Document Type : Research Paper
Authors
Abstract
In this paper, to make flexible job shop scheduling problem (FJSP)
more realistic, an operational factor is considered in its model. This
factor, which is called optimizing total consumed electric power per
month, is known as the most important factor in calculation of the
electric cost of the industries. Considering this factor, specifically
after subsides elimination of the country, has became more important.
In addition to this objective, two other common objectives, called
complementation time and critical work load of machines, are
considered. To solve the multi-objective model, two algorithms,
called multi-objective biogeography-based optimization algorithm
(MOBBO) and multi-objective harmony search algorithm (MOHS),
are developed and introduced to scheduling area for the first time.
Finally, by developing some famous libraries of the problem,
performance of the algorithms is compared statistically
Keywords
1. Barnes, J.W., Chambers, J.B., Flexible job shop scheduling by tabu search.
Graduate program in operations research and industrial engineering. University of
Texas, Austin, Technical Report Series, ORP96-09, 1996.
2. Bhattacharya, A., Chattopadhyay, P.K., Solving complex economic load dispatch
problems using Biogeography-based optimization. Expert Systems with
Applications 37, 3605–3615, 2010.
3. Brandimarte, P., Routing and scheduling in a flexible job shop by taboo search.
Annual Operation Research 41, 157–183, 1993.
4. Brucker, P., Schlie, R., Job-shop scheduling with multipurpose machines.
Computing 45(4), 369–375, 1990.
5. Chen, J.C., Chen, K.H., Wu, J.J., Chen, C.W., A study of the flexible job shop
scheduling problem with parallel machines and reentrant process. International
Journal of Advance Manufacturing Technology 39(3–4), 344–354, 2008.
6. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T., A fast elitist non-dominated
sorting genetic algorithm for multi-Objective optimization: NSGA-II. In:
Proceedings of the parallel problem solving from nature VI (PPSN-VI) conference,
849-858, 2000.
7. Fattahi, Parviz, Jolai, Fariborz, Arkat, Jamal, Flexible job shop scheduling with
overlapping in operations. Applied Mathematical Modeling 33, 3076–3087,
2009.
8. Fattahi, Parviz, Saidi Mehrabad, Mohammad, Jolai, Fariborz, Mathematical
modeling and heuristic approaches to flexible job shop scheduling problems,
International Journal of Advance Manufacturing Technology. DOI
10.1007/s10845-007-0026-8, 18:331–342, 2007.
9. Frutos, Mariano, Olivera, Ana Carolina, Tohmé, Fernando, A memetic algorithm
based on a NSGAII scheme for the flexible job-shop scheduling problem.
Annual Operation Research, DOI 10.1007/s10479-010-0751-9, 2010.
10. Gao, J., Gen, M., Sun, L.Y., Zhao, X.H., A hybrid of genetic algorithm and
bottleneck shifting for multiobjective flexible job shop scheduling problems.
Computer and Industrial Engineering 53(1), 149–162, 2007.
11. Geem, Z.W., Kim, J.-H., Loganathan, G.V., A new heuristic optimization
algorithm: harmony search, Simulation 76 (2) 60–68, 2011.
12. Hollander, M., Wolfe, D.A., Non-parametric Statistical Methods. John Wiley &
Sons, 1973.
13. Hurink, E., Jurisch, B., Thole, M., Tabu search for the job shop scheduling
problem with multi-purpose machine. Operations Research Spektrum 15 (4),
205–215, 1994.
14. Kacem, I., Hammadi, S., Borne, P., Approach by localization multi-objective
evolutionary optimization for flexible job-shops scheduling problems. IEEE
Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews
32 (1), 1–13, 2002.
15. Karimi, N., Zandieh, M., Karamooz, H.R., Bi-objective group scheduling in
hybrid flexible flow shop: A multi-phase approach. Expert Systems with
Applications 37, 4024–4032, 2010.
16. Kundra, H., Kaur, A., Panchal, V., An integrated approach to biogeography
based optimization with case based reasoning for retrieving groundwater
possibility. In: Proceedings of the Eighth Annual Asian Conference and Exhibition
on Geospatial Information, Technology and Applications, August, Singapore,
2009.
