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A modified teaching learning metaheuristic algorithm with opposite-based learning for permutation flow-shop scheduling problem

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Abstract

Teaching-Learning-Based Optimization is one of the well-known metaheuristic algorithm in the research industry. Recently, various population-based algorithms have been developed for solving optimization problems. In this paper, a random scale factor approach is proposed to modify the simple TLBO algorithm. Modified Teaching-Learning-Based Optimization with Opposite-Based-Learning algorithm is applied to solve the Permutation Flow-Shop-Scheduling Problem with the purpose of minimizing the makespan. The OBL approach is used to enhance the quality of the initial population and convergence speed. PFSSP is used extensively for solving scheduling problem, which belongs to the category of NP-hard optimization problems. First, MTLBO is developed to effectively determine the PFSSP using the Largest Order Value rule-based random key, so that individual job schedules are converted into discrete schedules. Second, new initial populations are generated in MTLBO using the Nawaz–Enscore–Ham heuristic mechanism. Finally, the local exploitation ability is enhanced in the MTLBO using effective swap, insert and inverse structures. The performance of proposed algorithm is validated using ten benchmark functions and the Wilcoxon rank test. The computational results and comparisons indicate that the proposed algorithm outperformed over five well-known datasets such as Carlier, Reeves, Heller, Taillards and VRF benchmark test functions, compared to other metaheuristic algorithms. The p-value indicated the significance and superiority of the proposed algorithm over other metaheuristic algorithms.

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References

  1. Pinedo ML (2016) Scheduling: theory, algorithms, and systems. Springer, Berlin. https://doi.org/10.1007/978-1-4614-2361-4

    Book  MATH  Google Scholar 

  2. Grabowski J, Pempera J (2000) Sequencing of jobs in some production system. Eur J Oper Res 125(3):535–550. https://doi.org/10.1016/S0377-2217(99)00224-6

    Article  MathSciNet  MATH  Google Scholar 

  3. Du W, Tang Y, Leung SYS, Tong L, Vasilakos AV, Qian F (2018) Robust order scheduling in the discrete manufacturing industry: a multiobjective optimization approach. IEEE Trans Ind Inf 14(1):253–264. https://doi.org/10.1109/TII.2017.2664080

    Article  Google Scholar 

  4. Hidri L, Gharbi A (2017) New efficient lower bound for the hybrid flow shop scheduling problem with multiprocessor tasks. IEEE Access 5:6121–6133. https://doi.org/10.1109/ACCESS.2017.2696118

    Article  Google Scholar 

  5. Bargaoui H, Driss OB, Ghédira K (2017) Towards a distributed implementation of chemical reaction optimization for the multi-factory permutation flowshop scheduling problem. Procedia Comput Sci 112:1531–1541. https://doi.org/10.1016/j.procs.2017.08.057

    Article  Google Scholar 

  6. Deng F, He Y, Zhou S, Yu Y, Cheng H, Wu X (2018) Compressive strength prediction of recycled concrete based on deep learning. Constr Build Mater 175:562–569

    Article  Google Scholar 

  7. Cho HM, Jeong IJ (2017) A two-level method of production planning and scheduling for bi-objective reentrant hybrid flow shops. Comput Ind Eng 106:174–181. https://doi.org/10.1016/j.cie.2017.02.010

    Article  Google Scholar 

  8. Pan QK (2016) An effective co-evolutionary artificial bee colony algorithm for steelmaking-continuous casting scheduling. Eur J Oper Res 250(3):702–714. https://doi.org/10.1016/j.ejor.2015.10.007

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang Y, Wang J, Liu Y (2017) Game theory based real-time multi-objective flexible job shop scheduling considering environmental impact. J Clean Prod 167:665–679. https://doi.org/10.1016/j.jclepro.2017.08.068

    Article  Google Scholar 

  10. Johnson SM (1954) Optimal two and three stage production schedules with setup times included. Naval Res Logist Q 1(1):61–68. https://doi.org/10.1002/nav.3800010110

    Article  MATH  Google Scholar 

  11. Ruiz R, Stützle T (2008) An iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives. Eur J Oper Res 187(3):1143–1159. https://doi.org/10.1016/j.ejor.2006.07.029

