Multi-objective reconfigurable production line scheduling for smart home appliances

doi:10.23919/JSEE.2021.000026

Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (2): 297-317.doi: 10.23919/JSEE.2021.000026

• INTELLIGENT OPTIMIZATION AND SCHEDULING • Previous Articles Next Articles

Multi-objective reconfigurable production line scheduling for smart home appliances

Shiyun LI(), Sheng ZHONG(), Zhi PEI*(), Wenchao YI(), Yong CHEN(), Cheng WANG(), Wenzhu ZHANG()

¹ College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, China

Received:2020-10-28 Online:2021-04-29 Published:2021-04-29
Contact: Zhi PEI E-mail:lishiyun@zjut.edu.cn;zsheng2811@qq.com;peizhi@zjut.edu.cn;yiwenchao@zjut.edu.cn;cy@zjut.edu.cn;cwang@zjut.edu.cn;wzzhang@zjut.edu.cn
About author:|LI Shiyun was born in 1978. He received his B.E. degree in mechanical manufacturing and automation from Beijing Institute of Technology, China, in 2001, and his Ph.D. degree in management information technology in digital design and manufacture from Beijing Institute of Technology, China, in 2006. He is currently working as a lecturer at the College of Mechanical Engineering, Zhejiang University of Technology, China. His research interests include mathematical modeling and optimization as well as their applications in design and manufacturing management. E-mail: lishiyun@zjut.edu.cn||ZHONG Sheng was born in 1995. He is currently working toward his master degree in the College of Mechanical Engineering, Zhejiang University of Technology. His research interests are intelligent algorithm design and application. E-mail: zsheng2811@qq.com||PEI Zhi was born in 1982. He received his B.S. and Ph.D. degrees in industrial engineering from Tsinghua University, Beijing, China, in 2005 and 2011, respectively. He was a visiting professor with North Carolina State University, Raleigh, USA, in 2015. He is currently an associate professor with the College of Mechanical Engineering, Zhejiang University of Technology, China. His current research interests include manufacturing system modeling, machine scheduling, nonlinear optimization, and queuing theory. E-mail: peizhi@zjut.edu.cn||YI Wenchao was born in 1989. She received her B.S. and Ph.D. degrees in industrial engineering from Huazhong University of Science and Technology, China, in 2011 and 2016, respectively. She is currently an associate professor with the College of Mechanical Engineering, Zhejiang University of Technology, China. Her current research interests include evolutionary algorithms and scheduling. E-mail: yiwenchao@zjut.edu.cn||CHEN Yong was born in 1973. He received his B.S., M.S. and Ph.D. degrees in mechanical engineering from Zhejiang University, in 1995, 1997 and 2000 respectively. Since 2009, he has been a professor with the College of Mechanical Engineering, Zhejiang University of Technology. He is the author of more than 50 academic arti-cles and holds five patents and 40 software copyrights. His research interests include intelligent system planning and intelligent algorithms. E-mail: cy@zjut.edu.cn||WANG Cheng was born in 1982. He received his B.S. degree in industrial engineering from Zhejiang University of Technology in 2005 and Ph.D. degree in systems engineering from Tianjin University, China in 2010. Since 2016, he has been an associate professor with the College of Mechanical Engineering, Zhejiang University of Technology. His research interests include data driven decision making, complex systems, game theory and mechanism design. E-mail: cwang@zjut.edu.cn||ZHANG Wenzhu was born in 1990. She received her B.S. degree in management science and engineering from Huazhong University of Science and Technology in 2013, and Ph.D. degree in management science and engineering from Fudan University in 2020. She was a visiting scholar with Washington University in Saint Louis, USA, in 2016. She is currently an assistant professor with the College of Mechanical Engineering, Zhejiang University of Technology, China. Her current research interests include game theory, operations management, and optimization. E-mail: wzzhang@zjut.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (71871203; 52005447; L1924063), and Zhejiang Provincial Natural Science Foundation of China (LY18G010017; LQ21E050014);This work was supported by the National Natural Science Foundation of China (71871203; 52005447; L1924063), and Zhejiang Provincial Natural Science Foundation of China (LY18G010017; LQ21E050014)

Abstract

Abstract:

In a typical discrete manufacturing process, a new type of reconfigurable production line is introduced, which aims to help small- and mid-size enterprises to improve machine utilization and reduce production cost. In order to effectively handle the production scheduling problem for the manufacturing system, an improved multi-objective particle swarm optimization algorithm based on Brownian motion (MOPSO-BM) is proposed. Since the existing MOPSO algorithms are easily stuck in the lo-cal optimum, the global search ability of the proposed method is enhanced based on the random motion mechanism of the BM. To further strengthen the global search capacity, a strategy of fitting the inertia weight with the piecewise Gaussian cumulative distribution function (GCDF) is included, which helps to maintain an excellent convergence rate of the algorithm. Based on the commonly used indicators generational distance (GD) and hypervolume (HV), we compare the MOPSO-BM with several other latest algorithms on the benchmark functions, and it shows a better overall performance. Furthermore, for a real reconfigurable production line of smart home appliances, three algorithms, namely non-dominated sorting genetic algorithm-II (NSGA-II), decomposition-based MOPSO (dMOPSO) and MOPSO-BM, are applied to tackle the scheduling problem. It is demonstrated that MOPSO-BM outperforms the others in terms of convergence rate and quality of solutions.

