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doi: 10.3934/jimo.2022063
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Collaborative optimization for energy saving and service composition in multi-granularity heavy-duty equipment cloud manufacturing environment

Hao Song 1,2, , Xiaonong Lu 1,2,, , Xu Zhang 1,2, , Xiaoan Tang 1,2, and  Qiang Zhang 1,2,

1. 

School of Management, Hefei University of Technology, Hefei 230009, China
2. 

Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei 230009, China

*Corresponding author: Xiaonong Lu

Received  May 2021 Revised  February 2022 Early access April 2022

Efficient service scheduling is an important technique supporting collaborative manufacturing platforms such as cloud manufacturing. To achieve a more efficient task execution, heavy-duty equipment manufacturing, an important field of cloud manufacturing, must be explored beyond parameters of cost and time. The manufacturing service composition problem of heavy-duty equipment has the characteristics of task complexity, high process energy consumption, and multi-granularity nature of service (MGNoS). In the manufacturing process of heavy-duty equipment, the energy consumption of required logistics accounts for 30% the total energy consumption. However, to date, research has investigated the problem almost always from the task level, and MGNoS has received little attentions, which may lead to redundant energy consumption in logistics during manufacturing execution. In this paper, the problem of manufacturing service scheduling with integrating energy saving and service composition in cloud manufacturing is considered. Based on the mathematical description, a cross-granularity task chain reconfiguration algorithm is presented for mitigating the adverse effects of MGNoS and developing the adaptive non-dominated sorting genetic algorithm Ⅲ for solving the service composition scheme to generate optimal scheduling solutions. The effectiveness and efficiency performances of typical optimization algorithms are compared with the proposed approach. The results show that the proposed method achieves significant energy savings for all tasks in different scenarios.

Keywords: Heavy-duty equipment, service composition, cross-granularity task chain reconfiguration, quality of service.
Mathematics Subject Classification: Primary: 90C11; Secondary: 90B10.
Citation: Hao Song, Xiaonong Lu, Xu Zhang, Xiaoan Tang, Qiang Zhang. Collaborative optimization for energy saving and service composition in multi-granularity heavy-duty equipment cloud manufacturing environment. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022063
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show all references

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[19]

W. Xu, S. Tian, Q. Liu, Y. Xie, Z. Zhou and and D. T. Pham, An improved discrete bees algorithm for correlation-aware service aggregation optimization in cloud manufacturing, The International Journal of Advanced Manufacturing Technology, 84 (2016), 17-28.  doi: 10.1007/s00170-015-7738-2.

[20]

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[22]

J. Zhou and X. Yao, Hybrid teaching–learning-based optimization of correlation-aware service composition in cloud manufacturing, The International Journal of Advanced Manufacturing Technology, 91 (2017), 3515-3533.  doi: 10.1007/s00170-017-0008-8.

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B. Xu and Z. Sun, A fuzzy operator based bat algorithm for cloud service composition, International Journal of Wireless and Mobile Computing, 11 (2016), 42-46. 

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J. Zhou and X. Yao, Multi-objective hybrid artificial bee colony algorithm enhanced with lévy flight and self-adaption for cloud manufacturing service composition, Applied Intelligence, 47 (2017), 721-742.  doi: 10.1007/s10489-017-0927-y.

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F. Seghir and A. Khababa, A hybrid approach using genetic and fruit fly optimization algorithms for qos-aware cloud service composition, Journal of Intelligent Manufacturing, 29 (2018), 1773-1792.  doi: 10.1007/s10845-016-1215-0.

[27]

B. Liu and Z. Zhang, Qos-aware service composition for cloud manufacturing based on the optimal construction of synergistic elementary service groups, The International Journal of Advanced Manufacturing Technology, 88 (2017), 2757-2771.  doi: 10.1007/s00170-016-8992-7.

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J. Lartigau, X. Xu, L. Nie and and D. Zhan, Cloud manufacturing service composition based on qos with geo-perspective transportation using an improved artificial bee colony optimisation algorithm, International Journal of Production Research, 53 (2015), 4380-4404.  doi: 10.1080/00207543.2015.1005765.

[29]

J. Zhou and and X. Yao, Multi-population parallel self-adaptive differential artificial bee colony algorithm with application in large-scale service composition for cloud manufacturing, Applied Soft Computing, 56 (2017), 379-397.  doi: 10.1016/j.asoc.2017.03.017.

[30]

W. Zhang, Y. Yang, S. Zhang, D. Yu and and Y. Xu, A new manufacturing service selection and composition method using improved flower pollination algorithm, Mathematical Problems in Engineering, 2016 (2016), 1-12.  doi: 10.1155/2016/7343794.

