pp 1–24 | Cite as

Evolutionary algorithms for multi-objective dual-resource constrained flexible job-shop scheduling problem

  • M. Yazdani
  • M. ZandiehEmail author
  • R. Tavakkoli-Moghaddam
Application Article


This paper presents a multi-objective dual-resource constrained flexible job-shop scheduling problem (MODRCFJSP) with the objectives of minimizing the makespan, critical machine workload and total workload of machines simultaneously. Two types of multi-objective evolutionary algorithms including fast elitist non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are proposed for solving MODRCFJSP. Some efficient mutation and crossover operators are adapted to the special chromosome structure of the problem for producing new solutions in the algorithm’s generations. Besides, we provide controlled elitism based version of NSGA-II and NRGA, namely controlled elitist NSGA-II (CENSGA-II) and controlled elitist NRGA (CENRGA), to optimize MODRCFJSP. To show the performance of the four proposed algorithms, numerical experiments with randomly generated test problems are used. Moreover, different convergence and diversity performance metrics are employed to illustrate the relative performance of the presented algorithms.


Scheduling Flexible job-shop Dual-resource constrained Multi-objective optimization Multi-objective evolutionary algorithm Controlled elitism procedure 



  1. 1.
    Xianzhou, C., Zhenhe, Y.: An improved genetic algorithm for dual-resource constrained flexible job shop scheduling. In: Fourth International Conference on Intelligent Computation Technology and Automation (ICICTA), pp. 42–45 (2011)Google Scholar
  2. 2.
    Lei, D., Guo, X.: Variable neighbourhood search for dual-resource constrained flexible job shop scheduling. Int. J. Prod. Res. 52(9), 2519–2529 (2013)CrossRefGoogle Scholar
  3. 3.
    Yazdani, M., Zandieh, M., Tavakkoli-Moghaddam, R., Jolai, F.: Two meta-heuristic algorithms for the dual-resource constrained flexible job-shop scheduling problem. Scientia Iranica 22(3), 1242–1257 (2015)Google Scholar
  4. 4.
    Paksi, A.B.N., Ma’ruf, A.: Flexible Job-Shop Scheduling with Dual-Resource Constraints to Minimize Tardiness Using Genetic Algorithm. IOP Conference Series: Materials Science and Engineering, p. 114. IOP Publishing Ltd, Bristol (2016)Google Scholar
  5. 5.
    Zheng, X., Wang, L.: A knowledge-guided fruit fly optimization algorithm for dual resource constrained flexible job-shop scheduling problem. Int. J. Prod. Res. 18(1), 1–13 (2016)Google Scholar
  6. 6.
    Wu, R., Li, Y., Guo, S., Xu, W.: Solving the dual-resource constrained flexible job shop scheduling problem with learning effect by a hybrid genetic algorithm. Adv. Mech. Eng. 10(10), 1–14 (2018)Google Scholar
  7. 7.
    Liu, X.X., Lio, C.H., Tao, Z.: Research on Bi-objective scheduling of dual-resource constrained flexible job shop. Adv. Mater. Res. 211–212, 1091–1095 (2011)CrossRefGoogle Scholar
  8. 8.
    Lang, M.T.; Li, H.: Research on dual-resource multi-objective flexible job shop scheduling under uncertainty. In: Proceedings of 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce, pp. 1375–1378 (2011)Google Scholar
  9. 9.
    Gong, G., Deng, Q., Gong, X., Liu, W., Ren, Q.: A new double flexible job-shop scheduling problem integrating processing time, green production, and human factor indicators. J. Clean. Prod. 174(1), 560–576 (2017)Google Scholar
  10. 10.
    Zhang, J., Jie, J., Wang, W., Xu, X.: A hybrid particle swarm optimization for multi-objective flexible job-shop scheduling problem with dual-resources constrained. Int. J. Comput. Sci. Math. 8(6), 526–532 (2017)CrossRefGoogle Scholar