Key words: reconfigurable production line, improved particle swarm optimization (PSO), multi-objective optimization, flexible flowshop scheduling, smart home appliances

Shiyun LI, Sheng ZHONG, Zhi PEI, Wenchao YI, Yong CHEN, Cheng WANG, Wenzhu ZHANG. Multi-objective reconfigurable production line scheduling for smart home appliances[J]. Journal of Systems Engineering and Electronics, 2021, 32(2): 297-317.

Figures/Tables 32

Table 1

Closely related literature on the reconfigurable production line scheduling"

Study	Multi- objective	Flexible production line	Recon- figurable	Flow shop	Methodology	Application in industry
KUO et al. 1999 [2]		√			Colored timed petri net+balanced budget work standard algorithm+dispatch rules	Hybrid assembly line in automotive industry
Guo et al. 2006 [3]	√	√			Bi-level GA	Multi- and mixed-model in an apparel assembly
Huang et al. 2009 [4]	√	√		√	ACO+parameter tuning	—
Davoudpour et al. 2009 [5]	√	√		√	Greedy randomized adaptive search procedure+a non-regular optimization criterion	Hybrid line with sequence-dependent setup times
Dudas et al. 2011 [6]	√	√		√	Simulation-based innovization	Automotive machining line
Liu et al. 2011 [7]		√		√	Improved PSO	—
Chaube et al. 2012 [8]	√		√		NSGA-II+Reconfigurable process plan	—
Dai et al. 2013 [9]	√	√		√	GA+simulated annealing algorithm (SA)	Metalworking workshop
Jolai et al. 2013 [10]	√	√		√	SA+ normalized weighted multi-objective decision making (MODM)	—
Sheikh et al. 2013 [11]	√	√		√	GA+ linear programming	—
Tran et al. 2013 [12]	√	√		√	Hybrid water flow algorithm+landscape analysis+optimal Pareto solution set	—
Naderi et al. 2014 [13]				√	Hybrid PSO	—
Ghaleb et al. 2015 [14]		√		√	PSO+Tabu search	—
Choi et al. 2015 [15]	√		√		Dispatching rule based algorithm	Production line in motorcycle field
Dou et al. 2016 [16]	√		√	√	NSGA-II+ mixed integer programming	Parts processing simulation for production line
Zhao et al. 2017 [17]	√		√		Object oriented timed colored petri net (OOTCPN)-GASA	Wood manufacturing system
Asghar et al. 2018 [18]	√		√		GA	Part family production line
Gong et al. 2020 [19]	√	√		√	Hybrid evolutionary algorithm (HEA)+variable neighborhood search	Energy-efficient line with worker flexibility
Han et al. 2020 [20]	√			√	Heuristic+self-adaptive evolution operators	—
Hasani et al. 2020 [21]	√	√		√	NSGA-II+overall nondominated vector generation (ONVG)	—
This work	√	√	√	√	MOPSO based on Brownian motion (MOPSO-BM)	Smart home appliance manufacturing

Table 1

Fig.1

Fig.2

Fig.3

Table 2

Fig.4

Fig.5

Table 3

Multi-objective benchmark function-ZDT series"