    Article  MATH  Google Scholar 

  12. Ozolins A (2017) Improved bounded dynamic programming algorithm for solving the blocking flow shop problem. Central Eur J Oper Res. https://doi.org/10.1007/s10100-017-0488-5

    Article  MATH  Google Scholar 

  13. Toumi S, Jarboui B, Eddaly M, Rebaï A (2017) Branch-and-bound algorithm for solving blocking flowshop scheduling problems with makespan criterion. Int J Math Oper Res 10(1):34–48. https://doi.org/10.1504/IJMOR.2017.080743

    Article  MathSciNet  MATH  Google Scholar 

  14. Selen WJ, Hott DD (1986) A mixed-integer goal-programming formulation of the standard flow-shop scheduling problem. J Oper Res Soc 37(12):1121–1128. https://doi.org/10.1057/jors.1986.197

    Article  MATH  Google Scholar 

  15. Grabowski J, Wodecki M (2004) A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion. Comput Oper Res 31(11):1891–1909. https://doi.org/10.1016/S0305-0548(03)00145-X

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu J, Zhang J (2014) Exploration-exploitation tradeoffs in metaheuristics: survey and analysis. In: Proceedings of the 33rd Chinese control conference, pp 8633–8638. https://doi.org/10.1109/ChiCC.2014.6896450

  17. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99. https://doi.org/10.1023/A:1022602019183

    Article  Google Scholar 

  18. Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theoret Comput Sci 344(2):243–278. https://doi.org/10.1016/j.tcs.2005.05.020

    Article  MathSciNet  MATH  Google Scholar 

  19. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359. https://doi.org/10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  20. Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: Harmony search. SIMULATION 76(2):60–68. https://doi.org/10.1177/003754970107600201

    Article  Google Scholar 

  21. Yang XS (2009) Firefly algorithms for multimodal optimization. In: Proceedings of the 5th International Conference on Stochastic Algorithms: Foundations and Applications, Springer-Verlag, Berlin, Heidelberg, SAGA’09, pp 169–178

  22. Yang XS (2010) A new metaheuristic bat-inspired algorithm. Springer, Berlin, pp 65–74

    MATH  Google Scholar 

  23. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35. https://doi.org/10.1007/s00366-011-0241-y

    Article  Google Scholar 

  24. Rao R, Savsani V, Vakharia D (2011) Teaching learning based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315. https://doi.org/10.1016/j.cad.2010.12.015

    Article  Google Scholar 

  25. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  26. Wang GG, Deb S, Coelho L (2015a) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bioinspir Comput 12:1–22

    Google Scholar 

  27. Wang GG, Deb S, Cui Z (2015b) Monarch butterfly optimization. Neural Comput Appl. https://doi.org/10.1007/s00521-015-1923-y

    Article  Google Scholar 

  28. Karaboga D, Basturk B (2007) Artificial bee colony (abc) optimization algorithm for solving constrained optimization problems. In: Foundations of fuzzy logic and soft computing. Springer, Berlin, pp 789–798

  29. Rao R (2016) Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7(1):19–34

    Google Scholar 

  30. Wang GG (2016) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memet Comput. https://doi.org/10.1007/s12293-016-0212-3

    Article  Google Scholar 

  31. Zhang Y, fang Song X, wei Gong D, (2017) A return-cost-based binary firefly algorithm for feature selection. Inf Sci 418–419:561–574. https://doi.org/10.1016/j.ins.2017.08.047

    Article  Google Scholar 

  32. Reeves CR (1995) A genetic algorithm for flowshop sequencing. Comput Oper Res 22(1):5–13. https://doi.org/10.1016/0305-0548(93)E0014-K

    Article  MATH  Google Scholar 

  33. Mirabi M, Fatemi Ghomi SMT, Jolai F (2014) A novel hybrid genetic algorithm to solve the make-to-order sequence-dependent flow-shop scheduling problem. J Ind Eng Int 10(2):57. https://doi.org/10.1007/s40092-014-0057-7

    Article  Google Scholar 

  34. Tasgetiren MF, Liang YC, Sevkli M, Gencyilmaz G (2007) A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem. Eur J Oper Res 177(3):1930–1947. https://doi.org/10.1016/j.ejor.2005.12.024

