An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process

IEEE Transactions on Automation Science and Engineering

Volumn 12, Issue 3, 2015, Pages 1140-1152

  Mao, Kun ^a   Pan, Quan Ke ^a   Chai, Tianyou ^a   Luh, Peter B ^b  

^a STATE KEY LABORATORY OF SYNTHETICAL AUTOMATION FOR PROCESS INDUSTRIES   (China)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Hybrid flowshop; Lagrangian relaxation; manufacturing system; scheduling; subgradient optimization

Indexed keywords

ALGORITHMS; CONTINUOUS CASTING; DYNAMIC PROGRAMMING; LAGRANGE MULTIPLIERS; MANUFACTURE; STEELMAKING;

CONTINUOUS CASTING PROCESS; CONVERGENCE CONDITIONS; DYNAMIC PROGRAMMING ALGORITHM; HYBRID FLOW SHOP; IRON AND STEEL PRODUCTIONS; LAGRANGIAN RELAXATION; LAGRANGIAN RELAXATIONS; SUB-GRADIENT OPTIMIZATION;

SCHEDULING;

EID: 85027930422     PISSN: 15455955     EISSN: None     Source Type: Journal    
DOI: 10.1109/TASE.2014.2332511     Document Type: Article

References (40)

1. H. Missbauer, W. Hauberb, and W. Stadler, "A scheduling system for the steelmaking-continuous casting process: A case study from the steelmaking industry, " Int. J. Prod. Res., vol. 47, pp. 4147-4172, 2009.
2. D. P. Bertsekas, Nonlinear Programming, 2nd ed. Belmon, MA, USA: Athena, 1999.
3. P. B. Luh, D. J. Hoitomt, E. Max, and K. R. Pattipati, "Scheduling generation and reconfiguration for parallel machines, " IEEE Trans. Robot. Autom., vol. 6, pp. 687-696, Dec. 1990.
4. P. B. Luh and D. J. Hoitomt, "Scheduling of manufacturing systems using the Lagrangian relaxation technique, " IEEE Trans. Autom. Control, vol. 38, pp. 1066-1079, Jul. 1993.
5. T. Nishi, Y. Isoya, and M. Inuiguchi, "An integrated column generation and LAgrangian relaxation for flowshop scheduling problems, " in Proc. IEEE Int. Conf. Syst., Man, Cybern., 2009, pp. 299-304.
6. H. Chen, C. Chu, and J. M. Proth, "An improvement of the Lagrangian relaxation approach for job shop scheduling: A dynamic programming method, " IEEE Trans. Robot. Autom., vol. 14, pp. 786-795, Oct. 1998.
7. P. Baptiste, M. Flamini, and F. Sourd, "Lagrangian bounds for just-int-ime job-shop scheduling, " Comput. Oper. Res., vol. 35, pp. 905-915, 2008.
8. L. Tang, H. Xuan, and J. Liu, "A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time, " Comput. Oper. Res., vol. 33, pp. 3344-3359, 2006.
9. T. Nishi, Y. Hiranaka, and M. Inuiguchi, "Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness, " Comput. Oper. Res., vol. 37, pp. 189-198, 2010.
10. L. X. Tang, P. B. Luh, J. Y. Liu, and L. Fang, "Steelmaking process scheduling using Lagrangian relaxation, " Int. J. Prod. Res., vol. 40, pp. 55-70, 2002.
11. H. Xuan and L. Tang, "Scheduling a hybrid flowshop with batch production at the last stage, " Comput. Oper. Res., vol. 34, pp. 2178-2733, 2007.
12. M. Held and R. M. Karp, "The travelling salesman problem and minimization spanning tress: Part II, " Math. Program., vol. 1, pp. 6-25, 1971.
13. B. Guta, "Subgradient optimization methods in integer programming with an application to a radiation therapy problem, " Ph.D. dissertation, Teknishe Universitat Kaiserlautern, Kaiserlautern, Germany, 2003.
14. S. Kim, H. Ahn, and S. C. Cho, "Variable target value subgradient method, " Math. Program., vol. 49, pp. 359-369, 1991.
15. U. Brannlund, "On relaxation methods for nonsmooth convex optimization, " Ph.D. dissertation, Royal Inst. Technol., Stockholm, Sweden, 1993.
16. J. L. Goffin and K. C. Kiwiel, "Convergence of a simple subgradient level method, " Math. Program., vol. 85, pp. 207-211, 1999.
17. H. D. Sherali, G. Choi, and C. H. Tuncbilek, "A variable target value method for nondifferentiable optimization, " Oper. Res. Lett., vol. 26, pp. 1-8, 2000.
18. P. M. Camerini, L. Fratta, and F. Maffioli, "On improving relaxation methods by modified gradient techniques, " Math. Program. Study, vol. 3, pp. 26-34, 1975.
