Skip to main content
SpringerLink
Log in

Iterated Local Search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

We present an Iterated Local Search (ILS) algorithm for solving the single-machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness. The proposed ILS algorithm exhibits several distinguishing features, including a new neighborhood structure called Block Move and a fast incremental evaluation technique, for evaluating neighborhood solutions. Applying the proposed algorithm to solve 120 public benchmark instances widely used in the literature, we achieve highly competitive results compared with a recently proposed exact algorithm and five sets of best solutions of state-of-the-art metaheuristic algorithms in the literature. Specifically, ILS obtains the optimal solutions for 113 instances within a reasonable time, and it outperforms the previous best-known results obtained by metaheuristic algorithms for 34 instances and matches the best results for 82 instances. In addition, ILS is able to obtain the optimal solutions for the remaining seven instances under a relaxed time limit, and its computational efficiency is comparable with the state-of-the-art exact algorithm by Tanaka and Araki (Comput Oper Res 40:344–352, 2013). Finally, on analyzing some important features that affect the performance of ILS, we ascertain the significance of the proposed Block Move neighborhood and the fast incremental evaluation technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. Details of the problem instances are available at http://loki.stockton.edu/~cicirelv/benchmarks.html.

References

  • Anghinolfi, D., & Paolucci, M. (2008). A new ant colony optimization approach for the single machine total weighted tardiness scheduling problem. International Journal of Operations Research, 5(1), 44–60.

    Google Scholar 

  • Anghinolfi, D., & Paolucci, M. (2009). A new discrete particle swarm optimization approach for the single-machine total weighted tardiness scheduling problem with sequence-dependent setup times. European Journal of Operational Research, 193, 73–85.

    Article  Google Scholar 

  • Bilge, Ü., Kurtulan, M., & Kıraç, F. (2007). A tabu search algorithm for the single machine total weighted tardiness problem. European Journal of Operational Research, 176, 1423–1435.

    Article  Google Scholar 

  • Choobineh, F. F., Mohebbi, E., & Khoo, H. (2006). A multi-objective tabu search for a single-machine scheduling problem with sequence-dependent setup times. European Journal of Operational Research, 175, 318–337.

    Article  Google Scholar 

  • Chou, F.-D. (2009). An experienced learning genetic algorithm to solve the single machine total weighted tardiness scheduling problem. Expert Systems with Applications, 36, 3857–3865.

    Article  Google Scholar 

  • Cicirello, V.A. (2006). Non-wrapping order crossover: An order preserving crossover operator that respects absolute position. In Proceedings of the 8th annual conference on genetic and evolutionary computation, Seattle, WA (pp. 1125–1132).

  • Cicirello, V. A., & Smith, S. F. (2005). Enhancing stochastic search performance by value-biased randomization of heuristics. Journal of Heuristics, 11, 5–34.

    Article  Google Scholar 

  • França, P. M., Mendes, A., & Moscato, P. (2001). Theory and methodology: A memetic algorithm for the total tardiness single machine scheduling problem. European Journal of Operational Research, 132, 224–242.

    Article  Google Scholar 

  • Gagné, C., Price, W. L., & Gravel, M. (2002). Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times. Journal of the Operational Research Society, 53(8), 895–906.

    Article  Google Scholar 

  • Gupta, S. R., & Smith, J. S. (2006). Algorithms for single machine total tardiness scheduling with sequence dependent setups. European Journal of Operational Research, 175, 722–739.

    Article  Google Scholar 

  • Kao, G. K., Sewell, E. C., & Jacobson, S. H. (2009). A branch, bound, and remember algorithm for the \(1|r_{i}|\Sigma t_{i}\) scheduling problem. Journal of Scheduling, 12, 163–175.

    Article  Google Scholar 

  • Kirlik, G., & Oguz, C. (2012). A variable neighbourhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine. Computers & Operations Research, 39(7), 1506–1520.

    Article  Google Scholar 

  • Lawler, E. L. (1977). A “pseudopolynomial” algorithm for sequencing jobs to minimize total tardiness. Annals of Discrete Mathematics, 1, 331–342.

    Article  Google Scholar 

  • Lee, Y. H., Bhaskaram, K., & Pinedo, M. (1997). A heuristic to minimize the total weighted tardiness with sequence-dependent setups. IIE Transactions, 29, 45–52.

    Article  Google Scholar 

  • Liao, C. J., & Juan, H. C. (2007). An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups. Computers & Operations Research, 34, 1899–1909.