Function name	Objective function	Variable bound	D	Property of the Pareto front
ZDT1	$\left\{ {\begin{array}{*{20}{l}} {{f_1}(x) = {x_1}} \\ {{f_2}(x) = g(x)\left[ {1 - \sqrt {{{{x_1}} / {g(x)}}} } \right]} \\ g(x) = 1 + \dfrac{{9\left( {\displaystyle\sum\limits_{i = 2}^D {{x_i}} } \right)}}{{D - 1}} \end{array} } \right.$	${x_i} \in [0,1]$	30	Convex
ZDT2	$\left\{ {\begin{array}{*{20}{l}} {{f_1}(x) = {x_1}} \\ {{f_2}(x) = g(x)\left[ {1 - {{\left( {{{{x_1}} /{g(x)}}} \right)}^2}} \right]} \\ g(x) = 1 + \dfrac{{9\left( {\displaystyle\sum\limits_{i = 2}^D {{x_i}} } \right)}}{{D - 1}} \end{array} } \right.$	${x_i} \in [0,1]$	30	Nonconvex
ZDT3	$\left\{ {\begin{array}{*{20}{l}} {{f_1}(x) = {x_1}} \\ {{f_2}(x) = g(x)\left[ {1 - \sqrt {{{{x_1}} / {g(x)}}} - {{{x_1}\sin (10{\rm{{\text{π}}}} {x_1})} / {g(x)}}} \right]} \\ {g(x) = 1 + \dfrac{{9\left( {\displaystyle\sum\limits_{i = 2}^D {{x_i}} } \right)}}{{D - 1}}} \end{array} } \right.$	${x_i} \in [0,1]$	30	Convex disconnect
ZDT4	$\left\{ {\begin{array}{*{20}{l}} {{f_1}(x) = {x_1}} \\ {{f_2}(x) = g(x)\left[ {1 - \sqrt {{{{x_1}} / {g(x)}}} } \right]} \\ {g(x) = 1 + 10\left( {D - 1} \right) + \displaystyle\sum\limits_{i = 2}^n {\left[ {{x_i}^2 - 10\cos (4{\rm{{\text{π}}}} {x_i})} \right]} } \end{array} } \right.$	$\begin{array}{l} {x_i} \in [0,1] \\ {x_i} \in [ - 5,5]\; \\ i = 2, \cdot \cdot \cdot ,D \end{array}$	10	Nonconvex
ZDT6	$\left\{ {\begin{array}{*{20}{l} } { {f_1}(x) = 1 - { {\rm{e} }^{ - 4{x_1} } }{ {\sin }^6}(6{\rm{ {\text{π} } } } {x_1})} \\ { {f_2}(x) = g(x)\left[ {1 - { {\left( { { { {f_1}(x)} / {g(x)} } } \right)}^2} } \right]} \\ {g(x) = 1 + {9\;{ {\left[ \begin{array}{l}\\[-5pt]\dfrac{ {\left( {\displaystyle\sum\limits_{i = 2}^D { {x_i} } } \right)} }{ {D - 1} }\end{array} \right]}^{0.25} } } } \end{array} } \right.$	${x_i} \in [0,1]$	10	Nonconvex