17. Lee, K.S., Geem, Z.W., A new meta-heuristic algorithm for continuous
engineering optimization: harmony search theory and practice. Computer
Methods in Applied Mechanics and Engineering 194, 3902–3933, 2005.
18. Mastrolilli, M., Gambardella, L.M., Effective neighborhood functions for the
محاسبة میزان ناسازگاری ساختار سلسله مراتبی... 112
flexible job shop problem. Journal of Scheduling 3(1), 3–20¸ 2000.
19. Rahmati, S.H.A., Zandieh, M., A new biogeography-based optimization (BBO)
algorithm for the flexible job shop scheduling problem, International Journal
of Advance Manufacturing Technology, DOI 10.1007/s00170-011-3437-9, 2011.
20. Rashid M. H., Power Electronic. Academic press, 2001.
21. Schott, J. R., Fault tolerant design using single and multicriteria genetic
algorithms optimization. Master’s thesis, Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 1995.
22. Simon, D., Biogeography-based optimization. IEEE Transactions on
Evolutionary Computation 12, 702–713, 2008.
23. Sivasubramani, S., Swarup, K.S., Environmental/economic dispatch using
multi-objective harmony search algorithm, Electronic Power System and
Research, doi:10.1016/j.epsr.2011.04.007, 2011.
24. Torabi, S.A., Karimi, B., Fatemi, Ghomi S.M.T., The common cycle economic lot
scheduling in flexible job shops: The finite horizon case. International Journal
of Production Economics 97, 52–65, 2005.
25. Wang, S., Yu, J., An effective heuristic for flexible job-shop scheduling
problem with maintenance activities, Computers & Industrial Engineering, 59:
436-447, 2010.
26. Xia, W.J., Wu, Z.M., An effective hybrid optimization approach for multiobjective
flexible job-shop scheduling problems. Computer and Industrial
Engineering 48(2), 409–425, 2005.
27. Yazdani M., Amiri M., Zandieh M., Flexible job-shop scheduling with parallel
variable neighborhood search algorithm. Expert Systems with Applications 37,
678–687, 2010.
28. Zitzler E. Evolutionary Algorithms for Multiobjective Optimization: Methods
and Applications. PhD. Thesis, Dissertation ETH No. 13398, Swiss Federal
Institute of Technology (ETH), 1999
Graduate program in operations research and industrial engineering. University of
Texas, Austin, Technical Report Series, ORP96-09, 1996.
2. Bhattacharya, A., Chattopadhyay, P.K., Solving complex economic load dispatch
problems using Biogeography-based optimization. Expert Systems with
Applications 37, 3605–3615, 2010.
3. Brandimarte, P., Routing and scheduling in a flexible job shop by taboo search.
Annual Operation Research 41, 157–183, 1993.
4. Brucker, P., Schlie, R., Job-shop scheduling with multipurpose machines.
Computing 45(4), 369–375, 1990.
5. Chen, J.C., Chen, K.H., Wu, J.J., Chen, C.W., A study of the flexible job shop
scheduling problem with parallel machines and reentrant process. International
Journal of Advance Manufacturing Technology 39(3–4), 344–354, 2008.
6. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T., A fast elitist non-dominated
sorting genetic algorithm for multi-Objective optimization: NSGA-II. In:
Proceedings of the parallel problem solving from nature VI (PPSN-VI) conference,
849-858, 2000.
7. Fattahi, Parviz, Jolai, Fariborz, Arkat, Jamal, Flexible job shop scheduling with
overlapping in operations. Applied Mathematical Modeling 33, 3076–3087,
2009.
8. Fattahi, Parviz, Saidi Mehrabad, Mohammad, Jolai, Fariborz, Mathematical
modeling and heuristic approaches to flexible job shop scheduling problems,
International Journal of Advance Manufacturing Technology. DOI
10.1007/s10845-007-0026-8, 18:331–342, 2007.
