American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization
  • JIMO Home
  • This Issue
  • Next Article
    The loss-averse newsvendor problem with random supply capacity
July  2017, 13(3): 1431-1448. doi: 10.3934/jimo.2016081

Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm

Liangliang Sun 1,, , Fangjun Luan 1, , Yu Ying 1, and  Kun Mao 2,

1. 

Department of Information and Control Engineering, Shenyang Jianzhu University, No. 9, Hunnan East Road, Hunnan New District, Shenyang City, Liaoning 110168, China
2. 

Department of Information Science and Engineering, Northeastern University, NO. 3-11, Wenhua Road, Heping District, Shenyang City, Liaoning 110004, China

* Corresponding author:Liangliang Sun

Received  January 2015 Published  October 2016

Fund Project: The research is financially sponsored by the National Natural Science Foundation Committee of China (Subject Numbers: 61503259), Hanyu Plan of Shenyang Jianzhu University and Research Funding from the Networked Control System Key Laboratory of the Chinese Academy of Sciences.

This study investigates a challenging problem of rescheduling a hybrid flow shop in the steelmaking-continuous casting (SCC) process, which is a major bottleneck in the production of iron and steel. In consideration of uncertain disturbance during SCC process, we develop a time-indexed formulation to model the SCC rescheduling problem. The performances of the rescheduling problem consider not only the efficiency measure, which includes the total weighted completion time and the total waiting time, but also the stability measure, which refers to the difference in the number of operations processed on different machines for the different stage in the original schedule and revised schedule. With these objectives, this study develops a Lagrangian heuristic algorithm to solve the SCC rescheduling problem. The algorithm could provide a realizable termination criterion without having information about the problem, such as the distance between the initial iterative point and the optimal point. This study relaxes machine capacity constraints to decompose the relaxed problem into charge-level subproblems that can be solved using a polynomial dynamic programming algorithm. A heuristic based on the solution of the relaxed problem is presented for obtaining a feasible reschedule. An improved efficient subgradient algorithm is introduced for solving Lagrangian dual problems. Numerical results for different events and problem scales show that the proposed approach can generate high-quality reschedules within acceptable computational times.

Keywords: Rescheduling, steelmaking-continuous casting, subgradient algorithm, Lagrangian heuristic algorithm, dynamic programming.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Liangliang Sun, Fangjun Luan, Yu Ying, Kun Mao. Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1431-1448. doi: 10.3934/jimo.2016081
References:
[1]

A. Atighehchian, M. Bijari and H. Tarkesh, A novel hybrid algorithm for scheduling steelmaking continuous casting production, Computers and Operations Research, 36 (2009), 2450-2461.   Google Scholar

[2]

H. Aytug, M. Lawley, K. McKay, S. Mohan and R. Uzsoy, Executing production schedules in the face of uncertainties: A review and some future directions, European Journal of Operational Research, 161 (2005), 86-110.  doi: 10.1016/j.ejor.2003.08.027.  Google Scholar

[3]

A. Bellabdaoui and J. Teghem, A mixed-integer linear programming model for the continuous casting planning, International Journal of Production Economics, 104 (2006), 260-270.  doi: 10.1016/j.ijpe.2004.10.016.  Google Scholar

[4]

D. Bertsekas, Nonlinear Programming, 2$^{nd}$ edition, Athena Scientific, Massachusetts, 1999. doi: 10.1007/978-1-4612-0873-0.  Google Scholar

[5]

U. Brannlund, On Relaxation Methods for Nonsmooth Convex Optimization, Ph. D thesis, Royal Institute of Technology in Stockholm, 1993.  Google Scholar

[6]

P. Camerini, L. Fratta and F. Maffioli, On improving relaxation methods by modified gradient techniques, Mathematical Programming Study, 3 (1975), 26-34.   Google Scholar

[7]

H. Chen and P. Luh, An alternative framework to Lagrangian relaxation approach for job shop scheduling, European Journal of Operational Research, 149 (2003), 499-512.  doi: 10.1016/S0377-2217(02)00470-8.  Google Scholar