Table 3

Table 4

Fig.6

Fig.7

Fig.8

Fig.9

Table 5

Table 6

Fig.10

Fig.11

Fig.12

Fig.13

Table 7

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Table 8

Table 9

Table 10

Table 11

Table 12

Table 13

Fig.19

References 58

1	BAI D Y, XUE H Y, et al Effective algorithms for single-machine learning-effect scheduling to minimize completion-time-based criteria with release dates. Expert Systems with Applications, 2020, 156, 113445. doi: 10.1016/j.eswa.2020.113445
2	KUO C H, HUANG H P, WEI K C System modeling and real-time simulator for highly model-mixed assembly systems. Journal of Manufacturing Science and Engineering—Transactions of the ASME, 1999, 121 (2): 282- 289. doi: 10.1115/1.2831217
3	GUO Z X, WONG W K, LEUNG S Y S, et al A bi-level genetic algorithm for multi-objective scheduling of multi- and mixed-model apparel assembly lines. Multimedia Modeling, 2006, 4304, 934- 941.
4	HUANG R H, YANG C L Solving a multi-objective overlapping flow-shop scheduling. International Journal of Advanced Manufacturing Technology, 2009, 42 (9): 955- 962. doi: 10.1007/s00170-008-1652-9
5	DAVOUDPOUR H, ASHRAFI M Solving multi-objective SDST flexible flow shop using GRASP algorithm. International Journal of Advanced Manufacturing Technology, 2009, 44 (7): 737- 747.
6	DUDAS C, FRANTZEN M, NG A H C A synergy of multi-objective optimization and data mining for the analysis of a flexible flow shop. Robotics and Computer-Integrated Manufacturing, 2011, 27 (4): 687- 695. doi: 10.1016/j.rcim.2010.12.005
7	LIU Q M, DONG M Improved particle swarm optimization algorithm application of the variable batch flow-shop problem. Advanced Science Letters, 2011, 4 (6/7): 2369- 2373.
8	CHAUBE A, BENYOUCEF L, TIWARI M K An adapted NSGA-2 algorithm based dynamic process plan generation for a reconfigurable manufacturing system. Journal of Intelligent Manufacturing, 2012, 23 (4): 1141- 1155. doi: 10.1007/s10845-010-0453-9
9	DAI M, TANG D B, GIRET A, et al Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm. Robotics and Computer-Integrated Manufacturing, 2013, 29 (5): 418- 429. doi: 10.1016/j.rcim.2013.04.001
10	JOLAI F, ASEFI H, RABIEE M, et al Bi-objective simulated annealing approaches for no-wait two-stage flexible flow shop scheduling problem. Scientia Iranica, 2013, 20 (3): 861- 872.
11	SHEIKH S Multi-objective flexible flow lines with due window, time lag, and job rejection. International Journal of Advanced Manufacturing Technology, 2013, 64 (9−12): 1423- 1433. doi: 10.1007/s00170-012-4112-5
12	TRAN T H, NG K M A hybrid water flow algorithm for multi-objective flexible flow shop scheduling problems. Engineering Optimization, 2013, 45 (4): 483- 502. doi: 10.1080/0305215X.2012.685072
13	NADERI B, GOHARI S, YAZDANI M Hybrid flexible flowshop problems: models and solution methods. Applied Mathematical Modelling, 2014, 38 (24): 5767- 5780. doi: 10.1016/j.apm.2014.04.012
14	GHALEB M A, SURYAHATMAJA U S, ALHARKAN I M Metaheuristics for two-stage no-wait flexible flow shop scheduling problem. Proc. of the International Conference on Industrial Engineering and Operations Management, 2015, 1- 9. doi: 10.1109/IEOM.2015.7093943
15	CHOI Y C Dispatching rule-based scheduling algorithms in a single machine with sequence-dependent setup times and energy requirements. Procedia CIRP, 2016, 41, 135- 140. doi: 10.1016/j.procir.2015.12.109
16	DOU J P, LI J, SU C Bi-objective optimization of integrating configuration generation and scheduling for reconfigurable flow lines using NSGA-II. International Journal of Advanced Manufacturing Technology, 2016, 86 (5−8): 1945- 1962. doi: 10.1007/s00170-015-8291-8
17	ZHAO Y R, FENG X Y, SHI L P, et al. The study on reconfigurable algorithm of the wood flexible manufacturing system based on OOTCPN-GASA. Proc. of the 2nd International Conference on Control and Robotics Engineering, 2017. DOI: 10.1109/ICCRE.2017.7935044.
18	ASGHAR E, ZAMAN U K U, BAQAI A A, et al Optimum machine capabilities for reconfigurable manufacturing systems. International Journal of Advanced Manufacturing Technology, 2018, 95 (9−12): 4397- 4417. doi: 10.1007/s00170-017-1560-y
19	GONG G L, CHIONG R, DENG Q W, et al Energy-efficient flexible flow shop scheduling with worker flexibility. Expert Systems with Applications, 2020, 141, 112902. doi: 10.1016/j.eswa.2019.112902
20	HAN Y Y, LI J Q, SANG H Y, et al Discrete evolutionary multi-objective optimization for energy-efficient blocking flow shop scheduling with setup time. Applied Soft Computing, 2020, 93, 106343. doi: 10.1016/j.asoc.2020.106343
21	HASANI A, HOSSEINI S M H A bi-objective flexible flow shop scheduling problem with machine-dependent processing stages: trade-off between production costs and energy consumption. Applied Mathematics and Computation, 2020, 386, 125533. doi: 10.1016/j.amc.2020.125533
22	BOYSEN N, FLIEDNER M, SCHOLL A Sequencing mixed-model assembly lines: survey, classification and model critique. European Journal of Operational Research, 2009, 192 (2): 349- 373. doi: 10.1016/j.ejor.2007.09.013
23	MOORE J, CHAPMAN R. Application of particle swarm to multi-objective optimization. Auburn, Alabama: Auburn University, 1999.
24	GUAN T H, HAN F, HAN H A modified multi-objective particle swarm optimization based on Levy flight and double-archive mechanism. IEEE Access, 2019, 7, 183444- 183467. doi: 10.1109/ACCESS.2019.2960472
25	KENNEDY J, EBERHART R Particle swarm optimization. Proc. of the IEEE International Conference on Neural Networks, 1995, 4, 1942- 1948. doi: 10.1109/ICNN.1995.488968
26	COELHO L D S, AYALA V H, ALOTTO P A multi-objective Gaussian particle swarm approach applied to electromagnetic optimization. IEEE Trans. on Magnetics, 2010, 46 (8): 3289- 3292. doi: 10.1109/TMAG.2010.2047250
