Hybrid optimization algorithms by various structures for a real-world inverse scheduling problem with uncertain due-dates under single-machine shop systems

  • Jianhui Mou
  • Liang Gao
  • Qianjian Guo
  • Rufeng Xu
  • Xinyu Li
S.I. : Emergence in Human-like Intelligence towards Cyber-Physical Systems


This paper investigates the single-machine inverse scheduling problem with adjusted due-dates (SISPAD) which has a strong background in practical industries. In the SISPAD, the parameters values are uncertain, and the objective is to obtain the optimal schedule sequence through minimal adjusting processing parameters or the job sequence for a promising target. First, a SISPAD mathematical model is devised to handle uncertain processing parameters and scheduling problem at the same time. Then, this paper proposes three hybrid algorithms (HVNG) that combine variable neighborhood search (VNS) algorithm and genetic algorithm by using series, parallel, and insert structure for solving the SISPAD. In the proposed HVNG, a well-designed encoding strategy is presented to achieve processing operator and job parameter simultaneous optimization. To improve the diversity and quality of the individuals, a double non-optimal scheduling method is designed to construct initial population. Compared to the fixed neighborhood structure in regular VNS, a dynamic neighborhood set update mechanism is utilized to exploit the potential search space. In addition, three different neighborhood structures are used in the HVNG algorithm. Finally, two set public problem instances are provided for the HVNG algorithm. Empirical studies demonstrate that the proposed algorithm significantly outperforms its rivals.


Inverse scheduling Uncertain due-date Hybrid algorithm Variable neighborhood search 



The authors acknowledge the National Natural Science Foundation of China (Grants: 51605267, 51775216), the Natural Science Foundation of Shandong Province, China (Grant: ZR2016EEQ07), the Colleges and Universities of Shandong Province Science and Technology Plan Projects (Grant: J16LB04), and Program for HUST Academic Frontier Youth Team.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