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Figure 1.  Illustration of CMfg
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Figure 2.  The reciprocating path of manufacturing logistics caused by FbRS
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Figure 3.  Four representative task chain structures
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Figure 4.  Flow chart of the proposed adaptive non-dominated sorting genetic algorithm Ⅲ (A-NSGA-Ⅲ)
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Figure 5.  An example of encoding the service composition problem
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Figure 6.  YH98 series forging presses equipment
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Figure 7.  Abstract task chain (ATC) after CTRA for YH28 manufacturing task
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Figure 8.  Optimal solution for YH28 manufacturing task
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Figure 9.  The number of ST reduced by CTRA for tasks of different scales
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Figure 10.  The number of MVs reduced by CTRA for tasks of different scales
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Figure 11.  Carbon emissions with and without CTRA obtained by CPA
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Figure 12.  Difference in carbon emissions between CPA with and without CTRA
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Figure 13.  Comparison performance between CPA and other energy-aware service composition algorithms
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Table 1.  Summary of notations
Symbol Description
$ M{V_u} $ The $ u $th Manufacturing vendor $ u = 1, 2, \ldots , U $
$ C{S_{n, u}} $ The nth CS uploaded by uth manufacturing vendor,
$ n = 1, 2, \ldots , N $
$ S{T_j} $ The $ j $th subtask, $ j = 1, 2, \ldots , J $
$ CS_{n, u}^j $ Before CTRA and after clustering, the $ n $th CS of the $ u $th MV belongs to $ j $th subtask
$ {\Lambda _N}\left( {M{V_u}} \right) $ the set of N CS provided by $ u $th manufacturing vendor
$ CS{T_j} $ The $ j $th concrete subtask
$ AS{T_m} $ After CTRA, the $ m $th abstract subtask, $ m = 1, 2, \ldots , M $
$ ACS_{n, u}^m $ After CTRA, the $ n $th CS of the $ u $th MV belongs to $ m $th AST
$ {Q_k}(A_{n, u}^m) $ The $ k $th QoS attribute of $ ACS_{n, u}^m $, $ k = 1, 2, \ldots , K $
$ {Q_{co}}(ACS_{n, u}^m) $ The cost QoS attribute of $ ACS_{n, u}^m $
$ {Q_{ti}}(ACS_{n, u}^m) $ The time QoS attribute of $ ACS_{n, u}^m $
$ {Q_{av}}(ACS_{n, u}^m) $ The reliability QoS attribute of $ ACS_{n, u}^m $
$ {Q_{EC}}(ACS_{n, u}^m) $ The energy consumption QoS attribute of $ ACS_{n, u}^m $
$ L(A_{n, u}^m, A_{n', u'}^{m + 1}) $ Logistics transportation distance from $ ACS_{n, u}^m $ to $ ACS_{n', u'}^{m + 1} $
$ \Delta Ltt $ Difference between the latitudes of $ ACS_{n, u}^m $ and $ ACS_{n', u'}^{m + 1} $
$ \Delta Lgt $ Difference between the Longitude of $ ACS_{n, u}^m $ and $ ACS_{n', u'}^{m + 1} $
$ Prc $ Unit price of logistics transportation
$ PrcA $ Price per unit of aviation kerosene
$ PrcH $ Price per unit of heavy diesel fuel
$ PrcL $ Price per unit of light diesel fuel
$ {C_{exp}} $ Expected cost from MSD
$ MLT $ Maximum threshold for the logistics transport distance
$ \Theta $ Punctuality rate of land transportation
$ Av $ Punctuality rate of air transport relative to land
$ Mar $ Punctuality rate of sea transport relative to land
$ R{L_{exp}} $ Expected reliability from MSD
$ MTTF $ Mean time to failure
$ MTBF $ Mean operating time between failures
$ ECS(ACS_{n, u}^m) $ Energy consumption during the setup stage
$ ECT(ACS_{n, u}^m) $ Energy consumption during the material transportation stage
$ ECI(ACS_{n, u}^m) $ Energy consumption during the machine idle stage
$ CEL $ Carbon emissions unit liter of aviation kerosene
$ CEA $ Carbon emissions unit liter of heavy diesel fuel
$ CEH $ Carbon emissions unit liter of light diesel fuel
$ E{C_{exp}} $ Expected cost from service demander
$ {E_{quota}} $ Government policy restrictions