19. H. D. Sherali and O. Ulular, "A primal-dual conjugate subgradient algorithm for specially strucutured linear and convex programming problems, " Appl. Math. Optim., vol. 20, pp. 193-221, 1989.
20. T. Larsson, M. Patriksson, and A. B. Stromberg, "Conditional subgradient optimization: Theory and applications, " Eur. J. Oper. Res., vol. 88, pp. 382-403, 1996.
21. X. Zhao, P. B. Luh, and J. Wang, "Surrogate gradient algorithm for Lagrangian relaxation, " J. Optim. Theory Appl., vol. 100, pp. 699-712, 1999.
22. T. S. Chang, "Comments on surrogate gradient algorithm for Lagrangian relaxation, " J. Optim. Theory Appl., vol. 137, pp. 691-697, 2008.
23. R. Buil, M. A. Piera, and P. B. Luh, "Improvement of Lagrangian relaxation convergence for production scheduling, " IEEE Trans. Autom. Sci. Eng., vol. 9, no. 1, pp. 137-147, Jan. 2012.
24. M. R. Garey, D. S. Johnson, and R. Sethi, "The complexity of flowshop and jobshop scheduling, " Math. Oper. Res., vol. 1, pp. 117-129, 1976.
25. L. Tang, J. Liu, A. Rong, and Z. Yang, "A review of planning and scheduling systems and methods for integrated steel production, " Eur. J. Oper. Res., vol. 133, pp. 1-20, 2001.
26. G. Dutta and R. Fourer, "A survey of mathematical programming applications in integrated steel plants, " Manuf. Service Oper. Manage., vol. 3, pp. 387-400, 2001.
27. Q.-K. Pan, L. Wang, K. Mao, J.-H. Zhao, and M. Zhang, "An effective artificial bee colony algorithm for a real-world hybrid flowshop problem in steelmaking process, " IEEE Trans. Autom. Sci. Eng., vol. 10, no. 2, pp. 307-322, Apr. 2013.
28. V. Kumar, S. Kumar, F. T. S. Chan, and M. K. Tiwari, "Auctionbased approach to resolve the scheduling problem in the steelmaking process, " Int. J. Prod. Res., vol. 44, pp. 1503-1522, 2006.
29. J. Li, X. Xiao, Q. Tang, and C. A. Floudas, "Production scheduling of a large-scale steelmaking continuous casting process via unit specific event-based continuous-time models: Short-term and medium term scheduling, " Ind. Eng. Chem. Res., vol. 51, pp. 7300-7319, 2012.
30. A. Atighehchian, M. Bijari, and H. Tarkesh, "A novel hybrid algorithm for scheduling steelmaking continuous casting production, " Comput. Oper. Res., vol. 36, pp. 2450-2461, 2009.
31. J. P. Sousa and L. A. Wolsey, "A time indexed formulation of nonpreemptive single machine scheduling problems, " Math. Program., vol. 54, pp. 353-367, 1992.
32. A. B. Keha, K. Khowala, and J. W. Fowler, "Mixed integer programming formulations for single machine scheduling problems, " Comput. Ind. Eng., vol. 56, pp. 357-367, 2009.
33. H. Chen and P. B. Luh, "An alternative framework to Lagrangian relaxation approach for job shop scheduling, " Eur. J. Oper. Res., vol. 149, pp. 499-512, 2003.
34. J. K. Lenstra, K. A. Rinnooy, and P. Bruker, "Complexity of machine scheduling problems, " Ann. Discrete Math., vol. 1, pp. 343-362, 1977.
35. J. V. Demyanov and V. K. Somesova, "Conditional subdifferentials of convex functions, " Soviet Mathematics Doklady, vol. 19, pp. 1181-1185, 1978.
36. K. Mao, Q.-K. Pan, X. Pang, and T. Chai, "A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steel making continuous casting process, " Eur. J. Oper. Res., vol. 236, pp. 51-60, 2014.
37. J. E. Beasley, "Lagrangian heuristic for location problem, " Eur. J. Oper. Res., vol. 65, pp. 383-399, 1993.
38. S. Tragantalerngsak, J. Holt, and M. Bonnqvist, "Lagrangian heuristics for the two-echelon, single source, capacitated facility location problem, " Eur. J. Oper. Res., vol. 102, pp. 611-625, 1997.
39. S.-H. Wang, "An improved stepsize of the subgradient algorithm for solving the lagrangian relaxation problem, " Comput. Electr. Engineering, vol. 29, pp. 245-249, 2003.
40. S. Boyd and A. Mutapcic, "Subgradient methods, " in Lecture Notes of EE364b. Stanford, CA, USA: Stanford Univ., 2006-2007, Winter.