  11. 11.
    Zhong, Q., Yang, H., Tang, T.: Optimization algorithm simulation for dual-resource constrained job-shop scheduling. Int. J. Simul. Model. 17(1), 147–158 (2018)CrossRefGoogle Scholar
  12. 12.
    Deb, K., Agrawal, S., Pratap, A, Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the Parallel Problem Solving From Nature VI (PPSN-VI) Conference, pp. 849–858 (2000)Google Scholar
  13. 13.
    Deb, K.: Multi-objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)Google Scholar
  14. 14.
    Deb, K.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  15. 15.
    Al Jadaan, O., Rajamani, L., Rao, C.R.: Non-dominated ranked genetic algorithm for solving multi-objective optimisation problems: NRGA. J. Theor. Appl. Inf. Technol. 2, 60–67 (2008)Google Scholar
  16. 16.
    Deb, K., Goel, T.: Controlled Elitist Non-dominated Sorting Genetic Algorithms for Better Convergence. Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, pp. 67–81. Springer, Berlin (2001)Google Scholar
  17. 17.
    Suresh, R.K., Mohanasundaram, K.M.: Pareto archived simulated annealing for job shop scheduling with multiple objectives. Int. J. Adv. Manuf. Technol. 29(1–2), 184–196 (2006)CrossRefGoogle Scholar
  18. 18.
    Tavakkoli-Moghaddam, R., Rahimi-Vahed, A., Mirzaei, A.H.: A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: weighted mean completion time and weighted mean tardiness. Inf. Sci. 177(22), 5072–5090 (2007)CrossRefGoogle Scholar
  19. 19.
    Tavakkoli-Moghaddam, R., Rahimi-Vahed, A.R., Mirzaei, A.H.: Solving a multi-objective no-wait flow shop scheduling problem with an immune algorithm. Int. J. Adv. Manuf. Technol. 36(9), 969–981 (2008)CrossRefGoogle Scholar
  20. 20.
    Wang, X., Gao, L., Zhang, G., Shao, X.: A multi-objective genetic algorithm based on immune and entropy principle for flexible job-shop scheduling problem. Int. J. Adv. Manuf. Technol. 51(5–8), 757–767 (2010)CrossRefGoogle Scholar
  21. 21.
    Liang, Y.C., Lo, M.H.: Multi-objective redundancy allocation optimization using a variable neighborhood search algorithm. J. Heuristics 16(3), 511–535 (2010)CrossRefGoogle Scholar
  22. 22.
    Ekbal, A., Saha, S.: A multiobjective simulated annealing approach for classifier ensemble: named entity recognition in Indian languages as case studies. Expert Syst. Appl. 38(12), 14760–14772 (2011)CrossRefGoogle Scholar
  23. 23.
    Naderi, B., Aminnayeri, M., Piri, M., Ha’iri Yazdi, M.H.: Multi-objective no-wait flowshop scheduling problems: models and algorithms. Int. J. Prod. Res. 50(10), 2592–2608 (2012)CrossRefGoogle Scholar
  24. 24.
    Naderi, B., Mousakhani, M., Khalili, M.: Scheduling multi-objective open shop scheduling using a hybrid immune algorithm. Int. J. Adv. Manuf. Technol. 66(5–8), 895–905 (2013)CrossRefGoogle Scholar
  25. 25.
    Khalili-Damghani, K., Abtahi, A.R., Tavana, M.: A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems. Reliab. Eng. Syst. Saf. 111, 58–75 (2013)CrossRefGoogle Scholar
  26. 26.
    Rahmati, S.H.A., Zandieh, M., Yazdani, M.: Developing two multi-objective evolutionary algorithms for the multi-objective flexible job shop scheduling problem. Int. J. Adv. Manuf. Technol. 64(5–8), 915–932 (2013)CrossRefGoogle Scholar
  27. 27.
    Tavanaa, M., Abtahi, A.R., Khalili-Damghani, K.: A new multi-objective multi-mode model for solving preemptive time-cost-quality trade-off project scheduling problems. Expert Syst. Appl. 41(4), 1830–1846 (2014)CrossRefGoogle Scholar
  28. 28.
    Cheng, H.C., Chiang, T.C., Fu, L.C.: A two-stage hybrid memetic algorithm for multiobjective job shop scheduling. Expert Syst. Appl. 38(9), 10983–10998 (2011)CrossRefGoogle Scholar
