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November  2020, 16(6): 2943-2969. doi: 10.3934/jimo.2019088

An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility

Xuewen Huang 1, , Xiaotong Zhang 1, , Sardar M. N. Islam 2,, and  Carlos A. Vega-Mejía 2,3,

1. 

Faculty of Management and Economics, Dalian University of Technology, Dalian, Liaoning 116023, China
2. 

ISILC, Victoria University, Melbourne, Australia
3. 

Operations & Supply Chain Management Research Group, Universidad de La Sabana, Bogotá, Colombia

* Corresponding author: Sardar M. N. Islam

Received  November 2017 Revised  March 2019 Published  July 2019

Fund Project: Xuewen Huang is supported by the National Science and Technology Plan of China under Grant No. 2015BAF09B01 and the China Scholarship under Grant No. 201606060170

This paper considers the Flexible Job-shop Scheduling Problem with Operation and Processing flexibility (FJSP-OP) with the objective of minimizing the makespan. A Genetic Algorithm based approach is presented to solve the FJSP-OP. For the performance improvement, a new and concise Four-Tuple Scheme (FTS) is proposed for modeling a job with operation and processing flexibility. Then, with the FTS, an enhanced Genetic Algorithm employing a more efficient encoding strategy is developed. The use of this encoding strategy ensures that the classic genetic operators can be adopted to the utmost extent without generating infeasible offspring. Experiments have validated the proposed approach, and the results have shown the effectiveness and high performance of the proposed approach.

Keywords: IPPS, flexible job-shop scheduling, operation flexibility, processing flexibility, Genetic Algorithm.
Mathematics Subject Classification: Primary: 90B35, 90C59; Secondary: 68M20.
Citation: Xuewen Huang, Xiaotong Zhang, Sardar M. N. Islam, Carlos A. Vega-Mejía. An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2943-2969. doi: 10.3934/jimo.2019088
References:
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show all references

References:
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I. A. Chaudhry and M. Usman, Integrated process planning and scheduling using genetic algorithms, Tehnicki Vjesnik, 24 (2017), 1401-1409.  doi: 10.17559/TV-20151121212910.  Google Scholar

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[13]

G. Chryssolouris, S. Chan and W. Cobb, Decision making on the factory floor: An integrated approach to process planning and scheduling, Robotics & Comp. Integ. Manufacturing, 1 (1984), 315-319.  doi: 10.1016/0736-5845(84)90020-6.  Google Scholar

[14]

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[15]

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H. H. Doh, J. M. Yu, J. S. Kim, D. H. Lee and S. H. Nam, A priority scheduling approach for flexible job shops with multiple process plans, Int. J. of Prod. Research, 51 (2013), 3748-3764.  doi: 10.1080/00207543.2013.765074.  Google Scholar

[18]

D. B. Fogel, An evolutionary approach to the traveling salesman problem, Bio. Cybernetics, 60 (1988), 139-144.  doi: 10.1007/BF00202901.  Google Scholar

[19]

J. Gao, M. Gen, L. Sun and X. Zhao, A hybrid of genetic algorithm and bottleneck shifting for multiobjective flexible job shop scheduling problems, Comp. & Indust. Engineering, 53 (2007), 149-162.  doi: 10.1016/j.cie.2007.04.010.  Google Scholar

[20]

K. Z. Gao, P. N. Suganthan, T. J. Chua, C. S. Chong, T. X. Cai and Q. K. Pan, A two-stage artificial bee colony algorithm scheduling flexible job-shop scheduling problem with new job insertion, Expert Syst. with Appl., 42 (2015), 7652-7663.  doi: 10.1016/j.eswa.2015.06.004.  Google Scholar

[21]

M. Gen, Y. Tsujimura and E. Kubota, Solving job-shop scheduling problems by genetic algorithm, in IEEE International Conference on Systems, (1994), 576–579. doi: 10.1109/ICSMC.1994.400072.  Google Scholar

[22]

M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, John Wiley & Sons, 2000. doi: 10.1002/9780470172261.  Google Scholar

[23]

D. E. Goldberg and R. Lingle, Alleles, loci and the traveling salesman problem, Proc. of 1st Int. Conf. on Genetic Algorithms and Their Applications, 12 (1985), 154-159.   Google Scholar

[24]

N. B. Ho, J. C. Tay and M. K. Lai, An effective architecture for learning and evolving flexible job-shop schedules, European J. of Oper. Research, 179 (2007), 316-333.  doi: 10.1016/j.ejor.2006.04.007.  Google Scholar

[25]

Y. C. Ho and C. L. Moodie, Solving cell formation problems in a manufacturing environment with flexible processing and routing capabilities, Int. J. of Prod. Research, 34 (1996), 2901-2923.  doi: 10.1080/00207549608905065.  Google Scholar

