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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

* Corresponding author: Sardar M. N. Islam

Received  November 2017 Revised  March 2019 Published  November 2020 Early access  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.

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
References:
[1]

A. AzzouzM. 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.  doi: 10.4995/ijpme.2017.6618.

[2]

K. R. Baker, Introduction to Sequencing and Scheduling, Wiley, New York, 1974.

[3]

W. Banzhaf, The "molecula" traveling salesman, Bio. Cyber., 64 (1990), 7-14. 

[4]

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.

[5]

A. BaykasogluL. 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.

[6]

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. ChengM. 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. ChengM. 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. ChryssolourisS. 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. ChryssolourisS. 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. DabneyL. 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. DohJ. M. YuJ. S. KimD. 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. GaoM. GenL. 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. GaoP. N. SuganthanT. J. ChuaC. S. ChongT. 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.

[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. 

[24]

N. B. HoJ. 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. JinQ. TangC. ZhangX. 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. KimJ. Y. Kim and K. S. Shin, An asymmetric multileveled symbiotic evolutionary algorithm for integrated FMS scheduling, J. of Intell. Manufacturing, 18 (2007), 631-645.  doi: 10.1007/s10845-007-0037-5.

[31]

Y. K. KimK. Park and J. Ko, A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling, Comp. & Ops. Research, 30 (2003), 1151-1171.  doi: 10.1016/S0305-0548(02)00063-1.

[32]

T. Kis, Job-shop scheduling with processing alternatives, European J. of Oper. Research, 151 (2003), 307-332.  doi: 10.1016/S0377-2217(02)00828-7.

[33]

R. KumarM. K. Tiwari and R. Shankar, Scheduling of flexible manufacturing systems: An ant colony optimization approach, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 217 (2003), 1443-1453.  doi: 10.1243/095440503322617216.

[34]

A. Ławrynowicz, Integration of production planning and scheduling using an expert system and a genetic algorithm, J. of the Oper. Research Society, 59 (2008), 455-463.  doi: 10.1057/palgrave.jors.2602423.

[35]

H. Lee and S. S. Kim, Integration of process planning and scheduling using simulation based genetic algorithms, The Int. J. of Adv. Manufacturing Tech., 18 (2001), 586-590.  doi: 10.1007/s001700170035.

[36]

K. M. LeeT. Yamakawa and K. M. Lee, A genetic algorithm for general machine scheduling problems, Int. J. of Knowledge-Based Intell. Electronic Systems, 2 (1998), 60-66.  doi: 10.1109/KES.1998.725893.

[37]

X. Y. Li and L. Gao, An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem, Int. J. of Prod. Economics, 174 (2016), 93-110.  doi: 10.1016/j.ijpe.2016.01.016.

[38]

X. Y. LiL. GaoX. ShaoC. Zhang and C. Wang, Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Comp. & Ops. Research, 37 (2010), 656-667.  doi: 10.1016/j.cor.2009.06.008.

[39]

X. Y. LiL. Gao and X. Y. Shao, An active learning genetic algorithm for integrated process planning and scheduling, Expert Syst. with Appl., 39 (2012), 6683-6691.  doi: 10.1016/j.eswa.2011.11.074.

[40]

X. Y. LiX. Y. ShaoL. Gao and W. Qian, An effective hybrid algorithm for integrated process planning and scheduling, Int. J. of Prod. Economics, 126 (2010), 289-298.  doi: 10.1016/j.ijpe.2010.04.001.

[41]

X. Y. LiC. ZhangL. GaoW. Li and X. Y. Shao, An agent-based approach for integrated process planning and scheduling, Expert Syst. with Appl., 37 (2010), 1256-1264.  doi: 10.1016/j.eswa.2009.06.014.

[42]

Y. J. Lin and J. J. Solberg, Effectiveness of flexible routing control, Int. J. of Flexible Manufacturing Syst., 3 (1991), 189-211.  doi: 10.1007/BF00170206.

[43]

M. LiuS. Yi and P. Wen, Quantum-inspired hybrid algorithm for integrated process planning and scheduling, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 232 (2016), 1-18.  doi: 10.1177/0954405416661006.

[44]

G. LuoX. WenH. LiW. Ming and G. Xie, An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling, Int. J. of Adv. Manufacturing Tech., 91 (2017), 3145-3158.  doi: 10.1007/s00170-017-0020-z.

