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October  2016, 12(4): 1391-1415. doi: 10.3934/jimo.2016.12.1391

A priority-based genetic algorithm for a flexible job shop scheduling problem

1. 

Department of Industrial Engineering, İstanbul Technical University, 34367 İstanbul, Turkey, Turkey

2. 

ALGORITMI Research Centre, University of Minho, Campus Azurem, 4800-058 Guimarães, Portugal

3. 

Center for Applied Optimization Department of Industrial and Systems Engineering, University of Florida, 32611

Received  January 2015 Revised  June 2015 Published  January 2016

In this study, a genetic algorithm (GA) with priority-based representation is proposed for a flexible job shop scheduling problem (FJSP) which is one of the hardest operations research problems. Investigating the effect of the proposed representation schema on FJSP is the main contribution to the literature. The priority of each operation is represented by a gene on the chromosome which is used by a constructive algorithm performed for decoding. All active schedules, which constitute a subset of feasible schedules including the optimal, can be generated by the constructive algorithm. To obtain improved solutions, iterated local search (ILS) is applied to the chromosomes at the end of each reproduction process. The most widely used FJSP data sets generated in the literature are used for benchmarking and evaluating the performance of the proposed GA methodology. The computational results show that the proposed GA performed at the same level or better with respect to the makespan for some data sets when compared to the results from the literature.
Citation: Didem Cinar, José António Oliveira, Y. Ilker Topcu, Panos M. Pardalos. A priority-based genetic algorithm for a flexible job shop scheduling problem. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1391-1415. doi: 10.3934/jimo.2016.12.1391
References:
[1]

N. Al-Hinai and T. Y. ElMekkawy, An efficient hybridized genetic algorithm architecture for the flexible job shop scheduling problem,, Flexible Services and Manufacturing Journal, 23 (2011), 64. doi: 10.1007/s10696-010-9067-y. Google Scholar

[2]

M. Amiri, M. Zandieh, M. Yazdani and A. Bagheri, A variable neighbourhood search algorithm for the flexible job-shop scheduling problem,, International Journal of Production Research, 48 (2010), 5671. doi: 10.1080/00207540903055743. Google Scholar

[3]

J. Arroyo, G. Nunes and E. Kamke, Iterative local search heuristic for the single machine scheduling problem with sequence dependent setup times and due dates,, in Hybrid Intelligent Systems, 1 (2009), 505. doi: 10.1109/HIS.2009.104. Google Scholar

[4]

A. Bagheri, M. Zandieh, I. Mahdavi and M. Yazdani, An artificial immune algorithm for the flexible job-shop scheduling problem,, Future Generation Computer Systems-the International Journal of Grid Computing-Theory Methods and Applications, 26 (2010), 533. doi: 10.1016/j.future.2009.10.004. Google Scholar

[5]

A. Baykasoglu, Linguistic-based meta-heuristic optimization model for flexible job shop scheduling,, International Journal of Production Research, 40 (2002), 4523. doi: 10.1080/00207540210147043. Google Scholar

[6]

A. Baykasoglu, L. Ozbakir and A. I. Sonmez, Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems,, Journal of Intelligent Manufacturing, 15 (2004), 777. doi: 10.1023/B:JIMS.0000042663.16199.84. Google Scholar

[7]

J. E. Beasley, Population heuristics,, in Handbook of Applied Optimization (eds. P. M. Pardalos and M. G. Resende), (2002). doi: 10.1007/978-1-4757-5362-2. Google Scholar

[8]

D. Behnke and M. J. Geiger, Test Instances for the Flexible Job Shop Scheduling Problem with Work Centers,, Technical report, (2012). Google Scholar

[9]

W. Bozejko, M. Uchronski and M. Wodecki, Parallel hybrid metaheuristics for the flexible job shop problem,, Computers and Industrial Engineering, 59 (2010), 323. doi: 10.1016/j.cie.2010.05.004. Google Scholar

[10]

P. Brandimarte, Routing and scheduling in a flexible job shop by tabu search,, Annals of Operations Research, 41 (1993), 157. Google Scholar

[11]

P. Brucker and R. Schlie, Job-shop scheduling with multipurpose machines,, Computing, 45 (1990), 369. doi: 10.1007/BF02238804. Google Scholar

[12]

M. Caramia and P. Dell'Olmo, Coloring graphs by iterated local search traversing feasible and infeasible solutions,, Discrete Applied Mathematics, 156 (2008), 201. doi: 10.1016/j.dam.2006.07.013. Google Scholar

[13]

J. B. Chambers and J. W. Barnes, Flexible job shop scheduling by tabu search,, 1996., (). Google Scholar

[14]

Y.-L. Chang and R. S. Sullivan, Schedule generation in a dynamic job shop,, International Journal of Production Research, 28 (1990), 65. doi: 10.1080/00207549008942684. Google Scholar

[15]

H. Chen, J. Ihlow and C. Lehmann, A genetic algorithm for flexible job-shop scheduling,, in Robotics and Automation, 2 (1999), 1120. doi: 10.1109/ROBOT.1999.772512. Google Scholar

[16]

T.-C. Chiang and H.-J. Lin, A simple and effective evolutionary algorithm for multiobjective flexible job shop scheduling,, International Journal of Production Economics, 141 (2013), 87. doi: 10.1016/j.ijpe.2012.03.034. Google Scholar

[17]

