AIV: A Heuristic Algorithm based on Iterated Local Search and Variable Neighborhood Descent for Solving the Unrelated Parallel Machine Scheduling Problem with Setup Times

Matheus Nohra Haddad, Luciano Perdigão Cota, Marcone Jamilson Freitas Souza, Nelson Maculan

Abstract

This paper deals with the Unrelated Parallel Machine Scheduling Problem with Setup Times (UPMSPST). The objective is to minimize the maximum completion time of the schedule, the so-called makespan. This problem is commonly found in industrial processes like textile manufacturing and it belongs to NP-Hard class. It is proposed an algorithm named AIV based on Iterated Local Search (ILS) and Variable Neighborhood Descent (VND). This algorithm starts from an initial solution constructed on a greedy way by the Adaptive Shortest Processing Time (ASPT) rule. Then, this initial solution is refined by ILS, using as local search the Random VND procedure, which explores neighborhoods based on swaps and multiple insertions. In this procedure, here called RVND, there is no fixed sequence of neighborhoods, because they are sorted on each application of the local search. In AIV each perturbation is characterized by removing a job from one machine and inserting it into another machine. AIV was tested using benchmark instances from literature. Statistical analysis of the computational experiments showed that AIV outperformed the algorithms of the literature, setting new improved solutions.

References

  1. Al-Salem, A. (2004). Scheduling to minimize makespan on unrelated parallel machines with sequence dependent setup times. Engineering Journal of the University of Qatar, 17(1):177-187.
  2. Arnaout, J., Rabadi, G., and Musa, R. (2010). A twostage ant colony optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times. Journal of Intelligent Manufacturing, 21(6):693-701.
  3. Baker, K. R. (1974). Introduction to Sequencing and Scheduling. John Wiley & Sons.
  4. Chang, P. and Chen, S. (2011). Integrating dominance properties with genetic algorithms for parallel machine scheduling problems with setup times. Applied Soft Computing, 11(1):1263-1274.
  5. de Optimización Aplicada, S. (2011). A web site that includes benchmark problem data sets and solutions for scheduling problems. Available at http://soa.iti.es/problem-instances.
  6. Fleszar, K., Charalambous, C., and Hindi, K. (2011). A variable neighborhood descent heuristic for the problem of makespan minimisation on unrelated parallel machines with setup times. Journal of Intelligent Manufacturing, 23(5):1949-1958. doi:10.1007/s10845-011-0522-8.
  7. Garey, M. and Johnson, D. (1979). Computers and intractability: A guide to the theory of np-completeness. WH Freeman & Co., San Francisco, 174.
  8. Graham, R., Lawler, E., Lenstra, J., and Kan, A. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of discrete Mathematics, 5(2):287-326.
  9. Helal, M., Rabadi, G., and Al-Salem, A. (2006). A tabu search algorithm to minimize the makespan for the unrelated parallel machines scheduling problem with setup times. International Journal of Operations Research, 3(3):182-192.
  10. Karp, R. M. (1972). Reducibility among combinatorial problems. Complexity of Computer Computations, 40(4):85-103.
  11. Kim, D. W., Na, D. G., and Frank Chen, F. (2003). Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective. Robotics and Computer-Integrated Manufacturing, 19:173-181.
  12. Logendran, R., McDonell, B., and Smucker, B. (2007). Scheduling unrelated parallel machines with sequence-dependent setups. Computers & Operations research, 34(11):3420-3438.
  13. Lourenc¸o, H. R., Martin, O., and Stützle, T. (2003). Iterated local search. In Glover, F. and Kochenberger, G., editors, Handbook of Metaheuristics, volume 57 of International Series in Operations Research & Management Science, pages 321-353. Kluwer Academic Publishers, Norwell, MA.
  14. Mladenovic, N. and Hansen, P. (1997). Variable neighborhood search. Computers and Operations Research, 24(11):1097-1100.
  15. Montgomery, D. (2007). Design and Analysis of Experiments. John Wiley & Sons, New York, NY, fifth edition.
  16. Pereira Lopes, M. J. and de Carvalho, J. M. (2007). A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. European Journal of Operational Research, 176:1508- 1527.
  17. Rabadi, G., Moraga, R. J., and Al-Salem, A. (2006). Heuristics for the unrelated parallel machine scheduling problem with setup times. Journal of Intelligent Manufacturing, 17(1):85-97.
  18. Souza, M., Coelho, I., Ribas, S., Santos, H., and Merschmann, L. (2010). A hybrid heuristic algorithm for the open-pit-mining operational planning problem. European Journal of Operational Research, 207(2):1041-1051.
  19. Subramanian, A., Drummond, L., Bentes, C., Ochi, L., and Farias, R. (2010). A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery. Computers & Operations Research, 37(11):1899- 1911.
  20. Vallada, E. and Ruiz, R. (2011). A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times. European Journal of Operational Research, 211(3):612-622.
  21. Weng, M. X., Lu, J., and Ren, H. (2001). Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective. International Journal of Production Economics, 70:215-226.
  22. Ying, K.-C., Lee, Z.-J., and Lin, S.-W. (2012). Makespan minimisation for scheduling unrelated parallel machines with setup times. Journal of Intelligent Manufacturing, 23(5):1795-1803.
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Paper Citation


in Harvard Style

Nohra Haddad M., Perdigão Cota L., Jamilson Freitas Souza M. and Maculan N. (2014). AIV: A Heuristic Algorithm based on Iterated Local Search and Variable Neighborhood Descent for Solving the Unrelated Parallel Machine Scheduling Problem with Setup Times . In Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 1: ICEIS, ISBN 978-989-758-027-7, pages 376-383. DOI: 10.5220/0004884603760383


in Bibtex Style

@conference{iceis14,
author={Matheus Nohra Haddad and Luciano Perdigão Cota and Marcone Jamilson Freitas Souza and Nelson Maculan},
title={AIV: A Heuristic Algorithm based on Iterated Local Search and Variable Neighborhood Descent for Solving the Unrelated Parallel Machine Scheduling Problem with Setup Times},
booktitle={Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 1: ICEIS,},
year={2014},
pages={376-383},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004884603760383},
isbn={978-989-758-027-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 16th International Conference on Enterprise Information Systems - Volume 1: ICEIS,
TI - AIV: A Heuristic Algorithm based on Iterated Local Search and Variable Neighborhood Descent for Solving the Unrelated Parallel Machine Scheduling Problem with Setup Times
SN - 978-989-758-027-7
AU - Nohra Haddad M.
AU - Perdigão Cota L.
AU - Jamilson Freitas Souza M.
AU - Maculan N.
PY - 2014
SP - 376
EP - 383
DO - 10.5220/0004884603760383