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Symbol Description
$ M{V_u} $ The $ u $th Manufacturing vendor $ u = 1, 2, \ldots , U $
$ C{S_{n, u}} $ The nth CS uploaded by uth manufacturing vendor,
$ n = 1, 2, \ldots , N $
$ S{T_j} $ The $ j $th subtask, $ j = 1, 2, \ldots , J $
$ CS_{n, u}^j $ Before CTRA and after clustering, the $ n $th CS of the $ u $th MV belongs to $ j $th subtask
$ {\Lambda _N}\left( {M{V_u}} \right) $ the set of N CS provided by $ u $th manufacturing vendor
$ CS{T_j} $ The $ j $th concrete subtask
$ AS{T_m} $ After CTRA, the $ m $th abstract subtask, $ m = 1, 2, \ldots , M $
$ ACS_{n, u}^m $ After CTRA, the $ n $th CS of the $ u $th MV belongs to $ m $th AST
$ {Q_k}(A_{n, u}^m) $ The $ k $th QoS attribute of $ ACS_{n, u}^m $, $ k = 1, 2, \ldots , K $
$ {Q_{co}}(ACS_{n, u}^m) $ The cost QoS attribute of $ ACS_{n, u}^m $
$ {Q_{ti}}(ACS_{n, u}^m) $ The time QoS attribute of $ ACS_{n, u}^m $
$ {Q_{av}}(ACS_{n, u}^m) $ The reliability QoS attribute of $ ACS_{n, u}^m $
$ {Q_{EC}}(ACS_{n, u}^m) $ The energy consumption QoS attribute of $ ACS_{n, u}^m $
$ L(A_{n, u}^m, A_{n', u'}^{m + 1}) $ Logistics transportation distance from $ ACS_{n, u}^m $ to $ ACS_{n', u'}^{m + 1} $
$ \Delta Ltt $ Difference between the latitudes of $ ACS_{n, u}^m $ and $ ACS_{n', u'}^{m + 1} $
$ \Delta Lgt $ Difference between the Longitude of $ ACS_{n, u}^m $ and $ ACS_{n', u'}^{m + 1} $
$ Prc $ Unit price of logistics transportation
$ PrcA $ Price per unit of aviation kerosene
$ PrcH $ Price per unit of heavy diesel fuel
$ PrcL $ Price per unit of light diesel fuel
$ {C_{exp}} $ Expected cost from MSD
$ MLT $ Maximum threshold for the logistics transport distance
$ \Theta $ Punctuality rate of land transportation
$ Av $ Punctuality rate of air transport relative to land
$ Mar $ Punctuality rate of sea transport relative to land
$ R{L_{exp}} $ Expected reliability from MSD
$ MTTF $ Mean time to failure
$ MTBF $ Mean operating time between failures
$ ECS(ACS_{n, u}^m) $ Energy consumption during the setup stage
$ ECT(ACS_{n, u}^m) $ Energy consumption during the material transportation stage
$ ECI(ACS_{n, u}^m) $ Energy consumption during the machine idle stage
$ CEL $ Carbon emissions unit liter of aviation kerosene
$ CEA $ Carbon emissions unit liter of heavy diesel fuel
$ CEH $ Carbon emissions unit liter of light diesel fuel
$ E{C_{exp}} $ Expected cost from service demander
$ {E_{quota}} $ Government policy restrictions
Table 2.  Part of the sample data of MV
Task Chain Structures
Sequential model Parallel model Selective model Circular model
$ \sum\nolimits_{m = 1}^M {{Q_{co}}} $ $ \sum\nolimits_{m = 1}^M {{Q_{co}}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{co}} * P{r_m}} \right)} $ $ h * {Q_{co}} $
$ \sum\nolimits_{m = 1}^M {{Q_{ti}}} $ $ \max _{m = 1}^M{Q_{ti}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{ti}}*P{r_m}} \right)} $ $ h*{Q_{ti}} $
$ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{re}}} $ $ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{re}}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{re}} * P{r_m}} \right)} $ $ {\left( {{Q_{re}}} \right)^h} $
$ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{av}}} $ $ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{av}}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{av}} * P{r_m}} \right)} $] $ {\left( {{Q_{av}}} \right)^h} $
NOTE: In the case of selective model Prm is probability and $ \sum\nolimits_{m = 1}^M {P{r_m} = 1} $. In the case of circular model h is cycle number.
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Task Chain Structures
Sequential model Parallel model Selective model Circular model
$ \sum\nolimits_{m = 1}^M {{Q_{co}}} $ $ \sum\nolimits_{m = 1}^M {{Q_{co}}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{co}} * P{r_m}} \right)} $ $ h * {Q_{co}} $
$ \sum\nolimits_{m = 1}^M {{Q_{ti}}} $ $ \max _{m = 1}^M{Q_{ti}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{ti}}*P{r_m}} \right)} $ $ h*{Q_{ti}} $
$ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{re}}} $ $ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{re}}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{re}} * P{r_m}} \right)} $ $ {\left( {{Q_{re}}} \right)^h} $
$ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{av}}} $ $ \prod\nolimits_{m{\rm{ = 1}}}^M {{Q_{av}}} $ $ \sum\nolimits_{m = 1}^M {\left( {{Q_{av}} * P{r_m}} \right)} $] $ {\left( {{Q_{av}}} \right)^h} $
NOTE: In the case of selective model Prm is probability and $ \sum\nolimits_{m = 1}^M {P{r_m} = 1} $. In the case of circular model h is cycle number.
Table 3.  Part of the sample data of MV
ID Candidate Service Set N Location
$ {\rm{M}}{{\rm{V}}_{\rm{1}}} $ $ \left\{ {C{S_{{\rm{1, 1}}}}, {\rm{ C}}{{\rm{S}}_{{\rm{2, 1}}}}, {\rm{ C}}{{\rm{S}}_{{\rm{3, 1}}}}} \right\} $ 3 $ N28^\circ 17'7.81, {\rm{ }}E120^\circ 13'48.09 $
$ {\rm{M}}{{\rm{V}}_{\rm{2}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 2}}} \right\} $ 1 $ N32^\circ 09'32.76, {\rm{ }}E107^\circ 08' 2.51 $
$ {\rm{M}}{{\rm{V}}_{\rm{3}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 3}}, {\rm{ C}}{{\rm{S}}_{2, 3}}, {\rm{ C}}{{\rm{S}}_{{\rm{3}}{\rm{3}}}}, {\rm{ C}}{{\rm{S}}_{4, 3}}, {\rm{ C}}{{\rm{S}}_{5, 3}}} \right\} $ 5 $ N27^\circ 37'4.48, {\rm{ }}E109^\circ 43'36.35 $
$ {\rm{M}}{{\rm{V}}_{\rm{4}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 4}}, {\rm{ C}}{{\rm{S}}_{2, 4}}, {\rm{ C}}{{\rm{S}}_{3, 4}}} \right\} $ 3 $ N39^\circ 18' 59.17, {\rm{ }}E112^\circ 52'1.13 $
$ {\rm{M}}{{\rm{V}}_{\rm{5}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 5}}, {\rm{ C}}{{\rm{S}}_{2, 5}}} \right\} $ 2 $ N23^\circ 13'25.30, {\rm{ }}E113^\circ 02'8.07 $
$ {\rm{M}}{{\rm{V}}_{\rm{6}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 6}}, {\rm{ C}}{{\rm{S}}_{2, 6}}, {\rm{ C}}{{\rm{S}}_{3, 6}}, {\rm{ C}}{{\rm{S}}_{4, 6}}} \right\} $ 4 $ N29^\circ 29'8.31, {\rm{ }}E121^\circ 43'27.43 $
$ \ldots $
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ID Candidate Service Set N Location
$ {\rm{M}}{{\rm{V}}_{\rm{1}}} $ $ \left\{ {C{S_{{\rm{1, 1}}}}, {\rm{ C}}{{\rm{S}}_{{\rm{2, 1}}}}, {\rm{ C}}{{\rm{S}}_{{\rm{3, 1}}}}} \right\} $ 3 $ N28^\circ 17'7.81, {\rm{ }}E120^\circ 13'48.09 $
$ {\rm{M}}{{\rm{V}}_{\rm{2}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 2}}} \right\} $ 1 $ N32^\circ 09'32.76, {\rm{ }}E107^\circ 08' 2.51 $
$ {\rm{M}}{{\rm{V}}_{\rm{3}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 3}}, {\rm{ C}}{{\rm{S}}_{2, 3}}, {\rm{ C}}{{\rm{S}}_{{\rm{3}}{\rm{3}}}}, {\rm{ C}}{{\rm{S}}_{4, 3}}, {\rm{ C}}{{\rm{S}}_{5, 3}}} \right\} $ 5 $ N27^\circ 37'4.48, {\rm{ }}E109^\circ 43'36.35 $
$ {\rm{M}}{{\rm{V}}_{\rm{4}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 4}}, {\rm{ C}}{{\rm{S}}_{2, 4}}, {\rm{ C}}{{\rm{S}}_{3, 4}}} \right\} $ 3 $ N39^\circ 18' 59.17, {\rm{ }}E112^\circ 52'1.13 $
$ {\rm{M}}{{\rm{V}}_{\rm{5}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 5}}, {\rm{ C}}{{\rm{S}}_{2, 5}}} \right\} $ 2 $ N23^\circ 13'25.30, {\rm{ }}E113^\circ 02'8.07 $
$ {\rm{M}}{{\rm{V}}_{\rm{6}}} $ $ \left\{ {{\rm{C}}{{\rm{S}}_{1, 6}}, {\rm{ C}}{{\rm{S}}_{2, 6}}, {\rm{ C}}{{\rm{S}}_{3, 6}}, {\rm{ C}}{{\rm{S}}_{4, 6}}} \right\} $ 4 $ N29^\circ 29'8.31, {\rm{ }}E121^\circ 43'27.43 $
$ \ldots $
Table 4.  Part of the sample data of QoS of CS
ID QoS
co ti re av EC
(CNY) (Day) (%) (%) (Level)
$ {\rm{C}}{{\rm{S}}_{{\rm{2, 1}}}} $ 320k 23 73 54 C
$ {\rm{C}}{{\rm{S}}_{1, 2}} $ 1.9k 11 87 76 D
$ {\rm{C}}{{\rm{S}}_{2, 3}} $ 640k 57 77 89 E
$ {\rm{C}}{{\rm{S}}_{2, 4}} $ 275k 100 81 84 C
$ {\rm{C}}{{\rm{S}}_{1, 5}} $ 33k 68 65 71 C
$ {\rm{C}}{{\rm{S}}_{3, 6}} $ 835k 32 92 76 B
$ \ldots $
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ID QoS
co ti re av EC
(CNY) (Day) (%) (%) (Level)
$ {\rm{C}}{{\rm{S}}_{{\rm{2, 1}}}} $ 320k 23 73 54 C
$ {\rm{C}}{{\rm{S}}_{1, 2}} $ 1.9k 11 87 76 D
$ {\rm{C}}{{\rm{S}}_{2, 3}} $ 640k 57 77 89 E
$ {\rm{C}}{{\rm{S}}_{2, 4}} $ 275k 100 81 84 C
$ {\rm{C}}{{\rm{S}}_{1, 5}} $ 33k 68 65 71 C
$ {\rm{C}}{{\rm{S}}_{3, 6}} $ 835k 32 92 76 B
$ \ldots $
Table 5.  Task chain for YH28 manufacturing task
ID Manufacturing function
$ {\rm{S}}{{\rm{T}}_{\rm{1}}} $ C'shaped rack
$ {\rm{S}}{{\rm{T}}_{\rm{2}}} $ Vertical perforation system