[45]

V. K. ManupatiG. D. PutnikM. K. TiwariP. Ávila and M. M. Cruz-Cunha, Integration of process planning and scheduling using mobile-agent based approach in a networked manufacturing environment, Comp. & Industrial Engineering, 94 (2016), 63-73.  doi: 10.1016/j.cie.2016.01.017.

[46]

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Second edition, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-02830-8.

[47]

C. MoonY. H. LeeC. S. Jeong and Y. S. Yun, Integrated process planning and scheduling in a supply chain, Comp. & Indust. Engineering, 54 (2008), 1048-1061.  doi: 10.1016/j.cie.2007.06.018.

[48]

N. Morad and A. Zalzala, Genetic algorithms in integrated process planning and scheduling, J. of Intell. Manufacturing, 10 (1999), 169-179.  doi: 10.1023/a:1008976720878.

[49]

H. E. NouriO. B. Driss and K. Ghédira, Solving the flexible job shop problem by hybrid metaheuristics-based multiagent model, J. of Indust. Engineering Int., 14 (2018), 1-14.  doi: 10.1007/s40092-017-0204-z.

[50]

M. NouiriA. BekrarA. JemaiS. Niar and A. C. Ammari, An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem, J. of Intell. Manufacturing, 29 (2018), 603-615.  doi: 10.1007/s10845-015-1039-3.

[51]

C. ÖzgüvenL. Özbakır and Y. Yavuz, Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Appl. Math. Modelling, 34 (2010), 1539-1548.  doi: 10.1016/j.apm.2009.09.002.

[52]

J. J. PalaciosM. A. GonzálezC. R. VelaI. González-Rodríguez and J. Puente, Genetic tabu search for the fuzzy flexible job shop problem, Comp. & Ops. Research, 54 (2015), 74-89.  doi: 10.1016/j.cor.2014.08.023.

[53]

M. PetroviäJ. PetronijeviäM. MitiäN. VukoviäZ. Miljkoviä and B. Babiä, The ant lion optimization algorithm for integrated process planning and scheduling, Appl. Mechanics & Materials, 834 (2016), 187-192. 

[54]

R. K. PhandenA. Jain and R. Verma, Integration of process planning and scheduling: A state-of-the-art review, Int. J. of Comp. Integrated Manufacturing, 24 (2011), 517-534.  doi: 10.1080/0951192X.2011.562543.

[55]

L. Qiao and S. Lv, An improved genetic algorithm for integrated process planning and scheduling, The Int. J. of Adv. Manufacturing Tech., 58 (2012), 727-740.  doi: 10.1007/s00170-011-3409-0.

[56]

A. Rajabinasab and S. Mansour, Dynamic flexible job shop scheduling with alternative process plans: An agent-based approach, The Int. J. of Adv. Manufacturing Tech., 54 (2011), 1091-1107.  doi: 10.1007/s00170-010-2986-7.

[57]

C. Saygin and S. E. Kilic, Integrating flexible process plans with scheduling in flexible manufacturing systems, The Int. J. of Adv. Manufacturing Tech., 15 (1999), 268-280.  doi: 10.1007/s001700050066.

[58]

X. Y. ShaoX. Y. LiL. Gao and C. Y. Zhang, Integration of process planning and scheduling-a modified genetic algorithm-based approach, Comp. & Ops. Research, 36 (2009), 2082-2096.  doi: 10.1016/j.cor.2008.07.006.

[59]

O. Sobeyko and L. Mã¶Nch, Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics, Int. J. of Prod. Research, 55 (2017), 392-409.  doi: 10.1080/00207543.2016.1182227.

[60]

D. SreeramuluY. SagarP. Suman and A. S. Kumar, Integration of process planning and scheduling of a manufacturing systems using petri nets and genetic algorithm, Indian J. of Science & Tech., 9 (2016), 2-8.  doi: 10.17485/ijst/2016/v9i41/100874.

[61]

G. Syswerda, Uniform Crossover in Genetic Algorithms, International Conference on Genetic Algorithms, (1989), 2–9.

[62]

Z. Wang and T. Ju, The research about integration of process planning and production scheduling based on genetic algorithm, International Conference on Computer Science and Software Engineering, (2008), 9–12. doi: 10.1109/CSSE.2008.845.

[63]

T. N. WongC. W. LeungK. L. Mak and R. Y. K. Fung, An agent-based negotiation approach to integrate process planning and scheduling, Int. J. of Prod. Research, 44 (2006), 1331-1351.  doi: 10.1080/00207540500409723.