27	AL-DUWAISH H N Identification of Hammerstein models with known nonlinearity structure using particle swarm optimization. Arabian Journal for Science and Engineering, 2006, 36 (7): 1269- 1276. doi: 10.1007%2Fs13369-011-0120-2
28	JIANG S H, WANG Y, JI Z C A new design method for adaptive IIR system identification using hybrid particle swarm optimization and gravitational search algorithm. Nonlinear Dynamics, 2015, 79 (4): 2553- 2576. doi: 10.1007/s11071-014-1832-0
29	ZHAO J, SUN J, LAI C H, et al An improved quantum-behaved particle swarm optimization for multi-peak optimization problem. International Journal of Computer Mathematics, 2011, 88 (3): 517- 532. doi: 10.1080/00207160903521501
30	COELLO C A C, PULIDO G T, LECHUGA M S Handling multiple objectives with particle swarm optimization. IEEE Trans. on Evolutionary Computation, 2004, 8 (3): 256- 279. doi: 10.1109/TEVC.2004.826067
31	YANG J M, MU X W, CHE H J, et al. Improved multi-objective particle swarm optimization algorithm based on multiple strategies. Control and Decision, 2017, 32(3): 435–42. (in Chinese)
32	KIAN S L, BUYAMIN S, AHMAD A, et al An improved leader guidance in multi-objective particle swarm optimization. Proc. of the 6th Asia Modelling Symposium, 2012, 34- 39.
33	FAN J S An improving multi-objective particle swarm optimization. Web Information Systems and Mining, 2010, 6318, 1- 6.
34	ZHOU A M, QU B Y, LI H, et al Multi-objective evolutionary algorithms: a survey of the state of the art. Swarm and Evolutionary Computation, 2011, 1 (1): 32- 49. doi: 10.1016/j.swevo.2011.03.001
35	ZEINALZADEH A, MOHAMMADI Y, MORADI M H Optimal multi-objective placement and sizing of multiple DGs and shunt capacitor banks simultaneously considering load uncertainty via MOPSO approach. International Journal of Electrical Power & Energy Systems, 2015, 67, 336- 349.
36	TAVANA M, LI Z J, MOBIN M, et al Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS. Expert Systems with Applications, 2016, 50, 17- 39. doi: 10.1016/j.eswa.2015.11.007
37	SUN Y, GAO Y L. A multi-objective particle swarm optimization algorithm based on Gaussian mutation and an improved learning strategy. Mathematics, 2019. DOI: 10.3390/math7020148.
38	LEE C H, LEE Y C Nonlinear systems design by a novel fuzzy neural system via hybridization of electromagnetism-like mechanism and particle swarm optimisation algorithms. Information Sciences, 2012, 186, 59- 72. doi: 10.1016/j.ins.2011.09.036
39	HIGASHI N, IBA H Particle swarm optimization with Gaussian mutation. Proc. of the IEEE Swarm Intelligence Symposium, 2003, 72- 79.
40	HAN Z H, ZHANG Q An improved compact genetic algorithm for scheduling problems in a flexible flow shop with a multi-queue buffer. Processes, 2019, 7 (5): 302. doi: 10.3390/pr7050302
41	ABDECHIRI M, MEYBODI M R, BAHRAMI H Gases Brownian motion optimization: an algorithm for optimization (GBMO). Applied Soft Computing, 2013, 13 (5): 2932- 2946. doi: 10.1016/j.asoc.2012.03.068
42	ACI C I, GULCAN H A modified dragonfly optimization algorithm for single- and multiobjective problems using Brownian motion. Computational Intelligence and Neuroscience, 2019, 2019 (2): 1- 17.
43	HIDA T. Brownian motion. New York: Springer, 1980.
44	LIU J J, WU C Z, CAO J, et al A binary differential search algorithm for the 0-1 multidimensional knapsack problem. Applied Mathematical Modelling, 2016, 40 (23/24): 9788- 9805.
45	HAN L, ROMERO C E, YAO Z Economic dispatch optimization algorithm based on particle diffusion. Energy Conversion and Management, 2015, 105, 1251- 1260. doi: 10.1016/j.enconman.2015.08.071
46	ZITZLER E, DEB K, THIELE L Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation, 2000, 8 (2): 173- 195. doi: 10.1162/106365600568202
47	KACEM I, HAMMADI S, BORNE P Approach by localization and multi-objective evolutionary optimization for flexible job-shop scheduling problems. IEEE Trans. on Systems, Man, and Cybernetics—Part C, 2002, 32 (1): 1- 13. doi: 10.1109/TSMCC.2002.1009117
48	KACEM I, HAMMADI S, BORNE P Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic. Mathematics and Computers in Simulation, 2002, 60 (3−5): 245- 276. doi: 10.1016/S0378-4754(02)00019-8
49	XIA W J, WU Z M An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problem. Computers & Industrial Engineering, 2005, 48 (2): 409- 425.
50	VELDHUIZEN D A V, LAMONT G B. Evolutionary computation and convergence to a Pareto front. Late Breaking Papers at the Genetic Programming Conference, 1998: 221−228.
51	VELDHUIZEN D A V, LAMONT G B Multi-objective evolutionary algorithm test suites. Proc. of the ACM symposium on Applied Computing, 1999, 351- 357.
52	DEB K, PRATAP A, AGARWAL S A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation, 2002, 6 (2): 182- 197. doi: 10.1109/4235.996017
53	ZHANG Q F, LI H MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. on Evolutionary Computation, 2007, 11 (6): 712- 731. doi: 10.1109/TEVC.2007.892759
54	NEBRO A J, DURILLO J J, GARCIA-NIETO J, et al SMPSO: a new PSO-based metaheuristic for multi-objective optimization. Proc. of the IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making, 2009, 66- 73.
55	MARTINEZ S Z, COELLO C A C A multi-objective particle swarm optimizer based on decomposition. Proc. of the 13th Annual Genetic and Evolutionary Computation Conference, 2011, 69- 76.
56	TIAN Y, CHENG R, ZAHNG X Y, et al PlatEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Computational Intelligence Magazine, 2017, 12 (4): 73- 87. doi: 10.1109/MCI.2017.2742868
57	ZHANG H P, GEN M Multistage-based genetic algorithm for flexible job-shop scheduling problem. Journal of Complexity International, 2005, 11, 223- 232.
58	GAO J, SUN L Y, GEN M S A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems. Computers & Operations Research, 2008, 35 (9): 2892- 2907.

