Heuristic Algorithm for Uncertain Permutation Flow-shop Problem

Jerzy Józefczyk, Michał Ćwik


A complex population-based solution algorithm for an uncertain decision making problem is presented. The uncertain version of a permutation flow-shop problem with interval execution times is considered. The worst-case regret based on the makespan is used for the evaluation of permutations of tasks. The resulting complex minmax combinatorial optimization problem is solved. The heuristic algorithm is proposed which is based on the decomposition of the problem into three sequential sub-problems and employs a paradigm of evolutionary computing. The proposed algorithm solves the sub-problems sequentially. It is compared with the fast middle point heuristic algorithm via computer simulation experiments. The results show the usefulness of this heuristic algorithm for instances up to five machines.


  1. Aayyub, B. M., Klir, G. J. 2006. Uncertainty modeling and analysis in engineering and the sciences. Chapman&Hall/CRC: Boca Raton, London, New York.
  2. Aissi, H., Bazgan, C., Vanderpooten, D. 2009. Min-max and min--max regret versions of combinatorial optimization problems: A survey. European Journal of Operational Research, 197(2), 427-438.
  3. Averbakh, I. 2000. Minimax regret solutions for minimax optimization problems with uncertainty. Operations Research Letters, 27, 57-65.
  4. Averbakh, I. 2006. The minmax regret permutation flowshop problem with two jobs. Operations Research Letters, 169(3), 761-766.
  5. Averbakh, I., Pereira, J. 2011. Exact and heuristic algorithms for the interval data robust assignment problem. Computers & Operations Research, 38, 1153-1163.
  6. Conde, E. 2010. A 2-approximation for minmax regret problems via a mid-point scenario optimal solution. Operations Research Letters, 38(4), 326-327.
  7. Cwik, M., Józefczyk, J. 2015. Evolutionary algorithm for minmax regret flow-shop problem. Management and Production Engineering Review, 6(3), 3-9.
  8. Dutt, L.S., Kurian, M. 2013. Handling of Uncertainty - A Survey. International Journal of Scientific and Research Publications, 3, 2250-3153.
  9. Garey, M. R., Johnson, D. S., Sethi. R. 1976. The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research, 1, 117-129.
  10. Goldberg, D., E. 1989. Genetic Algorithms in Search. Optimization and Machine Learning. Addison-Wesley Longman Publishing Co., Inc. Boston, MA, USA.
  11. Józefczyk, J. 2008. Worst-case allocation algorithms in a complex of operations with interval parameters. Kybernetes. 37, 652-676.
  12. Józefczyk. J.. Siepak. M. 2013a. Worst-case regret algorithms for selected optimization problems with interval uncertainty. Kybernetes. 42 (3). 371-382.
  13. Józefczyk, J., Siepak, M. 2013b. Scatter Search based algorithms for min-max regret task scheduling problems with interval uncertainty. Control and Cybernetics, 42(3), 667-698.
  14. Kasperski, A.. Zielinski, P. 2008. A 2-approximation algorithm for interval data minmax regret sequencing problems with the total flow time criterion. Operations Research Letters, 42, 343-344.
  15. Kasperski, A., Kurpisz, A., Zielinski, P. 2012. Approximating a two-machine flow shop scheduling under discrete scenario uncertainty. Journal of Operational Research, 217, 36-43.
  16. Klir, G. J. 2006. Uncertainty and information: Foundations of generalized information theory, Wiley.
  17. Kouvelis, P., Daniels, R. L., Vairaktarakis, G. 2000. Robust scheduling of a two-machine flow shop with uncertain processing times. IIE Transactions, 32, 421- 432.
  18. Kouvelis, P., Yu, G. 1997. Robust Discrete Optimization and its Applications. Kluwer Academic Publishers, Dordrecht-Boston-London.
  19. Lebedev, V., Averbakh, I. 2006. Complexity of minimizing the total flow time with interval data and minmax regret criterion. Discrete Applied Mathematics, 154, 2167-2177.
  20. Lu, C. C., Lin, S. W., Ying, K., C. 2012. Robust scheduling on a single machine to minimize total flow time. Computers & Operations Research, 39, 1682- 1691.
  21. Nawaz, M., Enscore, Jr., E., Ham, I. 1983. A heuristic algorithm for the m-machine. n-job flow-shop sequencing problem. The International Journal of Management Science, 11, 91-95.
  22. Pereira, J. 2016. The robust (minmax regret) single machine scheduling with interval processing times and total weighted completion time objective. Computers & Operations Research, 66, 141-152.
  23. Pinedo. M. L. 2008. Scheduling-Theory. Algorithms and Systems. Springer.
  24. Pinedo, M. L., Schrage, L. 1982. Stochastic shop scheduling: A survey. In: Dempster. M. A. H. Lenstra, J. K., Rinooy Kann, A. H. G. (Eds.). Deterministic and Stochastic Scheduling, Reidel. Dordrecht.
  25. Siepak, M. Józefczyk, J. 2014. Solution algorithms for unrelated machines minmax regret scheduling problem with interval processing times and the total flow time criterion. Annals of Operations Research, 222, 517- 533.
  26. Volgenant, A., Duin, C. W. 2010. Improved polynomial algorithms for robust bottleneck problems with interval data. Computers & Operations Research, 37, 909-915.
  27. Yager, R.R. 1988. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. on SMC, 18, 183-190.

Paper Citation

in Harvard Style

Józefczyk J. and Ćwik M. (2016). Heuristic Algorithm for Uncertain Permutation Flow-shop Problem . In Proceedings of the 1st International Conference on Complex Information Systems - Volume 1: COMPLEXIS, ISBN 978-989-758-181-6, pages 119-127. DOI: 10.5220/0005874401190127

in Bibtex Style

author={Jerzy Józefczyk and Michał Ćwik},
title={Heuristic Algorithm for Uncertain Permutation Flow-shop Problem},
booktitle={Proceedings of the 1st International Conference on Complex Information Systems - Volume 1: COMPLEXIS,},

in EndNote Style

JO - Proceedings of the 1st International Conference on Complex Information Systems - Volume 1: COMPLEXIS,
TI - Heuristic Algorithm for Uncertain Permutation Flow-shop Problem
SN - 978-989-758-181-6
AU - Józefczyk J.
AU - Ćwik M.
PY - 2016
SP - 119
EP - 127
DO - 10.5220/0005874401190127