[64]

T. N. WongC. W. LeungK. L. Mak and R. Y. K. Fung, Integrated process planning and scheduling/rescheduling-an agent-based approach, Int. J. of Prod. Research, 44 (2006), 3627-3655.  doi: 10.1080/00207540600675801.

[65]

T. N. WongS. C. ZhangG. Wang and L. P. Zhang, Integrated process planning and scheduling – multi-agent system with two-stage ant colony optimisation algorithm, Int. J. of Prod. Research, 50 (2012), 6188-6201.  doi: 10.1080/00207543.2012.720393.

[66]

H. XiaX. Li and L. Gao, A hybrid genetic algorithm with variable neighborhood search for dynamic integrated process planning and scheduling, Comp. & Indust. Engineering, 102 (2016), 99-112.  doi: 10.1016/j.cie.2016.10.015.

[67]

L. Yin, L. Gao, X. Li and H. Xia, An improved genetic algorithm with rolling window technology for dynamic integrated process planning and scheduling problem, IEEE International Conference on Computer Supported Cooperative Work in Design, (2017), 414–419. doi: 10.1109/CSCWD.2017.8066730.

[68]

Y. Yuan and H. Xu, Multiobjective flexible job shop scheduling using memetic algorithms, IEEE Transactions on Automation Science and Engineering, 12 (2015), 336-353.  doi: 10.1109/TASE.2013.2274517.

[69]

G. Zhang, L. Zhang, X. Song, Y. Wang and C. Zhou, A variable neighborhood search based genetic algorithm for flexible job shop scheduling problem, Cluster Computing, (2018), 1–12. doi: 10.1007/s10586-017-1420-4.

[70]

S. Zhang and T. N. Wong, Integrated process planning and scheduling: An enhanced ant colony optimization heuristic with parameter tuning, J. of Intell. Manufacturing, 29 (2018), 585-601.  doi: 10.1007/s10845-014-1023-3.

[71]

L. Zhang and T. N. Wong, An object-coding genetic algorithm for integrated process planning and scheduling, European J. of Oper. Research, 244 (2015), 434-444.  doi: 10.1016/j.ejor.2015.01.032.

[72]

S. ZhangZ. YuW. ZhangD. Yu and Y. Xu, An extended genetic algorithm for distributed integration of fuzzy process planning and scheduling, Math. Problems in Engineering, 3 (2016), 1-13.  doi: 10.1155/2016/3763512.

show all references

References:
[1]

A. AzzouzM. 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.  doi: 10.4995/ijpme.2017.6618.

[2]

K. R. Baker, Introduction to Sequencing and Scheduling, Wiley, New York, 1974.

[3]

W. Banzhaf, The "molecula" traveling salesman, Bio. Cyber., 64 (1990), 7-14. 

[4]

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.

[5]

A. BaykasogluL. 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.

[6]

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. ChengM. 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. ChengM. 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. ChryssolourisS. 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. ChryssolourisS. 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. DabneyL. 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. DohJ. M. YuJ. S. KimD. 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. GaoM. GenL. 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. GaoP. N. SuganthanT. J. ChuaC. S. ChongT. 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.

[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. 

[24]

N. B. HoJ. 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. JinQ. TangC. ZhangX. 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. KimJ. Y. Kim and K. S. Shin, An asymmetric multileveled symbiotic evolutionary algorithm for integrated FMS scheduling, J. of Intell. Manufacturing, 18 (2007), 631-645.  doi: 10.1007/s10845-007-0037-5.

[31]

Y. K. KimK. Park and J. Ko, A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling, Comp. & Ops. Research, 30 (2003), 1151-1171.  doi: 10.1016/S0305-0548(02)00063-1.

[32]

T. Kis, Job-shop scheduling with processing alternatives, European J. of Oper. Research, 151 (2003), 307-332.  doi: 10.1016/S0377-2217(02)00828-7.

[33]

R. KumarM. K. Tiwari and R. Shankar, Scheduling of flexible manufacturing systems: An ant colony optimization approach, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 217 (2003), 1443-1453.  doi: 10.1243/095440503322617216.

[34]

A. Ławrynowicz, Integration of production planning and scheduling using an expert system and a genetic algorithm, J. of the Oper. Research Society, 59 (2008), 455-463.  doi: 10.1057/palgrave.jors.2602423.

[35]

H. Lee and S. S. Kim, Integration of process planning and scheduling using simulation based genetic algorithms, The Int. J. of Adv. Manufacturing Tech., 18 (2001), 586-590.  doi: 10.1007/s001700170035.