Symbol	Description
i	The ith product in N products, i = 1,2,···, N
j	The jth part in the $J $ parts of the product, j = 1,2,···, J
k	The kth step in the K processes, k = 1,2,···, K
r	The rth machine in the M machines, r = 1,2,···, M
T_ijkr	The processing time of the process k of the part j of the product i on the machine r
S_ijkr	The start time of the process k of the part j of the product i on the machine r
E_ijkr	The end time of the process k of the part j of the product i on the machine r
l_i	The order quantity of product i
W_h	The collection of each order quantity
cm	Machine operating cost per unit time
gm	Inventory cost per unit time
bm	The cost of efficiency loss per unit time
δ	The cost adjustment coefficient of efficiency loss per unit time
d_ij	The inventory time of the part j of the product i

Algorithm	Parameter
MOPSO-BM	$\begin{array}{l} {c_1} = {c_2} = 1.5,\;a = 0.4,\;b = 1,\;\\ {\mu _1} = 0.2,\;{\mu _2} = 0.8,\;{\omega _{\max}} = 0.9,\;\\ \eta {\rm{ = 0}}{\rm{.5,\;}}{\omega _{\min}} = 0.1,\;{\sigma _1}{\rm{ = }}{\sigma _2}{\rm{ = }}0.11,\;\\ {\rm rep}A{\rm size}=100,\;{\rm rep}B{\rm size}=30 \end{array}$
MOPSO-LFDA	$\omega \in \left[ {0.1,\;0.5} \right],\;T \in \left[ {5,\;30} \right],\;{\rm rep}A{\rm size}=100,\;{\rm rep}B {\rm size}=30,\;\theta ={\rm{5}}$
NSGA-Ⅱ	${\rm pro}C = {\rm pro}M = 1,\;{\rm dis}C = {\rm dis}M = 20$
MOEA/D	${\rm pro}C = {\rm pro}M = 1,\;{\rm dis}C = {\rm dis}M = 20$
SMPSO	$\omega =0.4,\;c_1 = c_2 = 1.5,\;pm = 1/n$
dMOPSO	$\omega =0.4,\;Ta = 2$

Function		MOPSO-BM	MOPSO-LFDA	NSGA-Ⅱ	MOEA/D	SMPSO	dMOPSO
ZDT1	Mean	1.74E-05	6.15E-05	1.58E-04	5.85E-04	9.72E-05	2.76E-03
ZDT1	Standard	1.23E-05	4.02E-05	3.55E-05	1.83E-04	2.40E-05	7.11E-04
ZDT2	Mean	5.88E-06	4.95E-05	1.44E-04	1.34E-03	8.00E-05	3.90E-03
ZDT2	Standard	2.47E-06	2.76E-05	3.55E-05	6.51E-04	2.53E-05	2.09E-03
ZDT3	Mean	3.35E-05	4.35E-05	7.61E-05	2.78E-03	1.05E-04	2.90E-03
ZDT3	Standard	3.97E-06	1.34E-05	1.91E-05	2.97E-03	3.67E-05	9.57E-04
ZDT4	Mean	6.69E-05	1.42E-04	2.10E-04	1.66E-03	5.48E-01	6.36E-04
ZDT4	Standard	2.01E-05	5.47E-05	9.73E-05	4.98E-04	4.10E-01	3.10E-04
ZDT6	Mean	2.41E-02	7.70E-02	4.16E-05	8.46E-04	9.97E-03	3.57E-04
ZDT6	Standard	2.23E-02	4.04E-02	2.84E-05	2.86E-04	2.45E-02	9.35E-04