J.-F. Cordeau, G. Laporte and F. Pasin, An iterated local search heuristic for the logistics network design problem with single assignment,, International Journal of Production Economics, 113 (2008), 626. doi: 10.1016/j.ijpe.2007.10.015. Google Scholar

[18]

M. den Besten, T. Stützle and M. Dorigo, Design of iterated local search algorithms,, in Applications of Evolutionary Computing (ed. E. Boers), (2037), 441. doi: 10.1007/3-540-45365-2_46. Google Scholar

[19]

I. Driss, K. Mouss and A. Laggoun, A new genetic algorithm for flexible job-shop scheduling problems,, Journal of Mechanical Science and Technology, 29 (2015), 1273. doi: 10.1007/s12206-015-0242-7. Google Scholar

[20]

M. Ennigrou and K. Ghedira, New local diversification techniques for flexible job shop scheduling problem with a multi-agent approach,, Autonomous Agents and Multi-Agent Systems, 17 (2008), 270. doi: 10.1007/s10458-008-9031-3. Google Scholar

[21]

I. Essafi, Y. Mati and S. Dauzère-P\'erès, A genetic local search algorithm for minimizing total weighted tardiness in the job-shop scheduling problem,, Computers & Operations Research, 35 (2008), 2599. doi: 10.1016/j.cor.2006.12.019. Google Scholar

[22]

H. Farughi, B. Yousefi Yegane and M. Fathian, A new critical path method and a memetic algorithm for flexible job shop scheduling with overlapping operations,, Simulation, 89 (2013), 264. Google Scholar

[23]

P. Fattahi, M. S. Mehrabad and F. Jolai, Mathematical modeling and heuristic approaches to flexible job shop scheduling problems,, Journal of Intelligent Manufacturing, 18 (2007), 331. doi: 10.1007/s10845-007-0026-8. Google Scholar

[24]

M. Frutos, A. C. Olivera and F. Tohme, A memetic algorithm based on a NSGAII scheme for the flexible job-shop scheduling problem,, Annals of Operations Research, 181 (2010), 745. doi: 10.1007/s10479-010-0751-9. Google Scholar

[25]

J. Gao, M. Gen and L. Y. Sun, Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm,, Journal of Intelligent Manufacturing, 17 (2006), 493. doi: 10.1007/s10845-005-0021-x. Google Scholar

[26]

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

[27]

J. Gao, L. Y. Sun and M. S. Gen, A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems,, Computers and Operations Research, 35 (2008), 2892. doi: 10.1016/j.cor.2007.01.001. Google Scholar

[28]

K. Gao, P. Suganthan, Q. Pan, T. Chua, T. Cai and C. Chong, Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling,, Information Sciences, 289 (2014), 76. doi: 10.1016/j.ins.2014.07.039. Google Scholar

[29]

L. Gao, C. Y. Zhang and X. J. Wang, An improved genetic algorithm for multi-objective flexible job-shop scheduling problem,, Advanced Materials Research, 97 (2010), 2449. Google Scholar

[30]

M. R. Garey, D. S. Johnson and R. Sethi, The complexity of flowshop and jobshop scheduling,, Mathematics of Operations Research, 1 (1976), 117. doi: 10.1287/moor.1.2.117. Google Scholar

[31]

B. Giffler and G. Thompson, Algorithms for solving production scheduling problems,, Operations Research, 8 (1960), 487. doi: 10.1287/opre.8.4.487. Google Scholar

[32]

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning,, Addison-Wesley, (1989). Google Scholar

[33]

R. Graham, E. Lawler, J. Lenstra and A. R. Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey,, Annals of Discrete Mathematics, 5 (1979), 287. doi: 10.1016/S0167-5060(08)70356-X. Google Scholar

[34]

J. Grobler, A. P. Engelbrecht, S. Kok and S. Yadavalli, Metaheuristics for the multi-objective fjsp with sequence-dependent set-up times, auxiliary resources and machine down time,, Annals of Operations Research, 180 (2010), 165. doi: 10.1007/s10479-008-0501-4. Google Scholar

[35]

H. Hashimoto, M. Yagiura and T. Ibaraki, An iterated local search algorithm for the time-dependent vehicle routing problem with time windows,, Discrete Optimization, 5 (2008), 434. doi: 10.1016/j.disopt.2007.05.004. Google Scholar

[36]

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

[37]

J. Hurink, B. Jurisch and M. Thole, Tabu search for the job-shop scheduling problem with multi-purpose machines,, OR Spectrum, 15 (1994), 205. doi: 10.1007/BF01719451. Google Scholar

[38]

A. S. Jain and S. Meeran, Deterministic job-shop scheduling: Past, present and future,, European Journal of Operational Research, 113 (1999), 390. doi: 10.1016/S0377-2217(98)00113-1. Google Scholar

[39]

H. Jia, A. Nee, J. Fuh and Y. Zhang, A modified genetic algorithm for distributed scheduling problems,, Journal of Intelligent Manufacturing, 14 (2003), 351. Google Scholar

[40]

S. Jia and Z.-H. Hu, Path-relinking tabu search for the multi-objective flexible job shop scheduling problem,, Computers & Operations Research, 47 (2014), 11. doi: 10.1016/j.cor.2014.01.010. Google Scholar

[41]

