Journal of Intelligent Manufacturing

, Volume 21, Issue 6, pp 777–785 | Cite as

Parallel path relinking method for the single machine total weighted tardiness problem with sequence-dependent setups

  • Wojciech Bożejko


We propose a new method of sequential and parallel speeding up of the process of solving a single machine scheduling problem with total tardiness cost function. This improvement is done on two levels: generating a neighborhood inside path relinking method (basing on new approach—blocks in solutions) and parallelization of generating paths. The obtained results are compared to the benchmark ones taken from the literature. It was possible to find new the best solutions for many benchmark instances by using the proposed method.


Scatter search Single machine Setups 


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  1. Alba E., Troya J.M. (2001) Analyzing synchronous and asynchronous parallel distributed genetic algorithms. Future Generation Computer Systems 17: 451–465CrossRefGoogle Scholar
  2. Badeau P., Guertin F., Gendreau M., Potvin J.Y., Taillard E. (1997) A parallel tabu search heuristic for the vehicle routing problem with time windows. Transportation Research-C 5: 109–122CrossRefGoogle Scholar
  3. Bożejko, W., & Wodecki, M. (2004). Parallel genetic algorithm for minimizing total weighted completion time. In Lecture Notes in Computer Science No. 3070 (pp. 400–405). Springer.Google Scholar
  4. Cicirello, V. A. (2006). Non-wrapping order crossover: An order preserving crossover operator that respect absolute position. In 8th Annual genetic and evolutionary computation conference GECCO 2006 (pp. 1125–1131). ACM Press.Google Scholar
  5. Cicirello V.A., Smith S.F. (2005) Enhancing stochastic search performance by value-based randomization of heuristics. Journal of Heuristics 11: 5–34CrossRefGoogle Scholar
  6. Crainic, T. G., & Toulouse, M. (1998). Parallel metaheuristics. In T. G. Crainic & G. Laporte (Eds.), Fleet management and logistics (pp. 205–251). Kluwer.Google Scholar
  7. Fiechter C.N. (1994) A parallel tabu search algorithm for large traveling salesman problems. Discrete Applied Mathematics 51: 243–267CrossRefGoogle Scholar
  8. 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: 895–906CrossRefGoogle Scholar
  9. James T., Rego C., Glover F. (2005) Sequential and Parallel Path-Relinking Algorithms for the Quadratic Assignment Problem. IEEE Intelligent Systems 20(4): 58–65Google Scholar
  10. Lee Y.H., Bhaskaran K., Pinedo M. (1997) A heuristic to minimize the total weighted tardiness with sequence-dependent setups. IIE Transactions 29: 45–52CrossRefGoogle Scholar
  11. Lenstra J.K., Rinnoy Kan A.G.H., Brucker P. (1977) Complexity of Machine Scheduling Problems. Annals of Discrete Mathematics 1: 343–362CrossRefGoogle Scholar
  12. Liao C.-J., Juan H.C. (2007) An ant opimization for single-machine tardiness shceduling with sequence-dependent setups. Computers & Operations Research 34: 1899–1909CrossRefGoogle Scholar
  13. 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(11–12): 1183–1190CrossRefGoogle Scholar
  14. Reeves C.R., Yamada T. (1998) Solving the Csum Permutation Flowshop Scheduling Problem by Genetic Local Search. IEEE International Conference on Evolutionary Computation 1998: 230–234Google Scholar
  15. Steinhöfel K., Albrecht A., Wong C.K. (2002) Fast parallel heuristics for the job shop scheduling problem. Computers and Operations Research 29: 151–169CrossRefGoogle Scholar
  16. Tan K.C., Narasimban R., Rubin P.A., Ragatz G.L. (2000) A comparison on four methods for minimizing total tardiness on a single procesor with sequence dependent setup times. Omega 28: 313–326CrossRefGoogle Scholar
  17. 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: 2388–2405CrossRefGoogle Scholar
  18. Wodecki M. (2008) A branch-and-bound parallel algorithm for single-machine total weighted tardiness problem. The International Journal of Advanced Manufacturing Technology 37(9–10): 996–1004CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of Computer Engineering, Control and RoboticsWrocław University of TechnologyWrocławPoland

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