$ {\rm{S}}{{\rm{T}}_{\rm{3}}} $ Side frame
$ {\rm{S}}{{\rm{T}}_{\rm{4}}} $ Electrical control system
$ {\rm{S}}{{\rm{T}}_{\rm{5}}} $ Combined movable beam
$ {\rm{S}}{{\rm{T}}_{\rm{6}}} $ Main working cylinder
$ {\rm{S}}{{\rm{T}}_{\rm{7}}} $ Return cylinder
$ {\rm{S}}{{\rm{T}}_{\rm{8}}} $ Synchronous balance cylinder
$ {\rm{S}}{{\rm{T}}_{\rm{9}}} $ Guide rod
$ {\rm{S}}{{\rm{T}}_{\rm{10}}} $ Mobile workbench
$ {\rm{S}}{{\rm{T}}_{\rm{11}}} $ Base
$ {\rm{S}}{{\rm{T}}_{\rm{12}}} $ Combined fixed lower beam
$ {\rm{S}}{{\rm{T}}_{\rm{13}}} $ Step up beam
$ {\rm{S}}{{\rm{T}}_{\rm{14}}} $ Upper beam
$ {\rm{S}}{{\rm{T}}_{\rm{15}}} $ Filling valve
$ {\rm{S}}{{\rm{T}}_{\rm{16}}} $ Hydraulic station
$ {\rm{S}}{{\rm{T}}_{\rm{17}}} $ Photoelectric safety protection device
$ {\rm{S}}{{\rm{T}}_{\rm{18}}} $ Movable beam safety device
$ {\rm{S}}{{\rm{T}}_{\rm{19}}} $ Automatic feeding device
$ {\rm{S}}{{\rm{T}}_{\rm{20}}} $ Servo buffer system
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ID Manufacturing function
$ {\rm{S}}{{\rm{T}}_{\rm{1}}} $ C'shaped rack
$ {\rm{S}}{{\rm{T}}_{\rm{2}}} $ Vertical perforation system
$ {\rm{S}}{{\rm{T}}_{\rm{3}}} $ Side frame
$ {\rm{S}}{{\rm{T}}_{\rm{4}}} $ Electrical control system
$ {\rm{S}}{{\rm{T}}_{\rm{5}}} $ Combined movable beam
$ {\rm{S}}{{\rm{T}}_{\rm{6}}} $ Main working cylinder
$ {\rm{S}}{{\rm{T}}_{\rm{7}}} $ Return cylinder
$ {\rm{S}}{{\rm{T}}_{\rm{8}}} $ Synchronous balance cylinder
$ {\rm{S}}{{\rm{T}}_{\rm{9}}} $ Guide rod
$ {\rm{S}}{{\rm{T}}_{\rm{10}}} $ Mobile workbench
$ {\rm{S}}{{\rm{T}}_{\rm{11}}} $ Base
$ {\rm{S}}{{\rm{T}}_{\rm{12}}} $ Combined fixed lower beam
$ {\rm{S}}{{\rm{T}}_{\rm{13}}} $ Step up beam
$ {\rm{S}}{{\rm{T}}_{\rm{14}}} $ Upper beam
$ {\rm{S}}{{\rm{T}}_{\rm{15}}} $ Filling valve
$ {\rm{S}}{{\rm{T}}_{\rm{16}}} $ Hydraulic station
$ {\rm{S}}{{\rm{T}}_{\rm{17}}} $ Photoelectric safety protection device
$ {\rm{S}}{{\rm{T}}_{\rm{18}}} $ Movable beam safety device
$ {\rm{S}}{{\rm{T}}_{\rm{19}}} $ Automatic feeding device
$ {\rm{S}}{{\rm{T}}_{\rm{20}}} $ Servo buffer system
Table 6.  MVs involved in the for YH28 manufacturing task
ID CS set
$ {\rm{S}}{{\rm{T}}_{\rm{1}}} $ $ \left\{ {{\rm{CS}}{{_{\rm{1}}^{\rm{1}}}_{{\rm{, 1}}}}{\rm{, CS}}_{{\rm{2, 1}}}^{\rm{2}}{\rm{, CS}}_{{\rm{3, 1}}}^{\rm{3}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{2}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 2}}}^{{\rm{15}}}{\rm{, CS}}_{2, 2}^{16}{\rm{, CS}}_{3, 2}^{17}{\rm{, CS}}_{4, 2}^{18}{\rm{, CS}}_{5, 2}^{19}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{3}}} $ $ \left\{ {{\rm{CS}}_{1, 3}^2{\rm{, CS}}_{2, 3}^3{\rm{, CS}}_{3, 3}^4{\rm{, CS}}_{4, 3}^5{\rm{, CS}}_{5, 3}^6{\rm{, CS}}_{6, 3}^7{\rm{, CS}}_{7, 3}^8{\rm{, CS}}_{8, 3}^9} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{4}}} $ $ \left\{ {{\rm{CS}}_{1, 4}^1{\rm{, CS}}_{2, 4}^5{\rm{, CS}}_{3, 4}^6{\rm{, CS}}_{4, 4}^7{\rm{, CS}}_{5, 4}^8{\rm{, CS}}_{6, 4}^9{\rm{, CS}}_{7, 4}^{11}{\rm{, CS}}_{8, 4}^{12}{\rm{, CS}}_{9, 4}^{13}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{5}}} $ $ \left\{ {{\rm{CS}}_{1, 5}^7{\rm{, CS}}_{2, 5}^8} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{6}}} $ $ \left\{ {{\rm{CS}}{}_{1, 6}^{17}{\rm{, CS}}_{2, 6}^{18}{\rm{, CS}}_{3, 6}^{19}{\rm{, CS}}_{4, 6}^{20}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{7}}} $ $ \left\{ {{\rm{CS}}_{1, 7}^6{\rm{, CS}}_{2, 7}^7{\rm{, CS}}_{3, 7}^8{\rm{, CS}}_{4, 7}^9{\rm{, CS}}_{5, 7}^{10}{\rm{, CS}}_{6, 7}^{11}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{8}}} $ $ \left\{ {{\rm{CS}}_{1, 8}^{11}{\rm{, CS}}_{2, 8}^{12}{\rm{, CS}}_{3, 8}^{13}{\rm{, CS}}_{4, 8}^{14}{\rm{, CS}}_{5, 8}^{15}{\rm{, CS}}_{6, 8}^{16}{\rm{, CS}}_{7, 8}^{17}{\rm{, CS}}_{8, 8}^{18}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{9}}} $ $\begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{1, 9}^3{\rm{, CS}}_{2, 9}^4{\rm{, CS}}_{3, 9}^5{\rm{, CS}}_{4, 9}^6{\rm{, CS}}_{5, 9}^7{\rm{, CS}}_{6, 9}^8{\rm{, CS}}_{7, 9}^9{\rm{, }}\\{\rm{CS}}_{8, 9}^{10}{\rm{, CS}}_{9, 9}^{11}{\rm{, CS}}_{10, 9}^{12}{\rm{, CS}}_{11, 9}^{13}{\rm{, CS}}_{12, 9}^{14} \end{array} \right\} \end{equation} $