I. Kacem, S. Hammadi and P. Borne, Approach by localization and multiobjective evolutionary optimization for flexible job-shop scheduling problems,, Ieee Transactions on Systems Man and Cybernetics Part C-Applications and Reviews, 32 (2002), 1. doi: 10.1109/TSMCC.2002.1009117. Google Scholar

[42]

I. Kacem, S. Hammadi and P. Borne, Pareto-optimality approach for flexible job-shop scheduling problems: Hybridization of evolutionary algorithms and fuzzy logic,, Mathematics and Computers in Simulation, 60 (2002), 245. doi: 10.1016/S0378-4754(02)00019-8. Google Scholar

[43]

H. Karimi, S. H. A. Rahmati and M. Zandieh, An efficient knowledge-based algorithm for the flexible job shop scheduling problem,, Knowledge-Based Systems, 36 (2012), 236. doi: 10.1016/j.knosys.2012.04.001. Google Scholar

[44]

S. Karthikeyan, P. Asokan and S. Nickolas, A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints,, The International Journal of Advanced Manufacturing Technology, 72 (2014), 1567. doi: 10.1007/s00170-014-5753-3. Google Scholar

[45]

C.-Y. Lee and M. Pinedo, Optimization and heuristics in scheduling,, in Handbook of Applied Optimization (eds. P. M. Pardalos and M. G. Resende), (2002), 569. Google Scholar

[46]

J. Li, Q. Pan, S. Xie and S. Wang, A hybrid artificial bee colony algorithm for flexible job shop scheduling problems,, International Journal of Computers Communications and Control, 6 (2011), 286. Google Scholar

[47]

J. Q. Li, Q. K. Pan and Y. C. Liang, An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems,, Computers and Industrial Engineering, 59 (2010), 647. doi: 10.1016/j.cie.2010.07.014. Google Scholar

[48]

J. Q. Li, Q. K. Pan, P. N. Suganthan and T. J. Chua, A hybrid tabu search algorithm with an efficient neighborhood structure for the flexible job shop scheduling problem,, International Journal of Advanced Manufacturing Technology, 52 (2011), 683. doi: 10.1007/s00170-010-2743-y. Google Scholar

[49]

J. Q. Li, Q. K. Pan and S. X. Xie, A hybrid variable neighborhood search algorithm for solving multi-objective flexible job shop problems,, Computer Science and Information Systems, 7 (2010), 907. doi: 10.2298/CSIS090608017L. Google Scholar

[50]

J.-Q. Li, Q.-K. Pan and M. F. Tasgetiren, A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities,, Applied Mathematical Modelling, 38 (2014), 1111. doi: 10.1016/j.apm.2013.07.038. Google Scholar

[51]

N. Liouane, I. Saad, S. Hammadi and P. Borne, Ant systems and local search optimization for flexible job shop scheduling production,, International Journal of Computers Communications and Control, 2 (2007), 174. Google Scholar

[52]

H. Lourenço, O. Martin and T. Stützle, Iterated local search,, in Handbook of Metaheuristics (eds. F. Glover and G. Kochenberger), (2003), 320. Google Scholar

[53]

H. Lourenço, O. Martin and T. Stützle, Iterated local search: Framework and applications,, in Handbook of Metaheuristics (eds. M. Gendreau and J.-Y. Potvin), (2010), 363. Google Scholar

[54]

M. Mastrolilli and L. Gambardella, Effective neighborhood functions for the flexible job shop problem,, Journal of Scheduling, 3 (2000), 3. doi: 10.1002/(SICI)1099-1425(200001/02)3:1<3::AID-JOS32>3.0.CO;2-Y. Google Scholar

[55]

Z. Michalewicz and D. Fogel, How to Solve It: Modern Heuristics,, Springer-Verlag, (2000). doi: 10.1007/978-3-662-04131-4. Google Scholar

[56]

E. Moradi, S. Ghomi and M. Zandieh, An efficient architecture for scheduling flexible job-shop with machine availability constraints,, International Journal of Advanced Manufacturing Technology, 51 (2010), 325. doi: 10.1007/s00170-010-2621-7. Google Scholar

[57]

E. Moradi, S. Ghomi and M. Zandieh, Bi-objective optimization research on integrated fixed time interval preventive maintenance and production for scheduling flexible job-shop problem,, Expert Systems with Applications, 38 (2011), 7169. doi: 10.1016/j.eswa.2010.12.043. Google Scholar

[58]

G. Moslehi and M. Mahnam, A pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search,, International Journal of Production Economics, 129 (2011), 14. doi: 10.1016/j.ijpe.2010.08.004. Google Scholar

[59]

M. Mousakhani, Sequence-dependent setup time flexible job shop scheduling problem to minimise total tardiness,, International Journal of Production Research, 51 (2013), 3476. doi: 10.1080/00207543.2012.746480. Google Scholar

[60]

M. A. Nascimento, Giffler and thompson's algorithm for job shop scheduling is still good for flexible manufacturing systems,, The Journal of the Operational Research Society, 44 (1993), 521. Google Scholar

[61]

J. A. Oliveira, L. Dias and G. Pereira, Solving the job shop problem with a random keys genetic algorithm with instance parameters,, in 2nd International Conference on Engineering Optimization, (2010). Google Scholar

[62]

I. Ono, M. Yamamura and S. Kobayashi, A genetic algorithm for job-shop scheduling problems using job-based order crossover,, in Evolutionary Computation, (1996), 547. doi: 10.1109/ICEC.1996.542658. Google Scholar