    Article  MATH  Google Scholar 

  35. Liu D, Tan KC, Goh CK, Ho WK (2007) A multiobjective memetic algorithm based on particle swarm optimization. IEEE Trans Syst Man Cybern Part B (Cybern) 37(1):42–50. https://doi.org/10.1109/TSMCB.2006.883270

    Article  Google Scholar 

  36. Gao J, Chen R, Deng W (2013) An efficient tabu search algorithm for the distributed permutation flowshop scheduling problem. Int J Prod Res 51(3):641–651. https://doi.org/10.1080/00207543.2011.644819

    Article  Google Scholar 

  37. Liu Y, Yin M, Gu W (2014) An effective differential evolution algorithm for permutation flow shop scheduling problem. Appl Math Comput 248:143–159. https://doi.org/10.1016/j.amc.2014.09.010

    Article  MATH  Google Scholar 

  38. Li X, Yin M (2013) A hybrid cuckoo search via lévy flights for the permutation flow shop scheduling problem. Int J Prod Res 51(16):4732–4754. https://doi.org/10.1080/00207543.2013.767988

    Article  Google Scholar 

  39. Sioud A, Gagné C (2018) Enhanced migrating birds optimization algorithm for the permutation flow shop problem with sequence dependent setup times. Eur J Oper Res 264(1):66–73. https://doi.org/10.1016/j.ejor.2017.06.027

    Article  MathSciNet  MATH  Google Scholar 

  40. Fernandez-Viagas V, Perez-Gonzalez P, Framinan JM (2018) The distributed permutation flow shop to minimise the total flowtime. Comput Ind Eng 118:464–477. https://doi.org/10.1016/j.cie.2018.03.014

    Article  Google Scholar 

  41. Meng T, Pan QK, Li JQ, Sang HY (2018) An improved migrating birds optimization for an integrated lot-streaming flow shop scheduling problem. Swarm Evol Comput 38:64–78. https://doi.org/10.1016/j.swevo.2017.06.003

    Article  Google Scholar 

  42. Han Y, Gong D, Li J, Zhang Y (2016) Solving the blocking flow shop scheduling problem with makespan using a modified fruit fly optimisation algorithm. Int J Prod Res 54(22):6782–6797. https://doi.org/10.1080/00207543.2016.1177671

    Article  Google Scholar 

  43. Baykasolu A, Hamzadayi A, Köse SY (2014) Testing the performance of teachinglearning based optimization (tlbo) algorithm on combinatorial problems: flow shop and job shop scheduling cases. Inf Sci 276:204–218. https://doi.org/10.1016/j.ins.2014.02.056

    Article  Google Scholar 

  44. Xie Z, Zhang C, Shao X, Lin W, Zhu H (2014) An effective hybrid teachinglearning-based optimization algorithm for permutation flow shop scheduling problem. Adv Eng Softw 77:35–47. https://doi.org/10.1016/j.advengsoft.2014.07.006

    Article  Google Scholar 

  45. Shao W, Pi D, Shao Z (2016) A hybrid discrete optimization algorithm based on teachingprobabilistic learning mechanism for no-wait flow shop scheduling. Knowl Based Syst 107:219–234. https://doi.org/10.1016/j.knosys.2016.06.011

    Article  Google Scholar 

  46. qing Li J, ke Pan Q, Mao K, (2015) A discrete teaching-learning-based optimisation algorithm for realistic flowshop rescheduling problems. Eng Appl Artif Intell 37:279–292. https://doi.org/10.1016/j.engappai.2014.09.015

    Article  Google Scholar 

  47. Shao W, Pi D, Shao Z (2017) An extended teaching-learning based optimization algorithm for solving no-wait flow shop scheduling problem. Appl Soft Comput 61:193–210. https://doi.org/10.1016/j.asoc.2017.08.020

    Article  Google Scholar 

  48. Buddala R, Mahapatra SS (2017) Improved teaching-learning-based and jaya optimization algorithms for solving flexible flow shop scheduling problems. J Ind Eng Int 1:1. https://doi.org/10.1007/s40092-017-0244-4