Function		MOPSO-BM	MOPSO-LFDA	NSGA-Ⅱ	MOEA/D	SMPSO	dMOPSO
ZDT1	Mean	7.21E-01	7.21E-01	7.19E-01	7.11E-01	7.19E-01	6.89E-01
ZDT1	Standard	4.51E-05	7.26E-05	2.09E-04	6.90E-03	3.12E-04	7.88E-03
ZDT2	Mean	4.45E-01	4.45E-01	4.44E-01	4.14E-01	4.44E-01	3.90E-01
ZDT2	Standard	3.15E-05	6.39E-05	1.62E-04	3.47E-02	3.20E-04	5.99E-02
ZDT3	Mean	6.07E-01	5.83E-01	6.05E-01	6.04E-01	6.01E-01	6.05E-01
ZDT3	Standard	7.20E-05	1.52E-04	2.25E-02	3.51E-02	4.05E-03	1.10E-02
ZDT4	Mean	7.21E-01	7.21E-01	7.17E-01	6.98E-01	1.29E-02	7.13E-01
ZDT4	Standard	1.49E-04	1.52E-04	1.26E-03	7.99E-03	4.59E-02	3.61E-03
ZDT6	Mean	3.90E-01	3.89E-01	3.88E-01	3.81E-01	3.88E-01	3.87E-01
ZDT6	Standard	2.57E-04	7.67E-05	3.19E-04	2.48E-03	2.09E-04	4.98E-03

Job	Process	Processing information	Job	Process	Processing information
J1	O1,1	SK539-lower cover	J19	O19,1	Laser lettering lower cover
J2	O2,1	SK539-upper cover		O19,2	Insert L pole
J3	O3,1	SK504-lower cover		O19,3	Insert N pole
J4	O4,1	SK504-upper cover		O19,4	Install PCB
J5	O5,1	SK517-lower cover		O19,5	Welding L, N pole
J6	O6,1	SK517-upper cover		O19,6	Insert clip
J7	O7,1	Button		O19,7	Welding clip
J8	O8,1	SK539-L pole		O19,8	Test continuity
J9	O9,1	SK539-N pole		O19,9	Attach the cover
J10	O10,1	SK504-L pole		O19,10	Lock screw
J11	O11,1	SK504-N pole		O19,11	Test function
J12	O12,1	SK517-L pole	J20	O20,1	Laser lettering lower cover
J13	O13,1	SK517-N pole		O20,2	Welding WIFI module
J14	O14,1	Clip		O20,3	Insert L pole
J15	O15,1	SK539-PCB		O20,4	Insert N pole
J16	O16,1	SK504-PCB		O20,5	Install PCB
J17	O17,1	SK517-PCB		O20,6	Welding L, N pole
J18	O18,1	Laser lettering lower cover		O20,7	Insert clip
	O18,2	Insert L pole		O20,8	Welding clip
	O18,3	Insert N pole		O20,9	Test continuity
	O18,4	Install PCB		O20,10	Attach the upper cover
	O18,5	Welding L, N pole		O20,11	Lock screw
	O18,6	Insert clip		O20,12	Test function
	O18,7	Welding clip		Final Assembly	Counting and packing (Beyond the scope of this paper)
	O18,8	Test continuity
	O18,9	Attach the upper cover
	O18,10	Ultrasonic welding
	O18,11	Test function

Multi-objective reconfigurable production line scheduling for smart home appliances

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 32

References 58

Related Articles 11

Recommended Articles

Metrics

Comments

Problem (n×m)	Objective	AL+CGA		PSO+SA		moGA	hGA	MOPSO-BM
Problem (n×m)	Objective	AL+CGA		PSO+SA		moGA	hGA	Result	Pop size
8×8	f₁	15	16	15	16	15	14	15	300
	f₂			12	13	14	12	12
	f₃	79	75	75	73	73	77	75
10×10	f₁	7		7		7	7	7	300
	f₂	5		6		5	5	5
	f₃	45		44		43	43	43
15×10	f₁	24		12			11	11	300
	f₂	11		11			11	11
	f₃	91		91			91	91

Machine number	Type of equipment
M1, M2	Injection molding machine
M3, M4	Stamping machine
M5, M6	SMT placement machine
M7	Laser engraving machine
M8?M24	Six-axis industrial robot

