	2/M₁₁₁	2/M₂₁₁	铣平面	6/M₁₆ 7/M₁₇	6/M₂₆ 8/M₂₇	钳	2/M₁₁₀	2/M₂₁₀	车端面	7/M₁₁ 8/M₁₂ 7/M₁₃	8/M₂₁ 7/M₂₂ 7/M₂₃	车槽	9/M₁₁ 10/M₁₂ 10/M₁₃	8/M₂₁ 10/M₂₂ 9/M₂₃	数控车	5/M₁₄ 6/M₁₅	5/M₂₄ 6/M₂₅
J₁₄	数控车	6/M₁₄ 6/M₁₅	7/M₂₄ 6/M₂₅	车槽	7/M₁₁ 8/M₁₂ 9/M₁₃	8/M₂₁ 7/M₂₂ 9/M₂₃	铣键槽	7/M₁₆ 7/M₁₇	7/M₂₆ 8/M₂₇	车端面	7/M₁₁ 5/M₁₂ 6/M₁₃	8/M₂₁ 6/M₂₂ 5/M₂₃	镗孔	3/M₁₈	3/M₂₈	检验	2/M₁₉	3/M₂₉
J₁₅	铣键槽	6/M₁₆ 7/M₁₇	7/M₂₆ 6/M₂₇	钳	2/M₁₁₀	3/M₂₁₀	镗孔	3/M₁₈	3/M₂₈	数控车	8/M₁₄ 6/M₁₅	8/M₂₄ 7/M₂₅	车端面	6/M₁₁ 8/M₁₂ 6/M₁₃	8/M₂₁ 8/M₂₂ 5/M₂₃	车外圆	8/M₁₁ 7/M₁₂ 5/M₁₃	7/M₂₁ 7/M₂₂ 5/M₂₃

Table 10

Table 11

Fig. 7

Table 12

Table 13

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参数	水平
参数	1	2	3
p	150	200	250
e_max	30 000	50 000	70 000
ρ	0.05	0.10	0.15
q_max	5	10	15

参数组合	p	e_max	ρ	q_max	C_avg
1	1	1	1	1	51.7
2	1	2	3	2	48.2
3	1	3	2	3	49.3
4	2	1	3	3	46.2
5	2	3	2	1	46.9
6	2	2	1	2	45.7
7	3	1	2	2	46.7
8	3	2	1	3	49.6
9	3	3	3	1	50.4

策略	CFHGWO-0	CFHGWO-1	CFHGWO-2	CFHGWO-3	CFHGWO-4	CFHGWO-5	CFHGWO-6	CFHGWO
捕猎机制	—	√	—	—	√	√	—	√
贪婪搜索猎物机制	—	—	√	—	√	—	√	√
局部搜索	—	—	—	√	—	√	√	√

t-检验	P-value (BRPD)	P-value (ARPD)
t-检验(CFHGWO, CFHGWO-0)	5.486 84e-06	5.563 92e-06
t-检验(CFHGWO, CFHGWO-1)	3.886 62e-04	4.844 08e-05
t-检验(CFHGWO, CFHGWO-2)	6.092 91e-06	1.182 06e-06
t-检验(CFHGWO, CFHGWO-3)	4.782 08e-06	1.331 15e-06
t-检验(CFHGWO, CFHGWO-4)	0.043 78	0.004 92
t-检验(CFHGWO, CFHGWO-5)	0.002 04	2.306 44e-04
t-检验(CFHGWO, CFHGWO-6)	6.136 87e-06	2.652 42e-06

算例	n × m× w	ABC		CA		GA		IGWO		CFHGWO
算例	n × m× w	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD	BRPD	ARPD
Mean		8.14	10.55	11.25	10.98	2.83	3.77	3.18	3.26	0.68	0.69
DMK01	10×6×5	4.00	14.22	15.96	16.67	11.11	14.79	14.29	14.61	0	0
DMK02	10×6×5	23.08	29.34	20	20.74	13.04	10.20	0	0	13.04	10.42
DMK03	15×8×7	2.31	3.70	7.30	6.51	1.55	7.60	1.55	1.31	0	0
DMK04	15×8×7	10.52	26.74	12.50	10.74	0	0	0	1.27	0	2.52
DMK05	15×4×4	10.29	15.43	15.52	14.85	2.04	2.79	1.74	0.58	0	0
DMK06	10×15×8	6.52	8.67	9.09	7.08	10	8.36	8.78	10.07	0	0
DMK07	20×5×4	8.75	8.60	16.96	11.77	4.55	10.13	7.46	6.73	0	0
DMK08	20×10×8	7.72	8.42	12.14	11.44	0.66	0.35	4.66	3.55	0	0
DMK09	20×10×8	7.66	10.99	11.81	13.18	0	1.87	4.82	7.51	0	0
DMK10	20×15×12	11.89	13.72	11.88	16.66	8.11	8.38	7.29	11.43	0	0
DLA01	10×5×4	0	0	0	0	0	0	0	0	0	0
DLA02	10×5×4	2.48	4.66	6.86	7.49	0	0	0	0	0	0
DLA03	10×5×4	14.56	14.75	14.57	19.32	0	2.83	0	0	0	0
DLA04	10×5×4	2.89	4.38	9.40	11.81	0	1.47	0	0	0	0.82
DLA05	10×5×4	0	0	0	0	0	0	0	0	0	0
DLA06	15×5×4	9.13	5.92	12.49	8.62	1.16	1.58	2.09	0.76	0	0
DLA07	15×5×4	8.30	9.84	9.86	10.99	0	1.79	0.46	2.70	0	0
DLA08	15×5×4	13.39	13.35	15.12	12.25	2.20	1.19	6.18	3.60	0	0
DLA09	15×5×4	9.55	7.47	13.73	10.72	0.92	0.25	4.26	0.92	0	0
DLA10	15×5×4	9.76	10.83	9.73	8.74	1.30	1.86	0	0.18	0.60	0