$ {\rm{S}}{{\rm{T}}_{\rm{10}}} $ $ \left\{ {{\rm{CS}}_{1, 10}^1{\rm{, CS}}_{2, 10}^2{\rm{, CS}}_{3, 10}^3{\rm{, CS}}_{4, 10}^{11}{\rm{, CS}}_{5, 10}^{12}{\rm{, CS}}_{6, 10}^{13}{\rm{, CS}}_{7, 10}^{14}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{11}}} $ $ \begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{1, 11}^1{\rm{, CS}}_{2, 11}^2{\rm{, CS}}_{3, 11}^3{\rm{, CS}}_{{\rm{4, 11}}}^{\rm{4}}{\rm{, CS}}_{{\rm{5, 11}}}^5{\rm{, }}\\{\rm{CS}}_{{\rm{6, 11}}}^{14}{\rm{, CS}}_{{\rm{7, 11}}}^{15}{\rm{, CS}}_{{\rm{8, 11}}}^{{\rm{16}}}{\rm{, CS}}_{9, 11}^{{\rm{19}}}{\rm{, CS}}_{10, 11}^{20} \end{array} \right\} \end{equation}$
$ {\rm{S}}{{\rm{T}}_{\rm{12}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 12}}}^{\rm{1}}{\rm{, CS}}_{{\rm{2, 12}}}^{\rm{2}}{\rm{, CS}}_{{\rm{3, 12}}}^{\rm{3}}{\rm{, CS}}_{{\rm{4, 12}}}^{11}{\rm{, CS}}_{{\rm{5, 12}}}^{12}{\rm{, CS}}_{{\rm{6, 12}}}^{{\rm{13}}}{\rm{, CS}}_{{\rm{7, 12}}}^{{\rm{14}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{13}}} $ $ \left\{ {{\rm{CS}}_{1, 13}^8{\rm{, CS}}_{2, 13}^9{\rm{, CS}}_{3, 13}^{10}{\rm{, CS}}_{4, 13}^{11}{\rm{, CS}}_{5, 13}^{12}{\rm{, CS}}_{6, 13}^{17}{\rm{, CS}}_{7, 13}^{18}{\rm{, CS}}_{8, 13}^{19}{\rm{, CS}}_{9, 13}^{20}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{14}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 14}}}^{\rm{1}}{\rm{, CS}}_{{\rm{2, 14}}}^2{\rm{, CS}}_{{\rm{3, 14}}}^{\rm{3}}{\rm{, CS}}_{{\rm{4, 14}}}^{\rm{4}}{\rm{, CS}}_{{\rm{5}}, 14}^{\rm{6}}{\rm{, CS}}_{{\rm{6, 14}}}^{\rm{7}}{\rm{, CS}}_{{\rm{7}}, 14}^{\rm{8}}{\rm{, CS}}_{{\rm{8, 14}}}^{\rm{9}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{15}}} $ $ \left\{ {{\rm{CS}}_{6, 15}^{{\rm{17}}}{\rm{, CS}}_{{\rm{7, 15}}}^{{\rm{18}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{16}}} $ $ \left\{ {{\rm{CS}}_{6, 16}^{{\rm{17}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{17}}} $ $ \begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{{\rm{1, 17}}}^{\rm{1}}{\rm{, CS}}_{{\rm{2, 17}}}^{\rm{2}}{\rm{, CS}}_{{\rm{3, 17}}}^{\rm{3}}{\rm{, CS}}_{{\rm{4, 17}}}^{\rm{4}}{\rm{, CS}}_{{\rm{5, 17}}}^{\rm{5}}{\rm{, CS}}_{{\rm{6, 17}}}^{\rm{6}}{\rm{, }}\\{\rm{CS}}_{{\rm{7, 17}}}^7{\rm{, CS}}_{{\rm{8, 17}}}^{\rm{9}}{\rm{, CS}}_{{\rm{9, 17}}}^{{\rm{10}}}{\rm{, CS}}_{{\rm{10, 17}}}^{{\rm{11}}}{\rm{, CS}}_{{\rm{11, 17}}}^{{\rm{12}}}{\rm{, CS}}_{{\rm{12, 17}}}^{{\rm{13}}} \end{array} \right\} \end{equation}$
$ {\rm{S}}{{\rm{T}}_{\rm{18}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 18}}}^{\rm{9}}{\rm{, CS}}_{{\rm{2, 18}}}^{{\rm{10}}}{\rm{, CS}}_{{\rm{3, 18}}}^{{\rm{11}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{19}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 19}}}^{{\rm{11}}}{\rm{, CS}}_{{\rm{2, 19}}}^{{\rm{12}}}{\rm{, CS}}_{{\rm{3, 19}}}^{{\rm{13}}}{\rm{, CS}}_{{\rm{4, 19}}}^{{\rm{14}}}{\rm{, CS}}_{{\rm{5, 19}}}^{{\rm{15}}}{\rm{, CS}}_{{\rm{6, 19}}}^{{\rm{18}}}{\rm{, CS}}_{{\rm{7, 19}}}^{{\rm{19}}}{\rm{, CS}}_{{\rm{8, 19}}}^{{\rm{20}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{20}}} $ $\begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{{\rm{1, 20}}}^{{\rm{10}}}{\rm{, CS}}_{{\rm{2, 20}}}^{{\rm{11}}}{\rm{, CS}}_{{\rm{3, 20}}}^{{\rm{12}}}{\rm{, CS}}_{{\rm{4, 20}}}^{{\rm{13}}}{\rm{, CS}}_{{\rm{5, 20}}}^{{\rm{14}}}{\rm{, }}\\{\rm{CS}}_{{\rm{6, 20}}}^{{\rm{15}}}{\rm{, CS}}_{{\rm{7, 20}}}^{{\rm{16}}}{\rm{, CS}}_{{\rm{8, 20}}}^{{\rm{17}}}{\rm{, CS}}_{{\rm{9, 20}}}^{{\rm{19}}}{\rm{, CS}}_{{\rm{10, 20}}}^{{\rm{20}}} \end{array} \right\} \end{equation} $
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ID CS set
