Skip to main content
SpringerLink
Log in

Scatter search for minimizing weighted tardiness in a single machine scheduling with setups

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

Single machine scheduling problems have many real-life applications and may be hard to solve due to the particular characteristics of some production environments. In this paper, we tackle the single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the weighted tardiness. To solve this problem, we propose a scatter search algorithm which uses path relinking in its core. This algorithm is enhanced with some procedures to speed-up the neighbors’ evaluation and with some diversification and intensification techniques, the latter taking some elements from iterated local search. We conducted an experimental study across a well-known set of instances to analyze the contribution of each component to the overall performance of the algorithm, as well as to compare our proposal with the state-of-the-art metaheuristics, obtaining competitive results. We also propose a new benchmark with larger and more challenging instances and provide the first results for them.

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

Similar content being viewed by others

Notes

  1. http://loki.stockton.edu/~cicirelv/benchmarks.html.

  2. https://www.passmark.com/.

  3. https://www.msu.edu/~rubin/files/research.html.

  4. http://www.uqac.ca/c3gagne/.

  5. Repository section in http://www.di.uniovi.es/iscop.

References

  • Adler, L., Fraiman, N., Kobacker, E., Pinedo, M., Plotnitcoff, J., Wu, T.: Bpss: a scheduling system for the packaging industry. Oper. Res. 41, 641–648 (1993)

    Article  Google Scholar 

  • Allahverdi, A., Ng, C., Cheng, T., Kovalyov, M.Y.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187, 985–1032 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Anghinolfi, D., Paolucci, M.: A new ant colony optimization approach for the single machine total weighted tardiness scheduling problem. Int. J. Oper. Res. 5(1), 44–60 (2008)

    MathSciNet  MATH  Google Scholar 

  • Anghinolfi, D., Paolucci, M.: A new discrete particle swarm optimization approach for the single-machine total weighted tardiness scheduling problem with sequence-dependent setup times. Eur. J. Oper. Res. 193, 73–85 (2009)

    Article  MATH  Google Scholar 

  • Bozejko, W.: Parallel path relinking method for the single machine total weighted tardiness problem with sequence-dependent setups. J. Intell. Manuf. 21, 777–785 (2010)

    Article  Google Scholar 

  • Bozejko, W., Wodecki, M.: Solving permutational routing problems by population-based metaheuristics. Comput. Ind. Eng. 57, 269–276 (2009)

    Article  Google Scholar 

  • Bülbül, K.: A hybrid shifting bottleneck-tabu serach heuristic for the job shop total weighted tardiness problem. Comput. Oper. Res. 38(6), 967–983 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Cano-Belmán, J., Ríos Mercado, R.Z., Bautista, J.: A scatter search based hyper-heuristic for sequencing a mixed-model assembly line. J. Heuristics 16(6), 749–770 (2010)

  • Chao, C., Liao, C.: A discrete electromagnetism-like mechanism for single machine total weighted tardiness problem with sequence-dependent setup times. Appl. Soft Comput. 12, 3079–3087 (2012)

    Article  Google Scholar 

  • Chiang, W., Fox, M., Ow, P.: Factory model and test data descriptions: opis experiments. In: Technical Reports CMU-RI-TR-90-05, The robotics institute, Carnegie Mellon University (1990)

  • Cicirello, V.: 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, pp. 1125–1132. Seattle, WA (2006)

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

    Article  MATH  Google Scholar 

  • Conner, G.: 10 questions. Manuf. Eng. Mag., pp. 93–99 (2009)

  • Escobar, J.W., Linfati, R., Toth, P., Baldoquin, M.G.: A hybrid granular tabu search algorithm for the multi-depot vehicle routing problem. J. Heuristics 20(5), 483–509 (2014)

    Article  Google Scholar 

  • Gagné, C., Price, W., Gravel, M.: Comparing an aco algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times. J. Oper. Res. Soc. 53, 895–906 (2002)

    Article  MATH  Google Scholar 

  • Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977)

    Article  Google Scholar 

  • Glover, F.: A template for scatter search and path relinking. In: Hao, J., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds.) Artificial Evolution, vol. 1363 of Lecture Notes in Computer Science, pp. 13–54. Springer, Berlin (1998)

    Google Scholar 

  • González, M.A., González-Rodríguez, I., Vela, C., Varela, R.: An efficient hybrid evolutionary algorithm for scheduling with setup times and weighted tardiness minimization. Soft Comput. 16, 2097–2113 (2012)

    Article  Google Scholar 

  • González, M.A., Oddi, A., Rasconi, R., Varela, R.: Scatter search with path relinking for the job shop with time lags and setup times. Comput. Oper. Res. 60, 37–54 (2015a)

    Article  MathSciNet  MATH  Google Scholar 

  • González, M.A., Vela, C.R., Varela, R.: Scatter search with path relinking for the flexible job shop scheduling problem. Eur. J. Oper. Res. 245(1), 35–45 (2015b)