[8]

P. Cowling, D. Ouelhadj and S. Petrovic, Dynamic scheduling of steel casting and milling using multi-agents, Production Planning and Control, 15 (2004), 178-188.  doi: 10.1080/09537280410001662466.  Google Scholar

[9]

V. Demjanov and V. Somesova, Conditional subdifferentials of convex functions, Soviet Mathematics Doklady, 19 (1978), 1181-1185.   Google Scholar

[10]

J. Goffin and K. Kiwiel, Convergence of a simple subgradient level method, Mathematical Programming, 85 (1999), 207-211.  doi: 10.1007/s101070050053.  Google Scholar

[11]

B. Guta, Subgradient Optimization Methods in Integer Programming with an Application to a Radiation Therapy Problem, Ph. D thesis, Teknishe Universitat Kaiserlautern in Kaiserlauter, 2003. Google Scholar

[12]

I. Harjunkoski and I. Grossmann, A decomposition approach for the scheduling of a steel plant production, Computers and Chemical Engineering, 25 (2001), 1647-1660.  doi: 10.1016/S0098-1354(01)00729-3.  Google Scholar

[13]

T. Larsson, M. Patriksson and A. Stromberg, Conditional subgradient optimization --theory and applications, European Journal of Operational Research, 88 (1996), 382-403.  doi: 10.1016/0377-2217(94)00200-2.  Google Scholar

[14]

J. Li, X. Xiao, Q. Tang and C. 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, Industrial and Engineering Chemistry Research, 51 (2012), 7300-7319.  doi: 10.1021/ie2015944.  Google Scholar

[15]

P. Luh and D. Hoitomt, Scheduling of manufacturing systems using the Lagrangian relaxation technique, IEEE Transactions on Automatic Control, 38 (1993), 1066-1079.  doi: 10.1109/9.231461.  Google Scholar

[16]

P. Luh, D. Hoitomt, E. Max and K. Pattipati, Scheduling generation and reconfiguration for parallel machines, IEEE Transactions on Robotics and Automation, 6 (1990), 687-696.   Google Scholar

[17]

K. Mao, Q. Pan, X. Pang and T. Chai, A novel Lagrangian relaxation approach for the hybrid flowshop scheduling problem in a steelmaking-continuous casting process, European Journal of Operational Research, 236 (2014), 51-60.  doi: 10.1016/j.ejor.2013.11.010.  Google Scholar

[18]

K. Mao, Q. Pan, X. Pang and T. Chai, An effective Lagrangian relaxation approach for rescheduling a steelmaking-continuous casting process, Control Engineering Practice, 30 (2014), 67-77.  doi: 10.1016/j.conengprac.2014.06.003.  Google Scholar

[19]

K. Mao, Q. Pan, X. Pang, T. Chai and P. Luh, An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process, IEEE Transactions on Automation Science and Engineering, 12 (2014), 1-13.  doi: 10.1109/TASE.2014.2332511.  Google Scholar

[20]

H. Missbauer, W. Hauber and W. Werner Stadler, A scheduling system for the steelmaking-continuous casting process: A case study from the steelmaking industry, International Journal of Production Research, 47 (2009), 4147-4172.  doi: 10.1080/00207540801950136.  Google Scholar

[21]

A. Nedic and D. Bertsekas, Incremental Subgradient Methods for Nondifferentiable Optimization, SIAM Journal on Optimization, 12 (2001), 109-138.  doi: 10.1137/S1052623499362111.  Google Scholar

[22]

T. Nishi, Y. Hiranaka and M. Inuiguchi, Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness, Computers and Operations Research, 37 (2010), 189-198.  doi: 10.1016/j.cor.2009.04.008.  Google Scholar

[23]

T. Nishi, Y. Isoya Y and M. Inuiguchi, An integrated column generation and lagrangian relaxation for flowshop scheduling problems, Proceedings of the 2009 IEEE International Conference on Systems, Man and Cybernetics, (2009), 209-304.  doi: 10.1109/ICSMC.2009.5346159.  Google Scholar

[24]