    Article  Google Scholar 

  • Lin, S. W., & Ying, K. C. (2007). Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics. International Journal of Advanced Manufacturing Technology, 34, 1183–1190.

    Article  Google Scholar 

  • Lourenço, H. R., Martin, O. C., & Stützle, T. (2001). A beginner’s introduction to Iterated Local Search. In Proceedings of 4th metaheuristics international conference, Porto (pp. 16–20).

  • Lourenço, H. R., Martin, O. C., & Stützle, T. (2003). Iterated Local Search. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 321–353). Norwell, MA: Kluwer Academic Publishers.

  • Lü, Z., & Hao, J. K. (2010). Adaptive tabu search for course timetabling. European Journal of Operational Research, 200, 235–244.

    Google Scholar 

  • Lü, Z., & Hao, J. K. (2012). Adaptive neighbourhood search for nurse rostering. European Journal of Operational Research, 218, 865–876.

    Article  Google Scholar 

  • Lü, Z., & Huang, W. (2009). Iterated tabu search for identifying community structure in complex networks. Physical Review E, 80, 026130.

    Article  Google Scholar 

  • Luo, X., & Chu, F. (2006). A branch and bound algorithm of the single machine schedule with sequence dependent setup times for minimizing total tardiness. Applied Mathematics and Computation, 183, 575–588.

    Article  Google Scholar 

  • Pisinger, D., & Ropke, S. (2010). Large neighbourhood search. In M. Gendreau & J.-Y. Potvin (Eds.), Handbook of metaheuristics (pp. 399–419). Boston: Springer.

    Chapter  Google Scholar 

  • Ronconi, D. P., & Powell, W. B. (2010). Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming. Journal of Scheduling, 13, 597–607.

    Article  Google Scholar 

  • Tanaka, S., & Araki, M. (2013). An exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times. Computers & Operations Research, 40, 344–352.

    Article  Google Scholar 

  • Tasgetiren, M. F., Liang, Y. C., Sevkli, M., & Gencyilmaz, G. (2006). Particle swarm optimization and differential evolution for the single machine total weighted tardiness problem. International Journal of Production Research, 44(22), 4737–4754.

    Article  Google Scholar 

  • Tasgetiren, M. F., Pan, Q. K., & Liang, Y. C. (2009). A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times. Computers & Operations Research, 36(6), 1900–1915.

    Article  Google Scholar 

  • Tasgetiren, M. F., Sevkli, M., Liang, Y. C., & Gencyilmaz, G. (2004). Particle swarm optimization algorithm for single machine total weighted tardiness problem. In Proceedings of the IEEE congress on evolutionary computation, Portland, OR (Vol. 2, pp. 1412–1419).

  • Valente, J. M. S., & Alves, R. A. F. S. (2008). Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups. Computers & Operations Research, 35(7), 2388–2405.

    Article  Google Scholar 

  • Van den Akker, J. M., Diepen, G., & Hoogeveen, J. A. (2010). Minimizing total weighted tardiness on a single machine with release dates and equal-length jobs. Journal of Scheduling, 13, 561–576.

    Article  Google Scholar 

  • Wang, X., & Tang, L. (2009). A population-based variable neighbourhood search for the single machine total weighted tardiness problem. Computers & Operations Research, 36, 2105–2110.

    Article  Google Scholar 

  • Ying, K. C., Lin, S. W., & Huang, C.-Y. (2009). Sequencing single-machine tardiness problems with sequence dependent setup times using an iterated greedy heuristic. Expert Systems with Applications, 36, 7087–7092.

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank four anonymous referees for their many helpful comments on earlier versions of our article. The research was supported in part by the Hong Kong Scholars Program, The Hong Kong Polytechnic University under Grant number G-YZ07, The National Natural Science Foundation of China under Grant number 61100144, and The Program for New Century Excellent Talents in University (NCET).

Author information

Authors and Affiliations

  1. SMART, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Hongyun Xu & Zhipeng Lü

  2. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Zhipeng Lü & T. C. E. Cheng

Authors
  1. Hongyun Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhipeng Lü
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. C. E. Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhipeng Lü.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, H., Lü, Z. & Cheng, T.C.E. Iterated Local Search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness. J Sched 17, 271–287 (2014). https://doi.org/10.1007/s10951-013-0351-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-013-0351-z

Keywords

Search

Navigation