A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints

  • S. KarthikeyanEmail author
  • P. Asokan
  • S. Nickolas


In this paper, a hybrid discrete firefly algorithm is presented to solve the multi-objective flexible job shop scheduling problem with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow a process sequence and each operation must be processed on an assigned machine. These constraints are used to balance between the resource limitation and machine flexibility. Three minimisation objectives—the maximum completion time, the workload of the critical machine and the total workload of all machines—are considered simultaneously. In this study, discrete firefly algorithm is adopted to solve the problem, in which the machine assignment and operation sequence are processed by constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. Meanwhile, local search method with neighbourhood structures is hybridised to enhance the exploitation capability. Benchmark problems are used to evaluate and study the performance of the proposed algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.


Flexible job shop scheduling Hybrid discrete firefly algorithm Multi-objective optimisation Limited resource constraints Local search 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pinedo M (2002) Scheduling: theory, algorithms and systems. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  2. 2.
    Garey MR, Johnson DS, Sethi R (1976) The complexity of flowshop and jobshop scheduling. Math Oper Res 1(2):117–129MathSciNetzbMATHGoogle Scholar
  3. 3.
    Du, X., Li, Z., & Xiong, W. (2008) Flexible job shop scheduling problem solving based on genetic algorithm with model constraints. IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2008, Singapore, pp 1239–1243Google Scholar
  4. 4.
    Xia WJ, Wu ZM (2005) An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Comput Ind Eng 48(2):409–425Google Scholar
  5. 5.
    Chan FTS, Wong TC, Chan LY (2006) Flexible job-shop scheduling problem under resource constraints. Int J Prod Res 44(11):2071–2089zbMATHGoogle Scholar
  6. 6.
    Aggoune R, Portmann MC (2006) Flow shop scheduling problem with limited machine availability: a heuristic approach. Int J Prod Econ 99(1):4–15Google Scholar
  7. 7.
    Gao J, Gen M, Sun L (2006) Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm. J Intell Manuf 17(4):493–507Google Scholar
  8. 8.
    Leon VJ, Wu SD (1992) On scheduling with ready times, due dates and vacations. Nav Res Logist 39(1):53–65zbMATHGoogle Scholar
  9. 9.
    Qi X, Chen T, Tu F (1999) Scheduling the maintenance on a single machine. J Oper Res Soc 1071–1078zbMATHGoogle Scholar
  10. 10.
    Schmidt G (2000) Scheduling with limited machine availability. Eur J Oper Res 121(1):1–15MathSciNetzbMATHGoogle Scholar
  11. 11.
    Gharbi A, Haouari M (2005) Optimal parallel machines scheduling with availability constraints. Discret Appl Math 148:63–87MathSciNetzbMATHGoogle Scholar
  12. 12.
    Liao CJ, Shyur DL, Lin CH (2005) Makespan minimization for two parallel machines with an availability constraint. Eur J Oper Res 160:445–456zbMATHGoogle Scholar
  13. 13.
    Aggoune R (2004) Minimizing the makespan for the flow shop scheduling problem with availability constraints. Eur J Oper Res 153:534–543MathSciNetzbMATHGoogle Scholar
  14. 14.
    Allaoui H, Artiba A (2006) Scheduling two-stage hybrid flow shop with availability. Comput Oper Res 33(5):1399–1419MathSciNetzbMATHGoogle Scholar
  15. 15.
    Mauguière P, Billaut JC, Bouquard JL (2005) New single machine and job-shop scheduling problems with availability constraints. J Sched 8(3):211–231MathSciNetzbMATHGoogle Scholar
  16. 16.
    Zribi N, El Kamel A, Borne P (2008) Minimizing the makespan for the MPM job-shop with availability constraints. Int J Prod Econ 112(1):151–160Google Scholar
  17. 17.
    Lei D (2010) Fuzzy job shop scheduling problem with availability constraints. Comput Ind Eng 58(4):610–617Google Scholar
  18. 18.
    Rajkumar M, Asokan P, Anilkumar N, Page T (2011) A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints. Int J Prod Res 49(8):2409–2423Google Scholar
  19. 19.
    Kacem I, Hammadi S, Borne P (2002) Approach by localization and multiobjective evolutionary optimization for flexible job-shop scheduling problems. IEEE Syst Man Cybern 32(1):1–13zbMATHGoogle Scholar
  20. 20.
    Kacem I, Hammadi S, Borne P (2002) Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic. Math Comput Simul 60(3):245–276MathSciNetzbMATHGoogle Scholar
  21. 21.
    Tay JC, Ho NB (2008) Evolving dispatching rules using genetic programming for solving multi-objective flexible job-shop problems. Comput Ind Eng 54(3):453–473Google Scholar