D. Ouelhadj, P. Cowling and S. Petrovic, Utility and stability measures for agent-based dynamic scheduling of steel continuous casting, Journal of Scheduling, 12 (2009), 417-431.  doi: 10.1109/ROBOT.2003.1241592.  Google Scholar

[25]

D. Ouelhadj and S. Petrovic, A survey of dynamic scheduling in manufacturing systems, Journal of Scheduling, 12 (2009), 417-431.  doi: 10.1007/s10951-008-0090-8.  Google Scholar

[26]

D. Ouelhadj, S. Petrovic, P. Cowling and A. Meisels, Inter-agent cooperation and communication for agent-based robust dynamic scheduling in steel production, Advanced Engineering Informatics, 18 (2004), 161-172.  doi: 10.1016/j.aei.2004.10.003.  Google Scholar

[27]

D. Pacciarelli and M. Pranzo, Production scheduling in a steelmaking-continuous casting plant, Computers and Chemical Engineering, 28 (2004), 2823-2835.  doi: 10.1016/j.compchemeng.2004.08.031.  Google Scholar

[28]

Q. Pan, L. Wang, K. Mao, J. Zhao and M. Zhang, An Effective Artificial Bee Colony Algorithm for a Real-World Hybrid Flowshop Problem in Steelmaking Process, IEEE Transactions on Automation Science and Engineering, 10 (2013), 307-322.  doi: 10.1109/TASE.2012.2204874.  Google Scholar

[29]

H. Sherali, G. Choi and C. Tuncbilek, A Variable Target Value Method for Nondifferentiable Optimization, Operation Research Letters, 26 (2000), 1-8.  doi: 10.1016/S0167-6377(99)00063-2.  Google Scholar

[30]

L. Sun, Research on the Optimal Scheduling Method for the productive Process of Steelmaking-Refining-Continuous Casting, Ph. D thesis, Northeastern University in Shenyang, 2015. Google Scholar

[31]

L. Tang, J. Liu, A. Rong and Z. Yang, A review of planning and scheduling systems and methods for integrated steel production, European Journal of Operational Research, 133 (2001), 1-20.  doi: 10.1016/S0377-2217(00)00240-X.  Google Scholar

[32]

L. Tang, P. Luh, J. Liu and L. Fang, Steelmaking process scheduling using Lagrangian relaxation, International Journal of Production Research, 40 (2002), 55-70.   Google Scholar

[33]

L. Tang, G. Wang and Z. Chen, Integrated charge batching and casting width selection at Baosteel, Operations Research, 62 (2014), 772-787.  doi: 10.1287/opre.2014.1278.  Google Scholar

[34]

L. Tang, Y. Zhao and J. Liu, An Improved Differential Evolution Algorithm for Practical Dynamic Scheduling in Steelmaking-continuous Casting Production, IEEE Transactions on Evolutionary Computation, 18 (2014), 209-213.  doi: 10.1109/TEVC.2013.2250977.  Google Scholar

[35]

G. Vieira, J. Hermann and E. Lin, Rescheduling manufacturing systems: a framework of strategies, policies and methods, Journal of Scheduling, 6 (2003), 36-92.  doi: 10.1023/A:1022235519958.  Google Scholar

[36]

R. Xiong, Y. Fan and C. Wu, A dynamic job shop scheduling method based on Lagrangian relaxation, Tsinghua Science and Technology, 4 (1999), 1297-1302.   Google Scholar

[37]

H. Xuan and L. Tang, Scheduling a hybrid flowshop with batch production at the last stage, Computers and Operations Research, 34 (2007), 2718-2733.  doi: 10.1016/j.cor.2005.10.014.  Google Scholar

[38]

S. Yu and Q. Pan, A Rescheduling Method for Operation Time Delay Disturbance in Steelmaking and Continuous Casting Production Process, International Journal of Iron and Steel Research, 19 (2012), 33-41.  doi: 10.1016/S1006-706X(13)60029-1.  Google Scholar

[39]