    Article  Google Scholar 

  49. Abdel-Basset M, Manogaran G, El-Shahat D, Mirjalili S (2018) A hybrid whale optimization algorithm based on local search strategy for the permutation flow shop scheduling problem. Future Gener Comput Syst 85:129–145. https://doi.org/10.1016/j.future.2018.03.020

    Article  Google Scholar 

  50. Rao RV, Patel V (2013) Multi-objective optimization of two stage thermoelectric cooler using a modified teachinglearning-based optimization algorithm. Eng Appl Artif Intell 26(1):430–445. https://doi.org/10.1016/j.engappai.2012.02.016

    Article  Google Scholar 

  51. Satapathy SC, Naik A (2011) Data clustering based on teaching-learning-based optimization. In: Panigrahi BK, Suganthan PN, Das S, Satapathy SC (eds) Swarm, evolutionary, and memetic computing. Springer, Heidelberg, pp 148–156

    Chapter  Google Scholar 

  52. Jin H, Wang Y (2014) A fusion method for visible and infrared images based on contrast pyramid with teaching learning based optimization. Infrared Phys Technol 64:134–142. https://doi.org/10.1016/j.infrared.2014.02.013

    Article  Google Scholar 

  53. Rao RV, Patel V (2013) An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems. Sci Iran 20(3):710–720. https://doi.org/10.1016/j.scient.2012.12.005

    Article  Google Scholar 

  54. Waghmare G (2013) Comments on a note on teachinglearning-based optimization algorithm. Inf Sci 229:159–169. https://doi.org/10.1016/j.ins.2012.11.009

    Article  Google Scholar 

  55. Das S, Konar A, Chakraborty UK (2005) Two improved differential evolution schemes for faster global search. In: Proceedings of the 7th annual conference on genetic and evolutionary computation. GECCO ’05. ACM, New York, pp 991–998. https://doi.org/10.1145/1068009.1068177

  56. Bean JC (1994) Genetic algorithms and random keys for sequencing and optimization. ORSA J Comput 6(2):154–160. https://doi.org/10.1287/ijoc.6.2.154

    Article  MATH  Google Scholar 

  57. Li X, Yin M (2013) An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure. Adv Eng Softw 55:10–31. https://doi.org/10.1016/j.advengsoft.2012.09.003

    Article  Google Scholar 

  58. Qian B, Wang L, Hu R, Wang WL, Huang DX, Wang X (2008) A hybrid differential evolution method for permutation flow-shop scheduling. Int J Adv Manuf Technol 38(7):757–777. https://doi.org/10.1007/s00170-007-1115-8

    Article  Google Scholar 

  59. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06), vol 1, pp 695–701. https://doi.org/10.1109/CIMCA.2005.1631345

  60. Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79. https://doi.org/10.1109/TEVC.2007.894200

    Article  Google Scholar 

  61. Wang H, Wu Z, Rahnamayan S, Kang L (2009) A scalability test for accelerated de using generalized opposition-based learning. In: 2009 ninth international conference on intelligent systems design and applications, pp 1090–1095. https://doi.org/10.1109/ISDA.2009.216

  62. Kaveh A, Ghazaan MI (2017) Enhanced whale optimization algorithm for sizing optimization of skeletal structures. Mech Based Des Struct Mach 45(3):345–362. https://doi.org/10.1080/15397734.2016.1213639

    Article  Google Scholar 

  63. Hansen P, Mladenovi N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130(3):449–467. https://doi.org/10.1016/S0377-2217(00)00100-4

    Article  MathSciNet  MATH  Google Scholar 

  64. Liang J, Qu B, Suganthan P, G A, (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Technical report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore, pp 3–18

  65. Eiben A, Smit S (2011) Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evol Comput 1(1):19–31. https://doi.org/10.1016/j.swevo.2011.02.001

    Article  Google Scholar 

  66. Carlier J, Pinson E (1989) An algorithm for solving the job-shop problem. Manage Sci 35(2):164–176. https://doi.org/10.1287/mnsc.35.2.164

    Article  MathSciNet  MATH  Google Scholar 

  67. Reeves CR, Yamada T (1998) Genetic algorithms, path relinking, and the flowshop sequencing problem. Evol Comput 6(1):45–60. https://doi.org/10.1162/evco.1998.6.1.45