  1. 1.
    Brucker P, Shakhlevich NV (2009) Inverse scheduling with maximum lateness objective. J Sched 12(5):475–488MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Heuberger C (2004) Inverse combinatorial optimization: a survey on problems, methods and results. J Comb Optim 8:329–361MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Brucker P, Shakhlevich NV (2011) Inverse scheduling: two-machine flow-shop problem. J Sched 14(3):239–256MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Koulamas C (2005) Inverse scheduling with controllable job parameters. Int J Serv Oper Manag 1(1):35–43Google Scholar
  5. 5.
    Chen RJ, Chen F, Tang GC (2005) Inverse problems of a single machine scheduling to minimize the total completion time. J Shanghai Second Polytech Univ 22(2):1–7Google Scholar
  6. 6.
    Chen RJ, Tang GC (2009) Inverse problems of supply chain scheduling and flow shop scheduling. Oper Res Manag Sci 18(2):80–84Google Scholar
  7. 7.
    Chen JF (2015) Unrelated parallel-machine scheduling to minimize total weighted completion time. J Intell Manuf 26(6):1099–1112CrossRefGoogle Scholar
  8. 8.
    Pham H, Lu XW (2012) Inverse problem of total weighted completion time objective with unit processing time on identical parallel machines. J East China Univ Sci Technol 38(6):757–761Google Scholar
  9. 9.
    Li SS, Brucker P, Ng CT, Cheng TE, Shakhlevich NV, Yuan JJ (2013) A note on reverse scheduling with maximum lateness objective. J Sched 16(4):417–422MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Li X, Gao L (2016) An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem. Int J Prod Econ 174:93–110CrossRefGoogle Scholar
  11. 11.
    Chiang TC, Cheng HC, Fu LC (2011) NNMA: an effective memetic algorithm for solving multiobjective permutation flow shop scheduling problems. Expert Syst Appl 38(5):5986–5999CrossRefGoogle Scholar
  12. 12.
    Moschakis IA, Karatza HD (2015) Towards scheduling for Internet-of-Things applications on clouds: a simulated annealing approach. Concurr Comput Pract Exp 27(8):1886–1899CrossRefGoogle Scholar
  13. 13.
    Yannibelli V, Amandi A (2013) Hybridizing a multi-objective simulated annealing algorithm with a multi-objective evolutionary algorithm to solve a multi-objective project scheduling problem. Expert Syst Appl 40(7):2421–2434CrossRefGoogle Scholar
  14. 14.
    Xie Z, Zhang C, Shao X et al (2014) An effective hybrid teaching–learning-based optimization algorithm for permutation flow shop scheduling problem. Adv Eng Softw 77:35–47CrossRefGoogle Scholar
  15. 15.
    Mladenovic N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24:1097–1100MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Hansen P, Mladenović N, Moreno Pérez JA (2010) Variable neighbourhood search: methods and applications. Ann Oper Res 175:367–407MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Djogatović Marko S, Stanojević Milorad J, Mladenović Nenad (2014) A variable neighborhood search particle filter for bearings-only target tracking. Comput Oper Res 52:192–202MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Thomas BW, Manni E (2014) Scheduled penalty variable neighborhood search. Comput Oper Res 52(52):170–180MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Li JQ, Pan QK, Wang FT (2014) A hybrid variable neighborhood search for solving the hybrid flow shop scheduling problem. Appl Soft Comput 24(24):63–77CrossRefGoogle Scholar
  20. 20.
    Adibi MA, Shahrabi J (2014) A clustering-based modified variable neighborhood search algorithm for a dynamic job shop scheduling problem. Int J Adv Manuf Technol 70(9–12):1955–1961CrossRefGoogle Scholar
  21. 21.
    Bilyk A, Mönch L (2012) A variable neighborhood search approach for planning and scheduling of jobs on unrelated parallel machines. J Intell Manuf 23(5):1621–1635CrossRefGoogle Scholar
  22. 22.
    Karimi N, Davoudpour H (2014) A high performing metaheuristic for multi-objective flowshop scheduling problem. Comput Oper Res 52:149–156MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Türkyılmaz A, Bulkan S (2015) A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution. Int J Prod Res 53(6):1832–1848CrossRefGoogle Scholar
  24. 24.
    Moslehi G, Khorasanian D (2014) A hybrid variable neighborhood search algorithm for solving the limited-buffer permutation flow shop scheduling problem with the makespan criterion. Comput Oper Res 52(1):260–268MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Kovačević D, Mladenović N, Petrović B et al (2014) DE-VNS: self-adaptive differential evolution with crossover neighborhood search for continuous global optimization. Comput Oper Res 52:157–169MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Shao W, Pi D (2015) A self-guided differential evolution with neighborhood search for permutation flow shop scheduling. Expert Syst Appl 51:161–176CrossRefGoogle Scholar
  27. 27.
    Marinakis Y, Marinaki M (2013) Particle swarm optimization with expanding neighborhood topology for the permutation flowshop scheduling problem. Soft Comput 17(7):1159–1173CrossRefzbMATHGoogle Scholar
  28. 28.
    Jin L, Zhang C, Shao X (2015) An effective hybrid honey bee mating optimization algorithm for integrated process planning and scheduling problems. Int J Adv Manuf Technol 80(5–8):1–12CrossRefGoogle Scholar
  29. 29.
    Cui Z, Gu X (2015) An improved discrete artificial bee colony algorithm to minimize the makespan on hybrid flow shop problems. Neurocomputing 148(148):248–259CrossRefGoogle Scholar
  30. 30.
    Verela R, Vela CR, Puente J, Gomez A (2003) A knowledge-based evolutionary strategy for scheduling problems with bottlenecks. Eur J Oper Res 145:57–71MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Lam AYS, Li VOK (2010) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput 14:381–399CrossRefGoogle Scholar
  32. 32.
    Jakobovic D, Budin L (2006) Dynamic scheduling with genetic programming. Lect Notes Comput Sci 3905:73–84CrossRefGoogle Scholar
  33. 33.
    Lu C, Xiao S, Li X et al (2016) An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production. Adv Eng Softw 99:161–176CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  • Jianhui Mou
    • 1
  • Liang Gao
    • 2
  • Qianjian Guo
    • 1
  • Rufeng Xu
    • 1
  • Xinyu Li
    • 2
  1. 1.School of Mechanical EngineeringShandong University of TechnologyZiboPeople’s Republic of China
  2. 2.The State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanPeople’s Republic of China

Personalised recommendations