# A Self-adaptive Iterated Local Search Algorithm on the Permutation Flow Shop Scheduling Problem

### Xingye Dong, Maciek Nowak, Ping Chen, Youfang Lin

#### Abstract

Iterated local search (ILS) is a simple, effective and efficient metaheuristic, displaying strong performance on the permutation flow shop scheduling problem minimizing total flow time. Its perturbation method plays an important role in practice. However, in ILS, current methodology does not use an evaluation of the search status to adjust the perturbation strength. In this work, a method is proposed that evaluates the neighborhoods around the local optimum and adjusts the perturbation strength according to this evaluation using a technique derived from simulated-annealing. Basically, if the neighboring solutions are considerably worse than the best solution found so far, indicating that it is hard to escape from the local optimum, then the perturbation strength is likely to increase. A self-adaptive ILS named SAILS is proposed by incorporating this perturbation strategy. Experimental results on benchmark instances show that the proposed perturbation strategy is effective and SAILS performs better than three state of the art algorithms.

#### References

- Costa, W., Goldbarg, M., and Goldbard, E. (2012a). Hybridizing VNS and path-relinking on a particle swarm framework to minimize total flowtime. Expert Systems with Applications, 39:13118-13126.
- Costa, W., Goldbarg, M., and Goldbard, E. (2012b). New VNS heuristic for total flowtime flowshop scheduling problem. Expert Systems with Applications, 39:8149- 8161.
- Dong, X., Chen, P., Huang, H., and Nowak, M. (2013). A multi-restart iterated local search algorithm for the permutation flow shop problem minimizing total flow time. Computers & Operations Research, 40:627- 632.
- Dong, X., Huang, H., and Chen, P. (2009). An iterated local search algorithm for the permutation flowshop problem with total flowtime criterion. Computers & Operations Research, 36:1664-1669.
- Garey, M., Johnson, D., and Sethi, R. (1976). The complexity of flowshop and jobshop scheduling. Mathematics of Operations Research, 1:117-129.
- Johnson, S. (1954). Optimal two and three-stage production schedule with setup times included. Naval Research Logistics Quarterly, 1(1):61-68.
- Liu, J. and Reeves, C. (2001). Constructive and composite heuristic solutions to the p// ? ci scheduling problem. European Journal of Operational Research, 132:439- 452.
- Lourenc¸o, H., Martin, O., and Stützle, T. (2010). Handbook of Metaheuristics, volume 146 of International Series in Operations Research & Management Science, chapter Iterated Local Search: Framework and Applications, pages 363-397. Springer US.
- Nikolaev, A. G. and Jacobson, S. H. (2010). Handbook of Metaheuristics, volume 146 of International Series in Operations Research & Management Science, chapter Simulated Annealing, pages 1-39. Springer US.
- Pan, Q.-K. and Ruiz, R. (2012). Local search methods for the flowshop scheduling problem with flowtime minimization. European Journal of Operational Research, 222:31-43.
- Pan, Q.-K., Tasgetiren, M., and Liang, Y.-C. (2008). A discrete differential evolution algorithm for the permutation flowshop scheduling problem. Computers and Industrial Engineering, 55:795-816.
- Pinedo, M. (2001). Scheduling: theory, algorithms, and systems. Prentice Hall, 2nd edition.
- Rajendran, C. and Ziegler, H. (2004). Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research, 155:426-438.
- Rajendran, C. and Ziegler, H. (2005). Two ant-colony algorithms for minimizing total flowtime in permutation flowshops. Computers and Industrial Engineering, 48:789-797.
- Ruiz, R. and Stützle, T. (2007). A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research, 177:2033-2049.
- Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64:278-285.
- Tasgetiren, M., Liang, Y.-C., Sevkli, M., and Gencyilmaz, G. (2007). A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem. European Journal of Operational Research, 177:1930-1947.
- Tasgetiren, M., Pan, Q.-K., Suganthan, P., and Chen, A. H.-L. (2011). A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops. Information Sciences, 181:3459- 3475.
- Tseng, L.-Y. and Lin, Y.-T. (2009). A hybrid genetic local search algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research, 198:84-92.
- Tseng, L.-Y. and Lin, Y.-T. (2010). A genetic local search algorithm for minimizing total flowtime in the permutation flowshop scheduling problem. International Journal of Production Economics, 127:121-128.
- Xu, X., Xu, Z., and Gu, X. (2011). An asynchronous genetic local search algorithm for the permutation flowshop scheduling problem with total flowtime minimization. Expert Systems with Applications, 38:7970-7979.
- Zhang, Y., Li, X., and Wang, Q. (2009). Hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization. European Journal of Operational Research, 196(3):869-876.

#### Paper Citation

#### in Harvard Style

Dong X., Nowak M., Chen P. and Lin Y. (2014). **A Self-adaptive Iterated Local Search Algorithm on the Permutation Flow Shop Scheduling Problem** . In *Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-039-0, pages 378-384. DOI: 10.5220/0005092003780384

#### in Bibtex Style

@conference{icinco14,

author={Xingye Dong and Maciek Nowak and Ping Chen and Youfang Lin},

title={A Self-adaptive Iterated Local Search Algorithm on the Permutation Flow Shop Scheduling Problem},

booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2014},

pages={378-384},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005092003780384},

isbn={978-989-758-039-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - A Self-adaptive Iterated Local Search Algorithm on the Permutation Flow Shop Scheduling Problem

SN - 978-989-758-039-0

AU - Dong X.

AU - Nowak M.

AU - Chen P.

AU - Lin Y.

PY - 2014

SP - 378

EP - 384

DO - 10.5220/0005092003780384