  22. 22.
    Gao J, Sun L, Gen M (2008) A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems. Comput Oper Res 35(9):2892–2907MathSciNetzbMATHGoogle Scholar
  23. 23.
    Zhang G, Shao X, Li P, Gao L (2009) An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem. Comput Ind Eng 56(4):1309–1318Google Scholar
  24. 24.
    Xing LN, Chen YW, Yang KW (2009) An efficient search method for multi-objective flexible job shop scheduling problems. J Intell Manuf 20:283–293Google Scholar
  25. 25.
    Li JQ, Pan QK, Liang YC (2010) An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems. Comput Ind Eng 59(4):647–662Google Scholar
  26. 26.
    Moslehi G, Mahnam M (2011) A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search. Int J Prod Econ 129(1):14–22Google Scholar
  27. 27.
    Li J, Pan Q, Xie S (2012) An effective shuffled frog-leaping algorithm for multi-objective flexible job shop scheduling problems. Appl Math Comput 218(18):9353–9371MathSciNetzbMATHGoogle Scholar
  28. 28.
    Rahmati SHA, Zandieh M, Yazdani M (2013) Developing two multi-objective evolutionary algorithms for the multi-objective flexible job shop scheduling problem. Int J Adv Manuf Technol 64(5–8):915–932Google Scholar
  29. 29.
    Shao X, Liu W, Liu Q, Zhang C (2013) Hybrid discrete particle swarm optimization for multi-objective flexible job-shop scheduling problem. Int J Adv Manuf Technol 67(9–12):2885–2901Google Scholar
  30. 30.
    Yang X (2008) Nature-inspired metaheuristic algorithm. Luniver Press, BristolGoogle Scholar
  31. 31.
    Yang XS (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-Inspired Comput 2(2):78–84Google Scholar
  32. 32.
    Łukasik S, Żak S (2009) Firefly algorithm for continuous constrained optimization tasks. In Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems, Springer Berlin Heidelberg pp 97–106Google Scholar
  33. 33.
    Sayadi MK, Ramezanian R, Ghaffari-Nasab N (2010) A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems. Int J Ind Eng Comput 1(1):1–10Google Scholar
  34. 34.
    Jati GK (2011) Evolutionary discrete firefly algorithm for travelling salesman problem. In Adaptive and intelligent systems. Springer Berlin Heidelberg, pp 393–403Google Scholar
  35. 35.
    Khadwilard A, Chansombat S, Thepphakorn T, Chainate W, Pongcharoen P (2012) Application of firefly algorithm and its parameter setting for job shop scheduling. J Ind Technol 8(1):49–58Google Scholar
  36. 36.
    Marichelvam MK, Prabaharan T, Yang XS (2012) A discrete firefly algorithm for the multi-objective hybrid flowshop scheduling problems. IEEE Transactions on Evolutionary Computation 99Google Scholar
  37. 37.
    Yang XS (2013) Multiobjective firefly algorithm for continuous optimization. Eng Comput 29(2):175–184Google Scholar
  38. 38.
    Vahedi Nouri B, Fattahi P, Ramezanian R (2013) Hybrid firefly-simulated annealing algorithm for the flow shop problem with learning effects and flexible maintenance activities. Int J Prod Res 51(12):3501–3515Google Scholar
  39. 39.
    Hsu T, Dupas R, Jolly D, Goncalves G (2002) Evaluation of mutation heuristics for solving a multiobjective flexible job shop by an evolutionary algorithm. IEEE Syst Man Cybern 5:6Google Scholar
  40. 40.
    Yang XS (2009) Firefly algorithm for multimodal optimization. In stochastic algorithms: Foundations and applications, 2009. Lecture notes in computer science vol 5792. Springer Berlin Heidelberg, pp 169--178 Google Scholar
  41. 41.
    Pezzella F, Morganti G, Ciaschetti G (2008) A genetic algorithm for the flexible job-shop scheduling problem. Comput Oper Res 35(10):3202–3212zbMATHGoogle Scholar
  42. 42.
    Brandimarte P (1993) Routing and scheduling in a flexible job shop by tabu search. Ann Oper Res 41(3):157–183zbMATHGoogle Scholar
  43. 43.
    Kuo I, Horng SJ, Kao TW, Lin TL, Lee CL, Terano T, Pan Y (2009) An efficient flow-shop scheduling algorithm based on a hybrid particle swarm optimization model. Expert Syst Appl 36(3):7027–7032Google Scholar
  44. 44.
    Wang X, Gao L, Zhang C, Shao X (2010) 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):757–767Google Scholar
  45. 45.
    Nowicki E, Smutnicki C (1996) A fast taboo search algorithm for the job shop problem. Management science 42(6):797–813zbMATHGoogle Scholar
  46. 46.
    Dell’Amico M, Trubian M (1993) Applying tabu search to the job-shop scheduling problem. Ann Oper Res 41(3):231–252zbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Production EngineeringNational Institute of TechnologyTiruchirappalliIndia
  2. 2.Department of Computer ApplicationsNational Institute of TechnologyTiruchirappalliIndia

Personalised recommendations