[63]

L. Paquete and T. Stützle, An experimental investigation of iterated local search for coloring graphs,, in Applications of Evolutionary Computing (eds. S. Cagnoni, (2279), 122. Google Scholar

[64]

P. M. Pardalos and O. V. Shylo, An algorithm for the job shop scheduling problem based on global equilibrium search techniques,, Computational Management Science, 3 (2006), 331. doi: 10.1007/s10287-006-0023-y. Google Scholar

[65]

F. Pezzella, G. Morganti and G. Ciaschetti, A genetic algorithm for the flexible job-shop scheduling problem,, Computers and Operations Research, 35 (2008), 3202. doi: 10.1016/j.cor.2007.02.014. Google Scholar

[66]

S. Rahmati, M. Zandieh and M. Yazdani, Developing two multi-objective evolutionary algorithms for the multi-objective flexible job shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 64 (2013), 915. doi: 10.1007/s00170-012-4051-1. Google Scholar

[67]

M. Rajkumar, P. Asokan, N. Anilkumar and T. Page, A grasp algorithm for flexible job-shop scheduling problem with limited resource constraints,, International Journal of Production Research, 49 (2011), 2409. doi: 10.1080/00207541003709544. Google Scholar

[68]

M. Rohaninejad, A. Kheirkhah, P. Fattahi and B. Vahedi-Nouri, A hybrid multi-objective genetic algorithm based on the electre method for a capacitated flexible job shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 77 (2015), 51. doi: 10.1007/s00170-014-6415-1. Google Scholar

[69]

V. Roshanaei, A. Azab and H. ElMaraghy, Mathematical modelling and a meta-heuristic for flexible job shop scheduling,, International Journal of Production Research, 51 (2013), 6247. doi: 10.1080/00207543.2013.827806. Google Scholar

[70]

C. R. Schrich, V. A. Armentano and M. Laguna, Tardiness minimization in a flexible job shop: A tabu search approach,, Journal of Intelligent Manufacturing, 15 (2004), 103. Google Scholar

[71]

X. Shao, W. Liu, Q. Liu and C. Zhang, Hybrid discrete particle swarm optimization for multi-objective flexible job-shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 67 (2013), 2885. doi: 10.1007/s00170-012-4701-3. Google Scholar

[72]

T. Stützle, Iterated local search for the quadratic assignment problem,, European Journal of Operational Research, 174 (2006), 1519. doi: 10.1016/j.ejor.2005.01.066. Google Scholar

[73]

L. Tang and X. Wang, Iterated local search algorithm based on very large-scale neighborhood for prize-collecting vehicle routing problem,, The International Journal of Advanced Manufacturing Technology, 29 (2006), 1246. doi: 10.1007/s00170-005-0014-0. Google Scholar

[74]

J. C. Tay and N. B. Ho, Evolving dispatching rules using genetic programming for solving multi-objective flexible job-shop problems,, Computers and Industrial Engineering, 54 (2008), 453. doi: 10.1016/j.cie.2007.08.008. Google Scholar

[75]

S. J. Wang, B. H. Zhou and L. F. Xi, A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem,, International Journal of Production Research, 46 (2008), 3027. Google Scholar

[76]

X. J. Wang, L. Gao, C. Y. Zhang and X. Y. Shao, A multi-objective genetic algorithm based on immune and entropy principle for flexible job-shop scheduling problem,, International Journal of Advanced Manufacturing Technology, 51 (2010), 757. doi: 10.1007/s00170-010-2642-2. Google Scholar

[77]

Y. Wang, H. Yin and K. Qin, A novel genetic algorithm for flexible job shop scheduling problems with machine disruptions,, The International Journal of Advanced Manufacturing Technology, 68 (2013), 1317. doi: 10.1007/s00170-013-4923-z. Google Scholar

[78]

W. J. Xia and Z. M. Wu, An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems,, Computers and Industrial Engineering, 48 (2005), 409. doi: 10.1016/j.cie.2005.01.018. Google Scholar

[79]

L. N. Xing, Y. W. Chen and K. W. Yang, Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems,, Computational Optimization and Applications, 48 (2011), 139. doi: 10.1007/s10589-009-9244-7. Google Scholar

[80]

M. Yazdani, M. Amiri and M. Zandieh, Flexible job-shop scheduling with parallel variable neighborhood search algorithm,, Expert Systems with Applications, 37 (2010), 678. doi: 10.1016/j.eswa.2009.06.007. Google Scholar

[81]

Y. Yuan and H. Xu, Flexible job shop scheduling using hybrid differential evolution algorithms,, Computers & Industrial Engineering, 65 (2013), 246. doi: 10.1016/j.cie.2013.02.022. Google Scholar

[82]

Y. Yuan and H. Xu, An integrated search heuristic for large-scale flexible job shop scheduling problems,, Computers & Operations Research, 40 (2013), 2864. doi: 10.1016/j.cor.2013.06.010. Google Scholar

[83]

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

[84]

Y. Yuan, H. Xu and J. Yang, A hybrid harmony search algorithm for the flexible job shop scheduling problem,, Applied Soft Computing, 13 (2013), 3259. doi: 10.1016/j.asoc.2013.02.013. Google Scholar

[85]

G. H. Zhang, X. Y. Shao, P. G. Li and L. Gao, An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem,, Computers and Industrial Engineering, 56 (2009), 1309. doi: 10.1016/j.cie.2008.07.021. Google Scholar