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Figure 1.  Alternative process plans networks
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Figure 2.  An illustrative chromosome applying the hierarchical encoding approach
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Figure 3.  Illustrative chromosomes applying the integrated encoding approach
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Figure 4.  Algorithm GENERATE-PROCESS-PLAN
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Figure 5.  A chromosome of the FJSP-OP
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Figure 6.  Algorithm GENERATE-SCHEDULING
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Figure 7.  Decoding a chromosome
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Figure 8.  Crossover operations
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Figure 9.  Mutation operations
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Figure 10.  The Gantt chart of Experiment 1
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Figure 11.  The Gantt chart of Experiment 3
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Figure 12.  The Gantt chart of Experiment 4
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Figure 13.  The Gantt chart of problem mk06 in Experiment 5
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Figure 14.  The Gantt chart of Experiment 6(b)
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Figure 15.  Performance curve of Experiment 4
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Figure A1.  The data of Experiment 3
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Table 1.  Comparison of results for Experiment 1
Solution approach EA Modified GA PBHA GA-OP
Makespan 16 14 14 14
Mean CPU time (ms) N/A N/A N/A 191
1 N/A means the result was not given by the author.
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Solution approach EA Modified GA PBHA GA-OP
Makespan 16 14 14 14
Mean CPU time (ms) N/A N/A N/A 191
1 N/A means the result was not given by the author.
Table 2.  Parameters and comparison of results on Experiment 3
Solution approach ALO Modified GA GA-OP
Parameters N/A $ PopSize=500 $ $ PopSize=50 $
$ P_c=0.8,P_m=0.1,IterNo=100 $
Makespan 161 162 145
Mean CPU time (ms) N/A N/A 309
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Solution approach ALO Modified GA GA-OP
Parameters N/A $ PopSize=500 $ $ PopSize=50 $
$ P_c=0.8,P_m=0.1,IterNo=100 $
Makespan 161 162 145
Mean CPU time (ms) N/A N/A 309
Table 3.  Parameters and comparison of results on Experiment 4
Solution approach ALGA GA-OP
Parameters $ PopSize=400 $ $ PopSize=200 $
$ P_c=0.8 $, $ P_m=0.1 $, $ IterNo=100 $
Makespan 188 181
Mean CPU time (ms) N/A 2,907
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Solution approach ALGA GA-OP
Parameters $ PopSize=400 $ $ PopSize=200 $
$ P_c=0.8 $, $ P_m=0.1 $, $ IterNo=100 $
Makespan 188 181
Mean CPU time (ms) N/A 2,907
Table 4.  Comparison of results for Experiment 5
Problem $ n \times m $ TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 40 40 40 40 41 40 40
mk02 10x6 26 26 26 26 26 26 26
mk03 15x8 204 204 204 204 207 204 204
mk04 15x8 60 60 60 60 65 60 60
mk05 15x4 173 172 172 172 171 173 172
mk06 10x15 60 57 59 57 61 58 57
mk07 20x5 139 139 139 139 173 144 139
mk08 20x10 523 523 523 523 523 523 523
mk09 20x10 307 307 307 307 307 307 307
mk10 20x15 202 198 202 197 312 198 198
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Problem $ n \times m $ TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 40 40 40 40 41 40 40
mk02 10x6 26 26 26 26 26 26 26
mk03 15x8 204 204 204 204 207 204 204
mk04 15x8 60 60 60 60 65 60 60
mk05 15x4 173 172 172 172 171 173 172
mk06 10x15 60 57 59 57 61 58 57
mk07 20x5 139 139 139 139 173 144 139
mk08 20x10 523 523 523 523 523 523 523
mk09 20x10 307 307 307 307 307 307 307
mk10 20x15 202 198 202 197 312 198 198