  29. 29.
    Zhou, A., Qu, B.Y., Li, H., Zhaob, S.Z., Suganthan, P.N., Zhang, Q.: Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evolut. Comput. 1, 32–49 (2011)CrossRefGoogle Scholar
  30. 30.
    Zhang, C., Li, P., Rao, Y., Li, S.: A new hybrid GA/SA algorithm for the job shop scheduling problem. In: European Conference on Evolutionary Computation in Combinatorial Optimization. Berlin, Heidelberg, pp. 246–259 (2005)Google Scholar
  31. 31.
    Zhang, C., Rao, Y., Li, P., Shao, X.: Bilevel genetic algorithm for the flexible job-shop scheduling problem. Chin. J. Mech. Eng. 43(4), 119–124 (2007)CrossRefGoogle Scholar
  32. 32.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evolut. Comput. 2, 117–132 (2003)CrossRefGoogle Scholar
  33. 33.
    Van Veldhuizen, D.A.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. Faculty of the Graduate School of Engineering of the Air Force Institute of Technology, Air University, Dissertation AFIT/DS/ENG/99-01 (1999)Google Scholar
  34. 34.
    Behnamian, J., Ghomi, S.F., Zandieh, M.: A multi-phase covering Pareto-optimal front method to multi-objective scheduling in a realistic hybrid flowshop using a hybrid metaheuristic. Expert Syst. Appl. 36(8), 11057–11069 (2009)CrossRefGoogle Scholar
  35. 35.
    Karimi, N., Zandieh, M., Karamooz, H.R.: Bi-objective group scheduling in hybrid flexible flowshop: a multi-phase approach. Expert Syst. Appl. 37(6), 4024–4032 (2010)CrossRefGoogle Scholar
  36. 36.
    Arabani, A.B., Zandieh, M., Ghomi, S.F.: Multi-objective genetic-based algorithms for a cross-docking scheduling problem. Appl. Soft Comput. 11(8), 4954–4970 (2011)CrossRefGoogle Scholar
  37. 37.
    Li, J.Q., Pan, Q.K., Tasgetiren, M.F.: A discrete artificial bee colony algorithm for the multi- objective flexible job-shop scheduling problem with maintenance activities. Appl. Math. Model. 38(3), 1111–1132 (2014)CrossRefGoogle Scholar
  38. 38.
    Okabe, T., Jin, Y., Sendhoff, B.: A critical survey of performance indices for multi-objective optimisation. In: Congress on Evolutionary Computation, Canberra (2003)Google Scholar
  39. 39.
    Schott, J.R.: Fault tolerant design using single and multicriteria genetic algorithms optimization. Master’s thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA (1995)Google Scholar
  40. 40.
    Tavakkoli-Moghaddama, R., Makui, A., Mazloomic, Z.: A new integrated mathematical model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm. J. Manuf. Syst. 29(2–3), 111–119 (2010)CrossRefGoogle Scholar
  41. 41.
    Tavakkoli-Moghaddam, R., Azarkish, M., Sadeghnejad-Barkousaraie, A.: A new hybrid multi-objective Pareto archive PSO algorithm for a bi-objective job shop scheduling. Expert Syst. Appl. 38(9), 10812–10821 (2011)CrossRefGoogle Scholar
  42. 42.
    Panahi, H., Tavakkoli-Moghaddam, R.: Solving a multi-objective open shop scheduling problem by a novel hybrid ant colony optimization. Expert Syst. Appl. 38(3), 2817–2822 (2011)CrossRefGoogle Scholar
  43. 43.
    Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Swiss Federal Institute of Technology (ETH), Zuerich, Switzerland, Dissertation ETH No. 13398 (1999)Google Scholar
  44. 44.
    Helbig, M., Engelbrecht, A.P.: Performance measures for dynamic multi-objective optimisation algorithms. Inf. Sci. 250(20), 61–81 (2013)CrossRefGoogle Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin BranchIslamic Azad UniversityQazvinIran
  2. 2.Department of Industrial Management, Management and Accounting FacultyShahid Beheshti University, G.C.TehranIran
  3. 3.School of Industrial Engineering, College of EngineeringUniversity of TehranTehranIran

Personalised recommendations