$ {\rm{S}}{{\rm{T}}_{\rm{1}}} $ $ \left\{ {{\rm{CS}}{{_{\rm{1}}^{\rm{1}}}_{{\rm{, 1}}}}{\rm{, CS}}_{{\rm{2, 1}}}^{\rm{2}}{\rm{, CS}}_{{\rm{3, 1}}}^{\rm{3}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{2}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 2}}}^{{\rm{15}}}{\rm{, CS}}_{2, 2}^{16}{\rm{, CS}}_{3, 2}^{17}{\rm{, CS}}_{4, 2}^{18}{\rm{, CS}}_{5, 2}^{19}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{3}}} $ $ \left\{ {{\rm{CS}}_{1, 3}^2{\rm{, CS}}_{2, 3}^3{\rm{, CS}}_{3, 3}^4{\rm{, CS}}_{4, 3}^5{\rm{, CS}}_{5, 3}^6{\rm{, CS}}_{6, 3}^7{\rm{, CS}}_{7, 3}^8{\rm{, CS}}_{8, 3}^9} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{4}}} $ $ \left\{ {{\rm{CS}}_{1, 4}^1{\rm{, CS}}_{2, 4}^5{\rm{, CS}}_{3, 4}^6{\rm{, CS}}_{4, 4}^7{\rm{, CS}}_{5, 4}^8{\rm{, CS}}_{6, 4}^9{\rm{, CS}}_{7, 4}^{11}{\rm{, CS}}_{8, 4}^{12}{\rm{, CS}}_{9, 4}^{13}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{5}}} $ $ \left\{ {{\rm{CS}}_{1, 5}^7{\rm{, CS}}_{2, 5}^8} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{6}}} $ $ \left\{ {{\rm{CS}}{}_{1, 6}^{17}{\rm{, CS}}_{2, 6}^{18}{\rm{, CS}}_{3, 6}^{19}{\rm{, CS}}_{4, 6}^{20}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{7}}} $ $ \left\{ {{\rm{CS}}_{1, 7}^6{\rm{, CS}}_{2, 7}^7{\rm{, CS}}_{3, 7}^8{\rm{, CS}}_{4, 7}^9{\rm{, CS}}_{5, 7}^{10}{\rm{, CS}}_{6, 7}^{11}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{8}}} $ $ \left\{ {{\rm{CS}}_{1, 8}^{11}{\rm{, CS}}_{2, 8}^{12}{\rm{, CS}}_{3, 8}^{13}{\rm{, CS}}_{4, 8}^{14}{\rm{, CS}}_{5, 8}^{15}{\rm{, CS}}_{6, 8}^{16}{\rm{, CS}}_{7, 8}^{17}{\rm{, CS}}_{8, 8}^{18}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{9}}} $ $\begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{1, 9}^3{\rm{, CS}}_{2, 9}^4{\rm{, CS}}_{3, 9}^5{\rm{, CS}}_{4, 9}^6{\rm{, CS}}_{5, 9}^7{\rm{, CS}}_{6, 9}^8{\rm{, CS}}_{7, 9}^9{\rm{, }}\\{\rm{CS}}_{8, 9}^{10}{\rm{, CS}}_{9, 9}^{11}{\rm{, CS}}_{10, 9}^{12}{\rm{, CS}}_{11, 9}^{13}{\rm{, CS}}_{12, 9}^{14} \end{array} \right\} \end{equation} $
$ {\rm{S}}{{\rm{T}}_{\rm{10}}} $ $ \left\{ {{\rm{CS}}_{1, 10}^1{\rm{, CS}}_{2, 10}^2{\rm{, CS}}_{3, 10}^3{\rm{, CS}}_{4, 10}^{11}{\rm{, CS}}_{5, 10}^{12}{\rm{, CS}}_{6, 10}^{13}{\rm{, CS}}_{7, 10}^{14}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{11}}} $ $ \begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{1, 11}^1{\rm{, CS}}_{2, 11}^2{\rm{, CS}}_{3, 11}^3{\rm{, CS}}_{{\rm{4, 11}}}^{\rm{4}}{\rm{, CS}}_{{\rm{5, 11}}}^5{\rm{, }}\\{\rm{CS}}_{{\rm{6, 11}}}^{14}{\rm{, CS}}_{{\rm{7, 11}}}^{15}{\rm{, CS}}_{{\rm{8, 11}}}^{{\rm{16}}}{\rm{, CS}}_{9, 11}^{{\rm{19}}}{\rm{, CS}}_{10, 11}^{20} \end{array} \right\} \end{equation}$
$ {\rm{S}}{{\rm{T}}_{\rm{12}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 12}}}^{\rm{1}}{\rm{, CS}}_{{\rm{2, 12}}}^{\rm{2}}{\rm{, CS}}_{{\rm{3, 12}}}^{\rm{3}}{\rm{, CS}}_{{\rm{4, 12}}}^{11}{\rm{, CS}}_{{\rm{5, 12}}}^{12}{\rm{, CS}}_{{\rm{6, 12}}}^{{\rm{13}}}{\rm{, CS}}_{{\rm{7, 12}}}^{{\rm{14}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{13}}} $ $ \left\{ {{\rm{CS}}_{1, 13}^8{\rm{, CS}}_{2, 13}^9{\rm{, CS}}_{3, 13}^{10}{\rm{, CS}}_{4, 13}^{11}{\rm{, CS}}_{5, 13}^{12}{\rm{, CS}}_{6, 13}^{17}{\rm{, CS}}_{7, 13}^{18}{\rm{, CS}}_{8, 13}^{19}{\rm{, CS}}_{9, 13}^{20}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{14}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 14}}}^{\rm{1}}{\rm{, CS}}_{{\rm{2, 14}}}^2{\rm{, CS}}_{{\rm{3, 14}}}^{\rm{3}}{\rm{, CS}}_{{\rm{4, 14}}}^{\rm{4}}{\rm{, CS}}_{{\rm{5}}, 14}^{\rm{6}}{\rm{, CS}}_{{\rm{6, 14}}}^{\rm{7}}{\rm{, CS}}_{{\rm{7}}, 14}^{\rm{8}}{\rm{, CS}}_{{\rm{8, 14}}}^{\rm{9}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{15}}} $ $ \left\{ {{\rm{CS}}_{6, 15}^{{\rm{17}}}{\rm{, CS}}_{{\rm{7, 15}}}^{{\rm{18}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{16}}} $ $ \left\{ {{\rm{CS}}_{6, 16}^{{\rm{17}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{17}}} $ $ \begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{{\rm{1, 17}}}^{\rm{1}}{\rm{, CS}}_{{\rm{2, 17}}}^{\rm{2}}{\rm{, CS}}_{{\rm{3, 17}}}^{\rm{3}}{\rm{, CS}}_{{\rm{4, 17}}}^{\rm{4}}{\rm{, CS}}_{{\rm{5, 17}}}^{\rm{5}}{\rm{, CS}}_{{\rm{6, 17}}}^{\rm{6}}{\rm{, }}\\{\rm{CS}}_{{\rm{7, 17}}}^7{\rm{, CS}}_{{\rm{8, 17}}}^{\rm{9}}{\rm{, CS}}_{{\rm{9, 17}}}^{{\rm{10}}}{\rm{, CS}}_{{\rm{10, 17}}}^{{\rm{11}}}{\rm{, CS}}_{{\rm{11, 17}}}^{{\rm{12}}}{\rm{, CS}}_{{\rm{12, 17}}}^{{\rm{13}}} \end{array} \right\} \end{equation}$