    Article  Google Scholar 

  68. Heller J (1960) Some numerical experiments for an m Œ j flow shop and its decision-theoretical aspects. Oper Res 8(2):178–184. https://doi.org/10.1287/opre.8.2.178

    Article  MathSciNet  MATH  Google Scholar 

  69. Taillard E (1993) Benchmarks for basic scheduling problems. Eur J Oper Res 64(2):278–285. https://doi.org/10.1016/0377-2217(93)90182-M

    Article  MathSciNet  MATH  Google Scholar 

  70. Vallada E, Ruiz R, Framinan JM (2015) New hard benchmark for flowshop scheduling problems minimising makespan. Eur J Oper Res 240(3):666–677. https://doi.org/10.1016/j.ejor.2014.07.033

    Article  MATH  Google Scholar 

  71. Zhao F, Liu Y, Zhang Y, Ma W, Zhang C (2017) A hybrid harmony search algorithm with efficient job sequence scheme and variable neighborhood search for the permutation flow shop scheduling problems. Eng Appl Artif Intell 65:178–199. https://doi.org/10.1016/j.engappai.2017.07.023

    Article  Google Scholar 

  72. Derrac J, Garcia S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18. https://doi.org/10.1016/j.swevo.2011.02.002

    Article  Google Scholar 

  73. Luo Q, Zhou Y, Xie J, Ma M, Li L (2014) Discrete bat algorithm for optimal problem of permutation flow shop scheduling. Sci World J

  74. Lin Q, Gao L, Li X, Zhang C (2015) A hybrid backtracking search algorithm for permutation flow-shop scheduling problem. Comput Ind Eng 85:437–446. https://doi.org/10.1016/j.cie.2015.04.009

    Article  Google Scholar 

  75. Hamdi Imen (2015) Upper and lower bounds for the permutation flowshop scheduling problem with minimal time lags. Optim Lett 9(3):465–482. https://doi.org/10.1007/s11590-014-0761-7

    Article  MathSciNet  MATH  Google Scholar 

  76. Davendra D, Bialic-Davendra M (2013) Scheduling flow shops with blocking using a discrete self-organising migrating algorithm. Int J Prod Res 51(8):2200–2218. https://doi.org/10.1080/00207543.2012.711968

    Article  MATH  Google Scholar 

  77. Ribas I, Companys R, Tort-Martorell X (2011) An iterated greedy algorithm for the flowshop scheduling problem with blocking. Omega 39(3):293–301. https://doi.org/10.1016/j.omega.2010.07.007

    Article  Google Scholar 

  78. Wang L, Pan QK, Tasgetiren MF (2011) A hybrid harmony search algorithm for the blocking permutation flow shop scheduling problem. Comput Ind Eng 61(1):76–83. https://doi.org/10.1016/j.cie.2011.02.013

    Article  Google Scholar 

  79. Nearchou AC (2004) A novel metaheuristic approach for the flow shop scheduling problem. Eng Appl Artif Intell 17(3):289–300. https://doi.org/10.1016/j.engappai.2004.02.008

    Article  Google Scholar 

  80. Zhang C, Ning J, Ouyang D (2010) A hybrid alternate two phases particle swarm optimization algorithm for flow shop scheduling problem. Comput Ind Eng 58(1):1–11. https://doi.org/10.1016/j.cie.2009.01.016

    Article  Google Scholar 

  81. Wang H, Wang W, Sun H, Cui Z, Rahnamayan S, Zeng S (2017) A new cuckoo search algorithm with hybrid strategies for flow shop scheduling problems. Soft Comput 21(15):4297–4307. https://doi.org/10.1007/s00500-016-2062-9

    Article  Google Scholar 

  82. Deb S, Tian Z, Fong S, Tang R, Wong R, Dey N (2018) Solving permutation flow-shop scheduling problem by rhinoceros search algorithm. Soft Comput 22(18):6025–6034. https://doi.org/10.1007/s00500-018-3075-3

    Article  Google Scholar 

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Balande, U., shrimankar, D. A modified teaching learning metaheuristic algorithm with opposite-based learning for permutation flow-shop scheduling problem. Evol. Intel. 15, 57–79 (2022). https://doi.org/10.1007/s12065-020-00487-5

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