[86]

Q. Zhang and J. Sun, Iterated local search with guided mutation,, 2006 IEEE International Conference on Evolutionary Computation, (): 924. Google Scholar

[87]

M. Ziaee, A heuristic algorithm for solving flexible job shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 71 (2014), 519. doi: 10.1007/s00170-013-5510-z. Google Scholar

[88]

N. Zribi, I. Kacem, A. El Kamel and P. Borne, Assignment and scheduling in flexible job-shops by hierarchical optimization,, Ieee Transactions on Systems Man and Cybernetics Part C-Applications and Reviews, 37 (2007), 652. doi: 10.1109/TSMCC.2007.897494. Google Scholar

show all references

References:
[1]

N. Al-Hinai and T. Y. ElMekkawy, An efficient hybridized genetic algorithm architecture for the flexible job shop scheduling problem,, Flexible Services and Manufacturing Journal, 23 (2011), 64. doi: 10.1007/s10696-010-9067-y. Google Scholar

[2]

M. Amiri, M. Zandieh, M. Yazdani and A. Bagheri, A variable neighbourhood search algorithm for the flexible job-shop scheduling problem,, International Journal of Production Research, 48 (2010), 5671. doi: 10.1080/00207540903055743. Google Scholar

[3]

J. Arroyo, G. Nunes and E. Kamke, Iterative local search heuristic for the single machine scheduling problem with sequence dependent setup times and due dates,, in Hybrid Intelligent Systems, 1 (2009), 505. doi: 10.1109/HIS.2009.104. Google Scholar

[4]

A. Bagheri, M. Zandieh, I. Mahdavi and M. Yazdani, An artificial immune algorithm for the flexible job-shop scheduling problem,, Future Generation Computer Systems-the International Journal of Grid Computing-Theory Methods and Applications, 26 (2010), 533. doi: 10.1016/j.future.2009.10.004. Google Scholar

[5]

A. Baykasoglu, Linguistic-based meta-heuristic optimization model for flexible job shop scheduling,, International Journal of Production Research, 40 (2002), 4523. doi: 10.1080/00207540210147043. Google Scholar

[6]

A. Baykasoglu, L. Ozbakir and A. I. Sonmez, Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems,, Journal of Intelligent Manufacturing, 15 (2004), 777. doi: 10.1023/B:JIMS.0000042663.16199.84. Google Scholar

[7]

J. E. Beasley, Population heuristics,, in Handbook of Applied Optimization (eds. P. M. Pardalos and M. G. Resende), (2002). doi: 10.1007/978-1-4757-5362-2. Google Scholar

[8]

D. Behnke and M. J. Geiger, Test Instances for the Flexible Job Shop Scheduling Problem with Work Centers,, Technical report, (2012). Google Scholar

[9]

W. Bozejko, M. Uchronski and M. Wodecki, Parallel hybrid metaheuristics for the flexible job shop problem,, Computers and Industrial Engineering, 59 (2010), 323. doi: 10.1016/j.cie.2010.05.004. Google Scholar

[10]

P. Brandimarte, Routing and scheduling in a flexible job shop by tabu search,, Annals of Operations Research, 41 (1993), 157. Google Scholar

[11]

P. Brucker and R. Schlie, Job-shop scheduling with multipurpose machines,, Computing, 45 (1990), 369. doi: 10.1007/BF02238804. Google Scholar

[12]

M. Caramia and P. Dell'Olmo, Coloring graphs by iterated local search traversing feasible and infeasible solutions,, Discrete Applied Mathematics, 156 (2008), 201. doi: 10.1016/j.dam.2006.07.013. Google Scholar

[13]

J. B. Chambers and J. W. Barnes, Flexible job shop scheduling by tabu search,, 1996., (). Google Scholar

[14]

Y.-L. Chang and R. S. Sullivan, Schedule generation in a dynamic job shop,, International Journal of Production Research, 28 (1990), 65. doi: 10.1080/00207549008942684. Google Scholar

[15]

H. Chen, J. Ihlow and C. Lehmann, A genetic algorithm for flexible job-shop scheduling,, in Robotics and Automation, 2 (1999), 1120. doi: 10.1109/ROBOT.1999.772512. Google Scholar

[16]

T.-C. Chiang and H.-J. Lin, A simple and effective evolutionary algorithm for multiobjective flexible job shop scheduling,, International Journal of Production Economics, 141 (2013), 87. doi: 10.1016/j.ijpe.2012.03.034. Google Scholar

[17]

J.-F. Cordeau, G. Laporte and F. Pasin, An iterated local search heuristic for the logistics network design problem with single assignment,, International Journal of Production Economics, 113 (2008), 626. doi: 10.1016/j.ijpe.2007.10.015. Google Scholar

[18]

M. den Besten, T. Stützle and M. Dorigo, Design of iterated local search algorithms,, in Applications of Evolutionary Computing (ed. E. Boers), (2037), 441. doi: 10.1007/3-540-45365-2_46. Google Scholar

[19]

I. Driss, K. Mouss and A. Laggoun, A new genetic algorithm for flexible job-shop scheduling problems,, Journal of Mechanical Science and Technology, 29 (2015), 1273. doi: 10.1007/s12206-015-0242-7. Google Scholar

[20]