9. Frutos, Mariano, Olivera, Ana Carolina, Tohmé, Fernando, A memetic algorithm
based on a NSGAII scheme for the flexible job-shop scheduling problem.
Annual Operation Research, DOI 10.1007/s10479-010-0751-9, 2010.
10. Gao, J., Gen, M., Sun, L.Y., Zhao, X.H., A hybrid of genetic algorithm and
bottleneck shifting for multiobjective flexible job shop scheduling problems.
Computer and Industrial Engineering 53(1), 149–162, 2007.
11. Geem, Z.W., Kim, J.-H., Loganathan, G.V., A new heuristic optimization
algorithm: harmony search, Simulation 76 (2) 60–68, 2011.
12. Hollander, M., Wolfe, D.A., Non-parametric Statistical Methods. John Wiley &
Sons, 1973.
13. Hurink, E., Jurisch, B., Thole, M., Tabu search for the job shop scheduling
problem with multi-purpose machine. Operations Research Spektrum 15 (4),
205–215, 1994.
14. Kacem, I., Hammadi, S., Borne, P., Approach by localization multi-objective
evolutionary optimization for flexible job-shops scheduling problems. IEEE
Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews
32 (1), 1–13, 2002.
15. Karimi, N., Zandieh, M., Karamooz, H.R., Bi-objective group scheduling in
hybrid flexible flow shop: A multi-phase approach. Expert Systems with
Applications 37, 4024–4032, 2010.
16. Kundra, H., Kaur, A., Panchal, V., An integrated approach to biogeography
based optimization with case based reasoning for retrieving groundwater
possibility. In: Proceedings of the Eighth Annual Asian Conference and Exhibition
on Geospatial Information, Technology and Applications, August, Singapore,
2009.
17. Lee, K.S., Geem, Z.W., A new meta-heuristic algorithm for continuous
engineering optimization: harmony search theory and practice. Computer
Methods in Applied Mechanics and Engineering 194, 3902–3933, 2005.
18. Mastrolilli, M., Gambardella, L.M., Effective neighborhood functions for the
محاسبة میزان ناسازگاری ساختار سلسله مراتبی... 112
flexible job shop problem. Journal of Scheduling 3(1), 3–20¸ 2000.
19. Rahmati, S.H.A., Zandieh, M., A new biogeography-based optimization (BBO)
algorithm for the flexible job shop scheduling problem, International Journal
of Advance Manufacturing Technology, DOI 10.1007/s00170-011-3437-9, 2011.
20. Rashid M. H., Power Electronic. Academic press, 2001.
21. Schott, J. R., Fault tolerant design using single and multicriteria genetic
algorithms optimization. Master’s thesis, Department of Aeronautics and
Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 1995.
22. Simon, D., Biogeography-based optimization. IEEE Transactions on
Evolutionary Computation 12, 702–713, 2008.
23. Sivasubramani, S., Swarup, K.S., Environmental/economic dispatch using
multi-objective harmony search algorithm, Electronic Power System and
Research, doi:10.1016/j.epsr.2011.04.007, 2011.
24. Torabi, S.A., Karimi, B., Fatemi, Ghomi S.M.T., The common cycle economic lot
scheduling in flexible job shops: The finite horizon case. International Journal
of Production Economics 97, 52–65, 2005.
25. Wang, S., Yu, J., An effective heuristic for flexible job-shop scheduling
problem with maintenance activities, Computers & Industrial Engineering, 59:
436-447, 2010.
26. Xia, W.J., Wu, Z.M., An effective hybrid optimization approach for multiobjective
flexible job-shop scheduling problems. Computer and Industrial
Engineering 48(2), 409–425, 2005.
27. Yazdani M., Amiri M., Zandieh M., Flexible job-shop scheduling with parallel
variable neighborhood search algorithm. Expert Systems with Applications 37,
678–687, 2010.
28. Zitzler E. Evolutionary Algorithms for Multiobjective Optimization: Methods
and Applications. PhD. Thesis, Dissertation ETH No. 13398, Swiss Federal
Institute of Technology (ETH), 1999
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