Table 5.  The experimental results (computational time in terms of seconds) of experiment 5
Problem n x m TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 3.36 5 20.16 0.06 N/A N/A 0.27
mk02 10x6 3.72 15 28.21 0.59 N/A N/A 3.75
mk03 15x8 1.56 2 53.76 0.16 N/A N/A 0.12
mk04 15x8 66.58 10 30.53 0.49 N/A N/A 3.41
mk05 15x4 78.45 18 36.36 4.57 N/A N/A 6.23
mk06 10x15 173.98 63 80.61 53.82 N/A N/A 65.14
mk07 20x5 66.19 33 37.74 20.01 N/A N/A 25.4
mk08 20x10 2.15 3 77.71 0.02 N/A N/A 0.2
mk09 20x10 304.43 24 75.23 0.86 N/A N/A 4.1
mk10 20x15 418.19 104 90.75 33.21 N/A N/A 73.12
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Problem n x m TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 3.36 5 20.16 0.06 N/A N/A 0.27
mk02 10x6 3.72 15 28.21 0.59 N/A N/A 3.75
mk03 15x8 1.56 2 53.76 0.16 N/A N/A 0.12
mk04 15x8 66.58 10 30.53 0.49 N/A N/A 3.41
mk05 15x4 78.45 18 36.36 4.57 N/A N/A 6.23
mk06 10x15 173.98 63 80.61 53.82 N/A N/A 65.14
mk07 20x5 66.19 33 37.74 20.01 N/A N/A 25.4
mk08 20x10 2.15 3 77.71 0.02 N/A N/A 0.2
mk09 20x10 304.43 24 75.23 0.86 N/A N/A 4.1
mk10 20x15 418.19 104 90.75 33.21 N/A N/A 73.12
Table 6.  Comparison of results on Experiment 6
Solution approach Experiment 6(a) Experiment 6(b)
ACO GA-OP Enhanced ACO GA-OP
Makespan 589 522 484 482
Mean CPU time (ms) 128,700 12,056 120534 12063
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Solution approach Experiment 6(a) Experiment 6(b)
ACO GA-OP Enhanced ACO GA-OP
Makespan 589 522 484 482
Mean CPU time (ms) 128,700 12,056 120534 12063
Table A1.  Alternative machines of each operation performed for each job
Operation Job
1 2 3 4 5 6
1 2, 4 2, 4 3, 5 3, 5 2, 4 2, 4
2 7, 8 7, 8 4, 6 4, 6 3, 5 3, 5
3 1, 2 1, 2 2, 3, 5 2, 3, 5 1, 2, 6 1, 2, 6
4 8, 6 8, 6 6, 7 6, 7 6, 8 6, 8
5 3, 5 3, 5 1, 8 1, 8 1, 7 1, 7
6 1, 2, 4 1, 2, 4 1, 4 1, 4 1, 3 1, 3
7 5, 6 5, 6 6, 7 6, 7 6, 7 6, 7
8 1, 7 1, 7 5, 8 5, 8 5, 8 5, 8
9 3, 8 3, 8 4, 2 4, 2 4, 3 4, 3
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Operation Job
1 2 3 4 5 6
1 2, 4 2, 4 3, 5 3, 5 2, 4 2, 4
2 7, 8 7, 8 4, 6 4, 6 3, 5 3, 5
3 1, 2 1, 2 2, 3, 5 2, 3, 5 1, 2, 6 1, 2, 6
4 8, 6 8, 6 6, 7 6, 7 6, 8 6, 8
5 3, 5 3, 5 1, 8 1, 8 1, 7 1, 7
6 1, 2, 4 1, 2, 4 1, 4 1, 4 1, 3 1, 3
7 5, 6 5, 6 6, 7 6, 7 6, 7 6, 7
8 1, 7 1, 7 5, 8 5, 8 5, 8 5, 8
9 3, 8 3, 8 4, 2 4, 2 4, 3 4, 3
Table A2.  Processing times on the alternative machines of each operation
Operation Job
1 2 3 4 5 6
1 18, 22 18, 22 12, 15 12, 15 18, 22 18, 22
2 39, 36 39, 36 24, 23 24, 23 12, 15 12, 15
3 11, 10 37, 39 30, 31, 29 30, 31, 29 50, 52, 54 50, 52, 54
4 31, 34 20, 21 21, 22 21, 22 19, 21 53, 51
5 21, 23 21, 23 32, 30 32, 30 32, 31 22, 24
6 10, 12, 15 10, 12, 15 22, 25 22, 25 22, 25 22, 25
7 32, 30 36, 38 24, 22 42, 44 24, 22 24, 22
8 45, 44 45, 44 20, 19 41, 43 20, 18 20, 18
9 26, 24 26, 24 27, 22 27, 22 27, 22 27, 22
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Operation Job
1 2 3 4 5 6
1 18, 22 18, 22 12, 15 12, 15 18, 22 18, 22
2 39, 36 39, 36 24, 23 24, 23 12, 15 12, 15
3 11, 10 37, 39 30, 31, 29 30, 31, 29 50, 52, 54 50, 52, 54
4 31, 34 20, 21 21, 22 21, 22 19, 21 53, 51
5 21, 23 21, 23 32, 30 32, 30 32, 31 22, 24
6 10, 12, 15 10, 12, 15 22, 25 22, 25 22, 25 22, 25
7 32, 30 36, 38 24, 22 42, 44 24, 22 24, 22
8 45, 44 45, 44 20, 19 41, 43 20, 18 20, 18
9 26, 24 26, 24 27, 22 27, 22 27, 22 27, 22
Table A3.  Transportation times between the machines
Machine number 1 2 3 4 5 6 7 8
1 0 3 7 10 3 5 8 12
2 3 0 4 7 5 3 5 8
3 7 4 0 3 8 5 3 5
4 10 7 3 0 10 8 5 3
5 3 5 8 10 0 3 7 10
6 5 3 5 8 3 0 4 7
7 8 5 3 5 7 4 0 3
8 12 8 5 3 10 7 3 0
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Machine number 1 2 3 4 5 6 7 8
1 0 3 7 10 3 5 8 12
2 3 0 4 7 5 3 5 8
3 7 4 0 3 8 5 3 5
4 10 7 3 0 10 8 5 3
5 3 5 8 10 0 3 7 10
6 5 3 5 8 3 0 4 7
7 8 5 3 5 7 4 0 3
8 12 8 5 3 10 7 3 0
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