M. Ennigrou and K. Ghedira, New local diversification techniques for flexible job shop scheduling problem with a multi-agent approach,, Autonomous Agents and Multi-Agent Systems, 17 (2008), 270. doi: 10.1007/s10458-008-9031-3. Google Scholar

[21]

I. Essafi, Y. Mati and S. Dauzère-P\'erès, A genetic local search algorithm for minimizing total weighted tardiness in the job-shop scheduling problem,, Computers & Operations Research, 35 (2008), 2599. doi: 10.1016/j.cor.2006.12.019. Google Scholar

[22]

H. Farughi, B. Yousefi Yegane and M. Fathian, A new critical path method and a memetic algorithm for flexible job shop scheduling with overlapping operations,, Simulation, 89 (2013), 264. Google Scholar

[23]

P. Fattahi, M. S. Mehrabad and F. Jolai, Mathematical modeling and heuristic approaches to flexible job shop scheduling problems,, Journal of Intelligent Manufacturing, 18 (2007), 331. doi: 10.1007/s10845-007-0026-8. Google Scholar

[24]

M. Frutos, A. C. Olivera and F. Tohme, A memetic algorithm based on a NSGAII scheme for the flexible job-shop scheduling problem,, Annals of Operations Research, 181 (2010), 745. doi: 10.1007/s10479-010-0751-9. Google Scholar

[25]

J. Gao, M. Gen and L. Y. Sun, Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm,, Journal of Intelligent Manufacturing, 17 (2006), 493. doi: 10.1007/s10845-005-0021-x. Google Scholar

[26]

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

[27]

J. Gao, L. Y. Sun and M. S. Gen, A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems,, Computers and Operations Research, 35 (2008), 2892. doi: 10.1016/j.cor.2007.01.001. Google Scholar

[28]

K. Gao, P. Suganthan, Q. Pan, T. Chua, T. Cai and C. Chong, Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling,, Information Sciences, 289 (2014), 76. doi: 10.1016/j.ins.2014.07.039. Google Scholar

[29]

L. Gao, C. Y. Zhang and X. J. Wang, An improved genetic algorithm for multi-objective flexible job-shop scheduling problem,, Advanced Materials Research, 97 (2010), 2449. Google Scholar

[30]

M. R. Garey, D. S. Johnson and R. Sethi, The complexity of flowshop and jobshop scheduling,, Mathematics of Operations Research, 1 (1976), 117. doi: 10.1287/moor.1.2.117. Google Scholar

[31]

B. Giffler and G. Thompson, Algorithms for solving production scheduling problems,, Operations Research, 8 (1960), 487. doi: 10.1287/opre.8.4.487. Google Scholar

[32]

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning,, Addison-Wesley, (1989). Google Scholar

[33]

R. Graham, E. Lawler, J. Lenstra and A. R. Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey,, Annals of Discrete Mathematics, 5 (1979), 287. doi: 10.1016/S0167-5060(08)70356-X. Google Scholar

[34]

J. Grobler, A. P. Engelbrecht, S. Kok and S. Yadavalli, Metaheuristics for the multi-objective fjsp with sequence-dependent set-up times, auxiliary resources and machine down time,, Annals of Operations Research, 180 (2010), 165. doi: 10.1007/s10479-008-0501-4. Google Scholar

[35]

H. Hashimoto, M. Yagiura and T. Ibaraki, An iterated local search algorithm for the time-dependent vehicle routing problem with time windows,, Discrete Optimization, 5 (2008), 434. doi: 10.1016/j.disopt.2007.05.004. Google Scholar

[36]

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

[37]

J. Hurink, B. Jurisch and M. Thole, Tabu search for the job-shop scheduling problem with multi-purpose machines,, OR Spectrum, 15 (1994), 205. doi: 10.1007/BF01719451. Google Scholar

[38]

A. S. Jain and S. Meeran, Deterministic job-shop scheduling: Past, present and future,, European Journal of Operational Research, 113 (1999), 390. doi: 10.1016/S0377-2217(98)00113-1. Google Scholar

[39]

H. Jia, A. Nee, J. Fuh and Y. Zhang, A modified genetic algorithm for distributed scheduling problems,, Journal of Intelligent Manufacturing, 14 (2003), 351. Google Scholar

[40]

S. Jia and Z.-H. Hu, Path-relinking tabu search for the multi-objective flexible job shop scheduling problem,, Computers & Operations Research, 47 (2014), 11. doi: 10.1016/j.cor.2014.01.010. Google Scholar

[41]

I. Kacem, S. Hammadi and P. Borne, Approach by localization and multiobjective evolutionary optimization for flexible job-shop scheduling problems,, Ieee Transactions on Systems Man and Cybernetics Part C-Applications and Reviews, 32 (2002), 1. doi: 10.1109/TSMCC.2002.1009117. Google Scholar

[42]

I. Kacem, S. Hammadi and P. Borne, Pareto-optimality approach for flexible job-shop scheduling problems: Hybridization of evolutionary algorithms and fuzzy logic,, Mathematics and Computers in Simulation, 60 (2002), 245. doi: 10.1016/S0378-4754(02)00019-8. Google Scholar

[43]

H. Karimi, S. H. A. Rahmati and M. Zandieh, An efficient knowledge-based algorithm for the flexible job shop scheduling problem,, Knowledge-Based Systems, 36 (2012), 236. doi: 10.1016/j.knosys.2012.04.001. Google Scholar

[44]