    Article  MathSciNet  MATH  Google Scholar 

  • González, M.A., Vela, C.R., Varela, R., González-Rodríguez, I.: An advanced scatter search algorithm for solving job shops with sequence dependent and non-anticipatory setups. AI Commun. 28, 179–193 (2015c)

    MathSciNet  Google Scholar 

  • González Rodríguez, I., Vela, C.R., Hernández-Arauzo, A., Puente, J.: Improved local search for job shop scheduling with uncertain durations. In: Proceedings of the Nineteenth International Conference on Automated Planning and Scheduling (ICAPS-2009), pp. 154–161. AAAI Press, Thesaloniki (2009)

  • Graham, R., Lawler, E., Lenstra, J., Rinnooy Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 4, 287–326 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • Graves, S.: A review of production scheduling. Oper. Res. 29, 646–675 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • Guo, Q., Tang, L.: An improved scatter search algorithm for the single machine total weighted tardiness scheduling problem with sequence-dependent setup times. Appl. Soft Comput. 29, 184–195 (2015)

    Article  Google Scholar 

  • Ibañez, O., Cordón, O., Damas, S., Santamaría, J.: An advanced scatter search design for skull-face overlay in craniofacial superimposition. Expert Syst. Appl. 39(1), 1459–1473 (2012)

    Article  Google Scholar 

  • Kirlik, G., Oguz, C.: A variable neighborhood search for minimizing total weighted tardiness with sequence dependent setup times on a single machine. Comput. Oper. Res. 39, 1506–1520 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Laguna, M., Gortázar, F., Gallego, M., Duarte, A., Martí, R.: A black-box scatter search for optimization problems with integer variables. J. Global Optim. 58, 497–516 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Laguna, M., Martí, R.: Scatter Search: Methodology and Implementations in C. Operations Research/Computer Science Interfaces Series. Springer, New York (2012)

    MATH  Google Scholar 

  • Lawler, E.: A ’pseudopolynomial’ algorithm for sequencing jobs to minimize total tardiness. Ann. Discrete Math. 1, 331–342 (1977)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Lenstra, J., Rinnooy Kan, A., Brucker, P.: Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  • Liao, C., Juan, H.: An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups. Comput. Oper. Res. 34, 1899–1909 (2007)

    Article  MATH  Google Scholar 

  • Liao, C., Tsou, H., Huang, K.: Neighborhood search procedures for single machine tardiness scheduling with sequence-dependent setups. Theor. Comput. Sci. 434, 45–52 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, S., Ying, K.: Solving single-machine total weighted tardiness problems with sequence-dependent setup times by meta-heuristics. Int. J. Adv. Manuf. Technol. 34(11–12), 1183–1190 (2007)

    Article  Google Scholar 

  • Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated Local Search, pp. 320–353. Springer, Boston (2003)

  • Luo, J., Hu, Y.: A new grasp and path relinking for single machine scheduling with sequence dependent setups. In: Proceedings of 2013 10th IEEE International Conference on Control and Automation (ICCA), pp. 490–495 (2013)

  • Naderi, B., Ruiz, R.: A scatter search algorithm for the distributed permutation flowshop scheduling problem. Eur. J. Oper. Res. 239(2), 323–334 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Nasiri, M., Kianfar, F.: A guided tabu search/path relinking algorithm for the job shop problem. Int. J. Adv. Manuf. Technol. 58(9–12), 1105–1113 (2012)

    Article  Google Scholar 

  • Nebro, A.J., Luna, F., Alba, E., Dorronsoro, B., Durillo, J.J., Beham, A.: Abyss: adapting scatter search to multiobjective optimization. IEEE Trans. Evolut. Comput. 12(4), 439–457 (2008)

    Article  Google Scholar 

  • Nguyen, P.K., Crainic, T.G., Toulouse, M.: A hybrid generational genetic algorithm for the periodic vehicle routing problem with time windows. J. Heuristics 20(4), 383–416 (2014)

    Article  Google Scholar 

  • Nowicki, E., Smutnicki, C.: An advanced tabu search algorithm for the job shop problem. J. Sched. 8(2), 145–159 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Nowicki, E., Smutnicki, C.: Some aspects of scatter search in the flow-shop problem. Eur. J. Oper. Res. 169(2), 654–666 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Palacios, J.J., González-Rodríguez, I., Vela, C.R., Puente, J.: Robust multiobjective optimisation for fuzzy job shops problems. Appl. Soft Comput. (2016). doi:10.1016/j.asoc.2016.07.004

  • Pantrigo, J.J., Martí, R., Duarte, A., Pardo, E.G.: Scatter search for the cutwidth minimization problem. Ann. Oper. Res. 199(1), 285–304 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Panwalkar, S., Dudek, R., Smith, M.: Sequencing research and the industrial scheduling problem. In: Symposium on the Theory of Scheduling and Its Applications. Springer, New York, pp. 29–38 (1973)

  • Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems. Prentice Hall, Upper Saddle River (1995)

  • Rahimi-Vahed, A., Crainic, T., Gendreau, M., Rei, W.: A path relinking algorithm for a multi-depot periodic vehicle routing problem. J. Heuristics 19(3), 497–524 (2013)

    Article  MATH  Google Scholar 

  • Raman, N., Rachamadugu, R., Talbot, F.: Real-time scheduling of an automated manufacturing center. Eur. J. Oper. Res. 40, 222–242 (1989)

    Article  MATH  Google Scholar 

  • Resende, M.G., Ribeiro, C.C., Glover, F., Martí, R.: Scatter Search and Path-Relinking: Fundamentals, Advances, and Applications, pp. 87–107. Springer, Boston (2010)

  • Rubin, P., Ragatz, G.: Scheduling in a sequence dependent setup environment with genetic search. Comput. Oper. Res. 22(1), 85–99 (1995)

    Article  MATH  Google Scholar 

  • Ruiz, R., Maroto, C.: A comprehensive review and evaluation of permutation flowshop heuristics. Eur. J. Oper. Res. 165(2), 479–494 (2005)

    Article  MATH  Google Scholar 

  • Russell, R.A., Chiang, W.-C.: Scatter search for the vehicle routing problem with time windows. Eur. J. Oper. Res. 169(2), 606–622 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Sen, T., Gupta, S.: A state-of-art survey of static scheduling research involving due date. OMEGA 12, 63–76 (1984)

    Article  Google Scholar 

  • Subramanian, A., Battarra, M., Potts, C.: An iterated local search heuristic for the single machine total weighted tardiness scheduling problem with sequence-dependent setup times. Int. J. Prod. Res. 52(9), 2729–2742 (2014)

    Article  Google Scholar 

  • Tanaka, S., Araki, M.: An exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times. Comput. Oper. Res. 40, 344–352 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Tasgetiren, M.F., Pan, Q.-K., Liang, Y.-C.: A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times. Comput. Oper. Res. 36, 1900–1915 (2009)

    Article  MATH  Google Scholar 

  • Valente, J., Alves, R.: Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups. Comput. Oper. Res. 35, 2388–2405 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Vela, C.R., Varela, R., González, M.A.: Local search and genetic algorithm for the job shop scheduling problem with sequence dependent setup times. J. Heuristics 16, 139–165 (2010)

    Article  MATH  Google Scholar 

  • Wang, X., Tang, L.: A hybrid metaheuristic for the prize-collecting single machine scheduling problem with sequence-dependent setup times. Comput. Oper. Res. 37(9), 1624–1640 (2010)

    Article  MATH  Google Scholar 

  • Wilbrecht, J., Prescott, W.: The influence of setup time on job shop performance. Manag. Sci. 16(4), 391–401 (1969)

    Article  Google Scholar 

  • Xu, H., Lu, Z., Cheng, T.: Iterated local search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness. J. Sched. 17(3), 271–287 (2014a)

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, H., Lu, Z., Yin, A., Shen, L., Buscher, U.: A study of hybrid evolutionary algorithms for single machine scheduling problem with sequence-dependent setup times. Comput. Oper. Res. 50, 47–60 (2014b)

    Article  MathSciNet  MATH  Google Scholar 

  • Yamada, T., Nakano, R.: Scheduling by genetic local search with multi-step crossover. In: Proceedings of Fourth International Conference On Parallel Problem Solving from Nature (PPSN IV 1996), pp. 960–969 (1996)

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

    Article  Google Scholar 

Download references

Acknowledgements

All authors are supported by the Spanish Government under research Project TIN2016-79190-R. We would like to thank Fatih Taçgetiren, Wojciech Boźejko, Hongyun Xu, Gokhan Kirlik, Maria Battarra and Jiaxiang Luo for sending us the detailed results and/or the source code of their excellent papers. We also thank our colleague of the University of Oviedo, Susana Montes, for her supervision in the statistical analysis.

Author information

Authors and Affiliations

  1. Department of Computing, University of Oviedo, Campus de Viesques, 33204, Gijón, Spain

    Miguel A. González, Juan José Palacios, Camino R. Vela & Alejandro Hernández-Arauzo

Authors
  1. Miguel A. González
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan José Palacios
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Camino R. Vela
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alejandro Hernández-Arauzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel A. González.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

González, M.A., Palacios, J.J., Vela, C.R. et al. Scatter search for minimizing weighted tardiness in a single machine scheduling with setups. J Heuristics 23, 81–110 (2017). https://doi.org/10.1007/s10732-017-9325-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-017-9325-1

Keywords

Search

Navigation