[36]

K. M. LeeT. Yamakawa and K. M. Lee, A genetic algorithm for general machine scheduling problems, Int. J. of Knowledge-Based Intell. Electronic Systems, 2 (1998), 60-66.  doi: 10.1109/KES.1998.725893.

[37]

X. Y. Li and L. Gao, An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem, Int. J. of Prod. Economics, 174 (2016), 93-110.  doi: 10.1016/j.ijpe.2016.01.016.

[38]

X. Y. LiL. GaoX. ShaoC. Zhang and C. Wang, Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Comp. & Ops. Research, 37 (2010), 656-667.  doi: 10.1016/j.cor.2009.06.008.

[39]

X. Y. LiL. Gao and X. Y. Shao, An active learning genetic algorithm for integrated process planning and scheduling, Expert Syst. with Appl., 39 (2012), 6683-6691.  doi: 10.1016/j.eswa.2011.11.074.

[40]

X. Y. LiX. Y. ShaoL. Gao and W. Qian, An effective hybrid algorithm for integrated process planning and scheduling, Int. J. of Prod. Economics, 126 (2010), 289-298.  doi: 10.1016/j.ijpe.2010.04.001.

[41]

X. Y. LiC. ZhangL. GaoW. Li and X. Y. Shao, An agent-based approach for integrated process planning and scheduling, Expert Syst. with Appl., 37 (2010), 1256-1264.  doi: 10.1016/j.eswa.2009.06.014.

[42]

Y. J. Lin and J. J. Solberg, Effectiveness of flexible routing control, Int. J. of Flexible Manufacturing Syst., 3 (1991), 189-211.  doi: 10.1007/BF00170206.

[43]

M. LiuS. Yi and P. Wen, Quantum-inspired hybrid algorithm for integrated process planning and scheduling, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 232 (2016), 1-18.  doi: 10.1177/0954405416661006.

[44]

G. LuoX. WenH. LiW. Ming and G. Xie, An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling, Int. J. of Adv. Manufacturing Tech., 91 (2017), 3145-3158.  doi: 10.1007/s00170-017-0020-z.

[45]

V. K. ManupatiG. D. PutnikM. K. TiwariP. Ávila and M. M. Cruz-Cunha, Integration of process planning and scheduling using mobile-agent based approach in a networked manufacturing environment, Comp. & Industrial Engineering, 94 (2016), 63-73.  doi: 10.1016/j.cie.2016.01.017.

[46]

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Second edition, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-02830-8.

[47]

C. MoonY. H. LeeC. S. Jeong and Y. S. Yun, Integrated process planning and scheduling in a supply chain, Comp. & Indust. Engineering, 54 (2008), 1048-1061.  doi: 10.1016/j.cie.2007.06.018.

[48]

N. Morad and A. Zalzala, Genetic algorithms in integrated process planning and scheduling, J. of Intell. Manufacturing, 10 (1999), 169-179.  doi: 10.1023/a:1008976720878.

[49]

H. E. NouriO. B. Driss and K. Ghédira, Solving the flexible job shop problem by hybrid metaheuristics-based multiagent model, J. of Indust. Engineering Int., 14 (2018), 1-14.  doi: 10.1007/s40092-017-0204-z.

[50]

M. NouiriA. BekrarA. JemaiS. Niar and A. C. Ammari, An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem, J. of Intell. Manufacturing, 29 (2018), 603-615.  doi: 10.1007/s10845-015-1039-3.

[51]

C. ÖzgüvenL. Özbakır and Y. Yavuz, Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Appl. Math. Modelling, 34 (2010), 1539-1548.  doi: 10.1016/j.apm.2009.09.002.

[52]

J. J. PalaciosM. A. GonzálezC. R. VelaI. González-Rodríguez and J. Puente, Genetic tabu search for the fuzzy flexible job shop problem, Comp. & Ops. Research, 54 (2015), 74-89.  doi: 10.1016/j.cor.2014.08.023.

[53]

M. PetroviäJ. PetronijeviäM. MitiäN. VukoviäZ. Miljkoviä and B. Babiä, The ant lion optimization algorithm for integrated process planning and scheduling, Appl. Mechanics & Materials, 834 (2016), 187-192. 

[54]

R. K. PhandenA. Jain and R. Verma, Integration of process planning and scheduling: A state-of-the-art review, Int. J. of Comp. Integrated Manufacturing, 24 (2011), 517-534.  doi: 10.1080/0951192X.2011.562543.

[55]

L. Qiao and S. Lv, An improved genetic algorithm for integrated process planning and scheduling, The Int. J. of Adv. Manufacturing Tech., 58 (2012), 727-740.  doi: 10.1007/s00170-011-3409-0.

