Figure 1.
Alternative process plans networks
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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
| 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 |
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 and Management Optimization,
2020, 16
(6)
: 2943-2969.
doi: 10.3934/jimo.2019088
![]()
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show all references
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A. Azzouz, M. Ennigrou and L. B. Said,
A hybrid algorithm for flexible job-shop scheduling problem with setup times, Int. J. of Prod. Mgmt. & Eng., 5 (2017), 23-30.
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W. Banzhaf,
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|
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A. Baykasoglu,
Linguistic-based meta-heuristic optimization model for flexible job shop scheduling, Int. J. of Prod. Research, 40 (2002), 4523-4543.
doi: 10.1080/00207540210147043. |
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A. Baykasoglu, L. Ozbakir and A. Sonmez,
Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems, J. of Intell. Manufacturing, 15 (2004), 777-785.
doi: 10.1023/B:JIMS.0000042663.16199.84. |
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S. Benjaafar and R. S. Ramakrishnan,
Modelling, measurement and evaluation of sequencing flexibility in manufacturing systems, Int. J. of Prod. Research, 34 (1996), 1195-1220.
doi: 10.1080/00207549608904961. |
| [7] |
C. Bierwirth, D. C. Mattfeld and H. Kopfer, On permutation representations for scheduling problems, in International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, 1141, Springer, Berlin, 1996,310–318.
doi: 10.1007/3-540-61723-X_995. |
| [8] |
C. Bierwirth and D. Mattfeld,
Production scheduling and rescheduling with genetic algorithms, Evol. Computation, 7 (1999), 1-17.
doi: 10.1162/evco.1999.7.1.1. |
| [9] |
P. Brandimarte,
Routing and scheduling in a flexible job shop by tabu search, Annals of Ops. Research, 41 (1993), 157-183.
doi: 10.1007/BF02023073. |
| [10] |
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. |
| [11] |
R. Cheng, M. Gen and Y. Tsujimura,
A tutorial survey of job-shop scheduling problems using genetic algorithms-Ⅰ. Representation, Comp. & Indust. Engineering, 30 (1996), 983-997.
doi: 10.1016/0360-8352(96)00047-2. |
| [12] |
R. Cheng, M. Gen and Y. Tsujimura,
A tutorial survey of job-shop scheduling problems using genetic algorithms: Part Ⅱ. Hybrid genetic search strategies, Comp. & Indust. Engineering, 37 (1999), 51-55.
doi: 10.1016/s0360-8352(99)00022-4. |
| [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. |
| [14] |
G. Chryssolouris, S. Chan and N. P. Suh,
An integrated approach to process planning and scheduling, CIRP Annals - Manufacturing Tech., 34 (1985), 413-417.
doi: 10.1016/S0007-8506(07)61801-0. |
| [15] |
D. A. Dabney, L. Green and V. Topalli,
A priority-based heuristic algorithm (PBHA) for optimizing integrated process planning and scheduling problem, J. of Criminal Justice Edu., 2 (2015), 44-68.
doi: 10.1080/23311916.2015.1070494. |
| [16] |
L. Davis, Job shop scheduling with genetic algorithms, In: International Conference on Genetic Algorithms, L. Erlbaum Asssociates Inc., Hillsdale, 1985, 136–140. |
| [17] |
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. |
| [18] |
D. B. Fogel,
An evolutionary approach to the traveling salesman problem, Bio. Cybernetics, 60 (1988), 139-144.
doi: 10.1007/BF00202901. |
| [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. |
| [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. |
| [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. |
| [22] |
M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, John Wiley & Sons, 2000.
doi: 10.1002/9780470172261. |
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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.
|
| [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. |
| [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. |
| [26] |
J. H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, Mich., 1975.
|
| [27] |
K. Ida and K. Oka,
Flexible job-shop scheduling problem by genetic algorithm, Electrical Engineering in Japan, 177 (2011), 28-35.
doi: 10.1002/eej.21194. |
| [28] |
L. Jin, Q. Tang, C. Zhang, X. Shao and G. Tian,
More MILP models for integrated process planning and scheduling, Int. J. of Prod. Research, 54 (2016), 4387-4402.
doi: 10.1080/00207543.2016.1140917. |
| [29] |
B. Khoshnevis and Q. M. Chen,
Integration of process planning and scheduling functions, J. of Intell. Manufacturing, 2 (1991), 165-175.
doi: 10.1007/BF01471363. |
| [30] |
Y. K. Kim, J. Y. Kim and K. S. Shin,
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Figure 2.
An illustrative chromosome applying the hierarchical encoding approach
Figure 3.
Illustrative chromosomes applying the integrated encoding approach
Figure 4.
Algorithm GENERATE-PROCESS-PLAN
Figure 5.
A chromosome of the FJSP-OP
Figure 6.
Algorithm GENERATE-SCHEDULING
Figure 7.
Decoding a chromosome
Figure 8.
Crossover operations
Figure 9.
Mutation operations
Figure 10.
The Gantt chart of Experiment 1
Figure 11.
The Gantt chart of Experiment 3
Figure 12.
The Gantt chart of Experiment 4
Figure 13.
The Gantt chart of problem mk06 in Experiment 5
Figure 14.
The Gantt chart of Experiment 6(b)
Figure 15.
Performance curve of Experiment 4
Figure A1.
The data of Experiment 3
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. | ||||
| 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 | ||
| Makespan | 161 | 162 | 145 |
| Mean CPU time (ms) | N/A | N/A | 309 |
| Solution approach | ALO | Modified GA | GA-OP |
| Parameters | N/A | ||
| 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 | ||
| Makespan | 188 | 181 |
| Mean CPU time (ms) | N/A | 2,907 |
| Solution approach | ALGA | GA-OP |
| Parameters | ||
| Makespan | 188 | 181 |
| Mean CPU time (ms) | N/A | 2,907 |
Table 4.
Comparison of results for Experiment 5
| Problem | 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 |
| Problem | 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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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