S. Karthikeyan, P. Asokan and S. Nickolas, A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints,, The International Journal of Advanced Manufacturing Technology, 72 (2014), 1567. doi: 10.1007/s00170-014-5753-3. Google Scholar

[45]

C.-Y. Lee and M. Pinedo, Optimization and heuristics in scheduling,, in Handbook of Applied Optimization (eds. P. M. Pardalos and M. G. Resende), (2002), 569. Google Scholar

[46]

J. Li, Q. Pan, S. Xie and S. Wang, A hybrid artificial bee colony algorithm for flexible job shop scheduling problems,, International Journal of Computers Communications and Control, 6 (2011), 286. Google Scholar

[47]

J. Q. Li, Q. K. Pan and Y. C. Liang, An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems,, Computers and Industrial Engineering, 59 (2010), 647. doi: 10.1016/j.cie.2010.07.014. Google Scholar

[48]

J. Q. Li, Q. K. Pan, P. N. Suganthan and T. J. Chua, A hybrid tabu search algorithm with an efficient neighborhood structure for the flexible job shop scheduling problem,, International Journal of Advanced Manufacturing Technology, 52 (2011), 683. doi: 10.1007/s00170-010-2743-y. Google Scholar

[49]

J. Q. Li, Q. K. Pan and S. X. Xie, A hybrid variable neighborhood search algorithm for solving multi-objective flexible job shop problems,, Computer Science and Information Systems, 7 (2010), 907. doi: 10.2298/CSIS090608017L. Google Scholar

[50]

J.-Q. Li, Q.-K. Pan and M. F. Tasgetiren, A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities,, Applied Mathematical Modelling, 38 (2014), 1111. doi: 10.1016/j.apm.2013.07.038. Google Scholar

[51]

N. Liouane, I. Saad, S. Hammadi and P. Borne, Ant systems and local search optimization for flexible job shop scheduling production,, International Journal of Computers Communications and Control, 2 (2007), 174. Google Scholar

[52]

H. Lourenço, O. Martin and T. Stützle, Iterated local search,, in Handbook of Metaheuristics (eds. F. Glover and G. Kochenberger), (2003), 320. Google Scholar

[53]

H. Lourenço, O. Martin and T. Stützle, Iterated local search: Framework and applications,, in Handbook of Metaheuristics (eds. M. Gendreau and J.-Y. Potvin), (2010), 363. Google Scholar

[54]

M. Mastrolilli and L. Gambardella, Effective neighborhood functions for the flexible job shop problem,, Journal of Scheduling, 3 (2000), 3. doi: 10.1002/(SICI)1099-1425(200001/02)3:1<3::AID-JOS32>3.0.CO;2-Y. Google Scholar

[55]

Z. Michalewicz and D. Fogel, How to Solve It: Modern Heuristics,, Springer-Verlag, (2000). doi: 10.1007/978-3-662-04131-4. Google Scholar

[56]

E. Moradi, S. Ghomi and M. Zandieh, An efficient architecture for scheduling flexible job-shop with machine availability constraints,, International Journal of Advanced Manufacturing Technology, 51 (2010), 325. doi: 10.1007/s00170-010-2621-7. Google Scholar

[57]

E. Moradi, S. Ghomi and M. Zandieh, Bi-objective optimization research on integrated fixed time interval preventive maintenance and production for scheduling flexible job-shop problem,, Expert Systems with Applications, 38 (2011), 7169. doi: 10.1016/j.eswa.2010.12.043. Google Scholar

[58]

G. Moslehi and M. Mahnam, A pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search,, International Journal of Production Economics, 129 (2011), 14. doi: 10.1016/j.ijpe.2010.08.004. Google Scholar

[59]

M. Mousakhani, Sequence-dependent setup time flexible job shop scheduling problem to minimise total tardiness,, International Journal of Production Research, 51 (2013), 3476. doi: 10.1080/00207543.2012.746480. Google Scholar

[60]

M. A. Nascimento, Giffler and thompson's algorithm for job shop scheduling is still good for flexible manufacturing systems,, The Journal of the Operational Research Society, 44 (1993), 521. Google Scholar

[61]

J. A. Oliveira, L. Dias and G. Pereira, Solving the job shop problem with a random keys genetic algorithm with instance parameters,, in 2nd International Conference on Engineering Optimization, (2010). Google Scholar

[62]

I. Ono, M. Yamamura and S. Kobayashi, A genetic algorithm for job-shop scheduling problems using job-based order crossover,, in Evolutionary Computation, (1996), 547. doi: 10.1109/ICEC.1996.542658. Google Scholar

[63]

L. Paquete and T. Stützle, An experimental investigation of iterated local search for coloring graphs,, in Applications of Evolutionary Computing (eds. S. Cagnoni, (2279), 122. Google Scholar

[64]

P. M. Pardalos and O. V. Shylo, An algorithm for the job shop scheduling problem based on global equilibrium search techniques,, Computational Management Science, 3 (2006), 331. doi: 10.1007/s10287-006-0023-y. Google Scholar

[65]

F. Pezzella, G. Morganti and G. Ciaschetti, A genetic algorithm for the flexible job-shop scheduling problem,, Computers and Operations Research, 35 (2008), 3202. doi: 10.1016/j.cor.2007.02.014. Google Scholar

[66]