Machine number	Process number	J18	J19	J20
M7	1	7	8	6
M8	2	9	9	10
M9	2	10	7	11
M10	3	11	14	12
M11	3	12	15	9
M12	4	9	11	10
M13	4	10	8	11
M14	5	11	10	9
M15	5	8	12	8
M16	6	3	4	4
M17	7	9	8	10
M18	7	7	11	8
M19	8	5	6	7
M20	9	12	11	12
M21	9	9	10	14
M22	10	7	8	5
M23	11	6	7	6
M24	12	X	X	6

Algorithm	Parameter	Setting
MOPSO-BM	$\begin{array}{l} {c_1} = {c_2} = 1.5,\;a = 0.4,\;b = 1,\;{\mu _1} = 0.2,\; \\\;\;\;\;\;\;{\mu _2} = 0.8,\;{\omega _{\rm max} } = 0.9,\;\eta {\rm{ = 0} }{\rm{.5,\;} } \\\;\;\;\;\;\;\;\;\;{\omega _{\rm min} } = 0.1,\;{\sigma _1}{\rm{ = } }{\sigma _2}{\rm{ = } }0.11,\; \\\;\;\;\;\;\;{\rm rep}A{\rm size}=100,\;{\rm rep}B{\rm size}=30 \end{array}$	$\begin{array}{l} \;\;\;\;\;\;\;\;n{\rm Pop}:100,\;{\rm{MaxIt} }:1 \;000,\;\\\;\;\;\;cm = 10,\;gm = 2.0,\;bm = 1.0,\;\\\;\;\;\;\;\;\;\;\;\;\;\;{ {{W} }_h} = [6,\;5,\;10,\;6,\;15],\;\\ { {{D} }_h} = [640,\;{\rm{ 5} }50,\;1\;050,\;640,\;1\;650] \end{array}$
NSGA-Ⅱ	${\rm pro}C = {\rm pro}M = 1,\;{\rm dis}C = {\rm dis}M = 20$
dMOPSO	$\omega =0.4,\;Ta = 2$

[1]	Jiaxin HU, Leping YANG, Huan HUANG, Yanwei ZHU. Optimal reconfiguration of constellation using adaptive innovation driven multiobjective evolutionary algorithm [J]. Journal of Systems Engineering and Electronics, 2021, 32(6): 1527-1538.
[2]	Zining WANG, Min LIN, Xiaogang TANG, Kefeng GUO, Shuo HUANG, Ming CHENG. Multi-objective robust secure beamforming for cognitive satellite and UAV networks [J]. Journal of Systems Engineering and Electronics, 2021, 32(4): 789-798.
[3]	Jianjiang WANG, Xuejun HU, Chuan HE. Reactive scheduling of multiple EOSs under cloud uncertainties: model and algorithms [J]. Journal of Systems Engineering and Electronics, 2021, 32(1): 163-177.
[4]	Zhen XU, Enze ZHANG, Qingwei CHEN. Rotary unmanned aerial vehicles path planning in rough terrain based on multi-objective particle swarm optimization [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 130-141.
[5]	Yan'gang LIANG, Zheng QIN. A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making [J]. Journal of Systems Engineering and Electronics, 2019, 30(3): 535-544.
[6]	Jiale GAO, Qinghua XING, Chengli FAN, Zhibing LIANG. Double adaptive selection strategy for MOEA/D [J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 132-143.
[7]	Jiting Li, Sheng Zhang, Xiaolu Liu, and Renjie He. Multi-objective evolutionary optimization for geostationary orbit satellite mission planning [J]. Systems Engineering and Electronics, 2017, 28(5): 934-945.
[8]	Ying Zhang, Rennong Yang, Jialiang Zuo, and Xiaoning Jing. Enhancing MOEA/D with uniform population initialization, weight vector design and adjustment using uniform design [J]. Journal of Systems Engineering and Electronics, 2015, 26(5): 1010-1022.
[9]	Haipeng Ren* and Yang Zhao. Immune particle swarm optimization of linear frequency modulation in acoustic communication [J]. Systems Engineering and Electronics, 2015, 26(3): 450-456.
[10]	Lixia Han, Shujuan Jiang, and Shaojiang Lan. Novel electromagnetism-like mechanism method for multiobjective optimization problems [J]. Journal of Systems Engineering and Electronics, 2015, 26(1): 182-.
[11]	Wei Jingxuan & Wang Yuping. Multi-objective fuzzy particle swarm optimization based on elite archiving and its convergence [J]. Journal of Systems Engineering and Electronics, 2008, 19(5): 1035-1040.

Objective function	NSGA-Ⅱ	dMOPSO	MOPSO-BM
f₁	391	379	378
f₂	174 112	168 819	168 378
f₃	103	104	103
f₄	42	42	42