$ {\rm{S}}{{\rm{T}}_{\rm{18}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 18}}}^{\rm{9}}{\rm{, CS}}_{{\rm{2, 18}}}^{{\rm{10}}}{\rm{, CS}}_{{\rm{3, 18}}}^{{\rm{11}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{19}}} $ $ \left\{ {{\rm{CS}}_{{\rm{1, 19}}}^{{\rm{11}}}{\rm{, CS}}_{{\rm{2, 19}}}^{{\rm{12}}}{\rm{, CS}}_{{\rm{3, 19}}}^{{\rm{13}}}{\rm{, CS}}_{{\rm{4, 19}}}^{{\rm{14}}}{\rm{, CS}}_{{\rm{5, 19}}}^{{\rm{15}}}{\rm{, CS}}_{{\rm{6, 19}}}^{{\rm{18}}}{\rm{, CS}}_{{\rm{7, 19}}}^{{\rm{19}}}{\rm{, CS}}_{{\rm{8, 19}}}^{{\rm{20}}}} \right\} $
$ {\rm{S}}{{\rm{T}}_{\rm{20}}} $ $\begin{equation} \left\{ \begin{array}{l} {\rm{CS}}_{{\rm{1, 20}}}^{{\rm{10}}}{\rm{, CS}}_{{\rm{2, 20}}}^{{\rm{11}}}{\rm{, CS}}_{{\rm{3, 20}}}^{{\rm{12}}}{\rm{, CS}}_{{\rm{4, 20}}}^{{\rm{13}}}{\rm{, CS}}_{{\rm{5, 20}}}^{{\rm{14}}}{\rm{, }}\\{\rm{CS}}_{{\rm{6, 20}}}^{{\rm{15}}}{\rm{, CS}}_{{\rm{7, 20}}}^{{\rm{16}}}{\rm{, CS}}_{{\rm{8, 20}}}^{{\rm{17}}}{\rm{, CS}}_{{\rm{9, 20}}}^{{\rm{19}}}{\rm{, CS}}_{{\rm{10, 20}}}^{{\rm{20}}} \end{array} \right\} \end{equation} $
Table 7.  Quality of service (QoS) constraint for YH28 manufacturing task
Parameters Cost Reliability EC Reputation
Constraint < 10 >50 >D good
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Parameters Cost Reliability EC Reputation
Constraint < 10 >50 >D good
Table 8.  Number of ST and number of MV after CTRA
Group 90 180 270 360 Group 90 180 270 360
$ \left| {{\bf{ST}}} \right| $ 20 11 12 12 12 $ \left| {{\bf{MV}}} \right| $ 20 49 103 128 129
30 17 16 17 17 30 65 123 155 213
40 21 19 21 21 40 66 135 195 255
50 25 25 25 26 50 76 138 210 278
60 28 29 29 29 60 80 153 220 282
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Group 90 180 270 360 Group 90 180 270 360
$ \left| {{\bf{ST}}} \right| $ 20 11 12 12 12 $ \left| {{\bf{MV}}} \right| $ 20 49 103 128 129
30 17 16 17 17 30 65 123 155 213
40 21 19 21 21 40 66 135 195 255
50 25 25 25 26 50 76 138 210 278
60 28 29 29 29 60 80 153 220 282
Table 9.  Parameter settings of CPA, NSGA-Ⅲ, FGA and AMOSA
Parameters CPA NSGA-Ⅲ FGA Parameters AMOSA
PoC 0.5 0.75 0.96 MaxVoT 200
PoM 0.1 1/n 0.02 MinVoT 10
DIC Self-adaption 30 30 NoIT 500
DIM 20 20 20 HCN 20
Cooling rate 0.8
NOTE:PoC denotes probability of crossover; PoM denotes probability of mutation; DIC denotes Distribution index for crossover; DIM denotes Distribution index for mutation; MaxVoT denotes Maximum value of the temperature; MinVoT denotes Minimum value of the temperature; NoIT denotes Number of iterations per temperature; HCN denotes hill-climb number.
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Parameters CPA NSGA-Ⅲ FGA Parameters AMOSA
PoC 0.5 0.75 0.96 MaxVoT 200
PoM 0.1 1/n 0.02 MinVoT 10
DIC Self-adaption 30 30 NoIT 500
DIM 20 20 20 HCN 20
Cooling rate 0.8
NOTE:PoC denotes probability of crossover; PoM denotes probability of mutation; DIC denotes Distribution index for crossover; DIM denotes Distribution index for mutation; MaxVoT denotes Maximum value of the temperature; MinVoT denotes Minimum value of the temperature; NoIT denotes Number of iterations per temperature; HCN denotes hill-climb number.
Table 10.  Comparison performance of the small scale
Algorithm Groups Groups in service composition Running time Haul ditance Carbon emission
CPA (20, 100) (11, 50) 3.8 304 3.2
(20, 120) (12, 70) 4.6 287 3
(20, 140) (12, 95) 4.6 261 2.9
NSGA-Ⅲ (20, 100) (20, 100) 5.1 598 4.6
(20, 120) (20, 120) 5.2 378 4.3
(20, 140) (20, 140) 5.4 449 4.5
FGA (20, 100) (20, 90) 8.7 673 4.2
(20, 120) (20, 105) 9.1 682 4.2
(20, 140) (20, 115) 11.5 594 3.9
AMOSA (20, 100) (20, 100) 29.8 482 4.1
(20, 120) (20, 120) 30.5 507 4.3
(20, 140) (20, 140) 30.3 413 4.4
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Algorithm Groups Groups in service composition Running time Haul ditance Carbon emission
CPA (20, 100) (11, 50) 3.8 304 3.2
(20, 120) (12, 70) 4.6 287 3
(20, 140) (12, 95) 4.6 261 2.9
NSGA-Ⅲ (20, 100) (20, 100) 5.1 598 4.6
(20, 120) (20, 120) 5.2 378 4.3
(20, 140) (20, 140) 5.4 449 4.5
FGA (20, 100) (20, 90) 8.7 673 4.2
(20, 120) (20, 105) 9.1 682 4.2
(20, 140) (20, 115) 11.5 594 3.9
AMOSA (20, 100) (20, 100) 29.8 482 4.1
(20, 120) (20, 120) 30.5 507 4.3
(20, 140) (20, 140) 30.3 413 4.4
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