S. Rahmati, M. Zandieh and M. Yazdani, Developing two multi-objective evolutionary algorithms for the multi-objective flexible job shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 64 (2013), 915. doi: 10.1007/s00170-012-4051-1. Google Scholar

[67]

M. Rajkumar, P. Asokan, N. Anilkumar and T. Page, A grasp algorithm for flexible job-shop scheduling problem with limited resource constraints,, International Journal of Production Research, 49 (2011), 2409. doi: 10.1080/00207541003709544. Google Scholar

[68]

M. Rohaninejad, A. Kheirkhah, P. Fattahi and B. Vahedi-Nouri, A hybrid multi-objective genetic algorithm based on the electre method for a capacitated flexible job shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 77 (2015), 51. doi: 10.1007/s00170-014-6415-1. Google Scholar

[69]

V. Roshanaei, A. Azab and H. ElMaraghy, Mathematical modelling and a meta-heuristic for flexible job shop scheduling,, International Journal of Production Research, 51 (2013), 6247. doi: 10.1080/00207543.2013.827806. Google Scholar

[70]

C. R. Schrich, V. A. Armentano and M. Laguna, Tardiness minimization in a flexible job shop: A tabu search approach,, Journal of Intelligent Manufacturing, 15 (2004), 103. Google Scholar

[71]

X. Shao, W. Liu, Q. Liu and C. Zhang, Hybrid discrete particle swarm optimization for multi-objective flexible job-shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 67 (2013), 2885. doi: 10.1007/s00170-012-4701-3. Google Scholar

[72]

T. Stützle, Iterated local search for the quadratic assignment problem,, European Journal of Operational Research, 174 (2006), 1519. doi: 10.1016/j.ejor.2005.01.066. Google Scholar

[73]

L. Tang and X. Wang, Iterated local search algorithm based on very large-scale neighborhood for prize-collecting vehicle routing problem,, The International Journal of Advanced Manufacturing Technology, 29 (2006), 1246. doi: 10.1007/s00170-005-0014-0. Google Scholar

[74]

J. C. Tay and N. B. Ho, Evolving dispatching rules using genetic programming for solving multi-objective flexible job-shop problems,, Computers and Industrial Engineering, 54 (2008), 453. doi: 10.1016/j.cie.2007.08.008. Google Scholar

[75]

S. J. Wang, B. H. Zhou and L. F. Xi, A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem,, International Journal of Production Research, 46 (2008), 3027. Google Scholar

[76]

X. J. Wang, L. Gao, C. Y. Zhang and X. Y. Shao, A multi-objective genetic algorithm based on immune and entropy principle for flexible job-shop scheduling problem,, International Journal of Advanced Manufacturing Technology, 51 (2010), 757. doi: 10.1007/s00170-010-2642-2. Google Scholar

[77]

Y. Wang, H. Yin and K. Qin, A novel genetic algorithm for flexible job shop scheduling problems with machine disruptions,, The International Journal of Advanced Manufacturing Technology, 68 (2013), 1317. doi: 10.1007/s00170-013-4923-z. Google Scholar

[78]

W. J. Xia and Z. M. Wu, An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems,, Computers and Industrial Engineering, 48 (2005), 409. doi: 10.1016/j.cie.2005.01.018. Google Scholar

[79]

L. N. Xing, Y. W. Chen and K. W. Yang, Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems,, Computational Optimization and Applications, 48 (2011), 139. doi: 10.1007/s10589-009-9244-7. Google Scholar

[80]

M. Yazdani, M. Amiri and M. Zandieh, Flexible job-shop scheduling with parallel variable neighborhood search algorithm,, Expert Systems with Applications, 37 (2010), 678. doi: 10.1016/j.eswa.2009.06.007. Google Scholar

[81]

Y. Yuan and H. Xu, Flexible job shop scheduling using hybrid differential evolution algorithms,, Computers & Industrial Engineering, 65 (2013), 246. doi: 10.1016/j.cie.2013.02.022. Google Scholar

[82]

Y. Yuan and H. Xu, An integrated search heuristic for large-scale flexible job shop scheduling problems,, Computers & Operations Research, 40 (2013), 2864. doi: 10.1016/j.cor.2013.06.010. Google Scholar

[83]

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

[84]

Y. Yuan, H. Xu and J. Yang, A hybrid harmony search algorithm for the flexible job shop scheduling problem,, Applied Soft Computing, 13 (2013), 3259. doi: 10.1016/j.asoc.2013.02.013. Google Scholar

[85]

G. H. Zhang, X. Y. Shao, P. G. Li and L. Gao, An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem,, Computers and Industrial Engineering, 56 (2009), 1309. doi: 10.1016/j.cie.2008.07.021. Google Scholar

[86]

Q. Zhang and J. Sun, Iterated local search with guided mutation,, 2006 IEEE International Conference on Evolutionary Computation, (): 924. Google Scholar

[87]

M. Ziaee, A heuristic algorithm for solving flexible job shop scheduling problem,, The International Journal of Advanced Manufacturing Technology, 71 (2014), 519. doi: 10.1007/s00170-013-5510-z. Google Scholar

[88]

N. Zribi, I. Kacem, A. El Kamel and P. Borne, Assignment and scheduling in flexible job-shops by hierarchical optimization,, Ieee Transactions on Systems Man and Cybernetics Part C-Applications and Reviews, 37 (2007), 652. doi: 10.1109/TSMCC.2007.897494. Google Scholar

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