[56]

A. Rajabinasab and S. Mansour, Dynamic flexible job shop scheduling with alternative process plans: An agent-based approach, The Int. J. of Adv. Manufacturing Tech., 54 (2011), 1091-1107.  doi: 10.1007/s00170-010-2986-7.

[57]

C. Saygin and S. E. Kilic, Integrating flexible process plans with scheduling in flexible manufacturing systems, The Int. J. of Adv. Manufacturing Tech., 15 (1999), 268-280.  doi: 10.1007/s001700050066.

[58]

X. Y. ShaoX. Y. LiL. Gao and C. Y. Zhang, Integration of process planning and scheduling-a modified genetic algorithm-based approach, Comp. & Ops. Research, 36 (2009), 2082-2096.  doi: 10.1016/j.cor.2008.07.006.

[59]

O. Sobeyko and L. Mã¶Nch, Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics, Int. J. of Prod. Research, 55 (2017), 392-409.  doi: 10.1080/00207543.2016.1182227.

[60]

D. SreeramuluY. SagarP. Suman and A. S. Kumar, Integration of process planning and scheduling of a manufacturing systems using petri nets and genetic algorithm, Indian J. of Science & Tech., 9 (2016), 2-8.  doi: 10.17485/ijst/2016/v9i41/100874.

[61]

G. Syswerda, Uniform Crossover in Genetic Algorithms, International Conference on Genetic Algorithms, (1989), 2–9.

[62]

Z. Wang and T. Ju, The research about integration of process planning and production scheduling based on genetic algorithm, International Conference on Computer Science and Software Engineering, (2008), 9–12. doi: 10.1109/CSSE.2008.845.

[63]

T. N. WongC. W. LeungK. L. Mak and R. Y. K. Fung, An agent-based negotiation approach to integrate process planning and scheduling, Int. J. of Prod. Research, 44 (2006), 1331-1351.  doi: 10.1080/00207540500409723.

[64]

T. N. WongC. W. LeungK. L. Mak and R. Y. K. Fung, Integrated process planning and scheduling/rescheduling-an agent-based approach, Int. J. of Prod. Research, 44 (2006), 3627-3655.  doi: 10.1080/00207540600675801.

[65]

T. N. WongS. C. ZhangG. Wang and L. P. Zhang, Integrated process planning and scheduling – multi-agent system with two-stage ant colony optimisation algorithm, Int. J. of Prod. Research, 50 (2012), 6188-6201.  doi: 10.1080/00207543.2012.720393.

[66]

H. XiaX. Li and L. Gao, A hybrid genetic algorithm with variable neighborhood search for dynamic integrated process planning and scheduling, Comp. & Indust. Engineering, 102 (2016), 99-112.  doi: 10.1016/j.cie.2016.10.015.

[67]

L. Yin, L. Gao, X. Li and H. Xia, An improved genetic algorithm with rolling window technology for dynamic integrated process planning and scheduling problem, IEEE International Conference on Computer Supported Cooperative Work in Design, (2017), 414–419. doi: 10.1109/CSCWD.2017.8066730.

[68]

Y. Yuan and H. Xu, Multiobjective flexible job shop scheduling using memetic algorithms, IEEE Transactions on Automation Science and Engineering, 12 (2015), 336-353.  doi: 10.1109/TASE.2013.2274517.

[69]

G. Zhang, L. Zhang, X. Song, Y. Wang and C. Zhou, A variable neighborhood search based genetic algorithm for flexible job shop scheduling problem, Cluster Computing, (2018), 1–12. doi: 10.1007/s10586-017-1420-4.

[70]

S. Zhang and T. N. Wong, Integrated process planning and scheduling: An enhanced ant colony optimization heuristic with parameter tuning, J. of Intell. Manufacturing, 29 (2018), 585-601.  doi: 10.1007/s10845-014-1023-3.

[71]

L. Zhang and T. N. Wong, An object-coding genetic algorithm for integrated process planning and scheduling, European J. of Oper. Research, 244 (2015), 434-444.  doi: 10.1016/j.ejor.2015.01.032.

[72]

S. ZhangZ. YuW. ZhangD. Yu and Y. Xu, An extended genetic algorithm for distributed integration of fuzzy process planning and scheduling, Math. Problems in Engineering, 3 (2016), 1-13.  doi: 10.1155/2016/3763512.

Figure 1.  Alternative process plans networks
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 $ 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
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
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
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
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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