H. Zhong, X Dong and H. Shi, Research on the load balancing scheduling problem of reentrant hybrid flowshops, Chinese High Technology Letters, 25 (2015), 70-81.   Google Scholar

[40]

H. Zhong, Y Zhu and S. Lin, A dynamic co-evolution compact genetic algorithm for E/T problem, The 17th IFAC Symposium on System Identification, (2015), 1433-1437.   Google Scholar

show all references

References:
[1]

A. Atighehchian, M. Bijari and H. Tarkesh, A novel hybrid algorithm for scheduling steelmaking continuous casting production, Computers and Operations Research, 36 (2009), 2450-2461.   Google Scholar

[2]

H. Aytug, M. Lawley, K. McKay, S. Mohan and R. Uzsoy, Executing production schedules in the face of uncertainties: A review and some future directions, European Journal of Operational Research, 161 (2005), 86-110.  doi: 10.1016/j.ejor.2003.08.027.  Google Scholar

[3]

A. Bellabdaoui and J. Teghem, A mixed-integer linear programming model for the continuous casting planning, International Journal of Production Economics, 104 (2006), 260-270.  doi: 10.1016/j.ijpe.2004.10.016.  Google Scholar

[4]

D. Bertsekas, Nonlinear Programming, 2$^{nd}$ edition, Athena Scientific, Massachusetts, 1999. doi: 10.1007/978-1-4612-0873-0.  Google Scholar

[5]

U. Brannlund, On Relaxation Methods for Nonsmooth Convex Optimization, Ph. D thesis, Royal Institute of Technology in Stockholm, 1993.  Google Scholar

[6]

P. Camerini, L. Fratta and F. Maffioli, On improving relaxation methods by modified gradient techniques, Mathematical Programming Study, 3 (1975), 26-34.   Google Scholar

[7]

H. Chen and P. Luh, An alternative framework to Lagrangian relaxation approach for job shop scheduling, European Journal of Operational Research, 149 (2003), 499-512.  doi: 10.1016/S0377-2217(02)00470-8.  Google Scholar

[8]

P. Cowling, D. Ouelhadj and S. Petrovic, Dynamic scheduling of steel casting and milling using multi-agents, Production Planning and Control, 15 (2004), 178-188.  doi: 10.1080/09537280410001662466.  Google Scholar

[9]

V. Demjanov and V. Somesova, Conditional subdifferentials of convex functions, Soviet Mathematics Doklady, 19 (1978), 1181-1185.   Google Scholar

[10]

J. Goffin and K. Kiwiel, Convergence of a simple subgradient level method, Mathematical Programming, 85 (1999), 207-211.  doi: 10.1007/s101070050053.  Google Scholar

[11]

B. Guta, Subgradient Optimization Methods in Integer Programming with an Application to a Radiation Therapy Problem, Ph. D thesis, Teknishe Universitat Kaiserlautern in Kaiserlauter, 2003. Google Scholar

[12]

I. Harjunkoski and I. Grossmann, A decomposition approach for the scheduling of a steel plant production, Computers and Chemical Engineering, 25 (2001), 1647-1660.  doi: 10.1016/S0098-1354(01)00729-3.  Google Scholar

[13]

T. Larsson, M. Patriksson and A. Stromberg, Conditional subgradient optimization --theory and applications, European Journal of Operational Research, 88 (1996), 382-403.  doi: 10.1016/0377-2217(94)00200-2.  Google Scholar

[14]

J. Li, X. Xiao, Q. Tang and C. 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, Industrial and Engineering Chemistry Research, 51 (2012), 7300-7319.  doi: 10.1021/ie2015944.  Google Scholar

[15]

P. Luh and D. Hoitomt, Scheduling of manufacturing systems using the Lagrangian relaxation technique, IEEE Transactions on Automatic Control, 38 (1993), 1066-1079.  doi: 10.1109/9.231461.  Google Scholar

[16]

P. Luh, D. Hoitomt, E. Max and K. Pattipati, Scheduling generation and reconfiguration for parallel machines, IEEE Transactions on Robotics and Automation, 6 (1990), 687-696.   Google Scholar

[17]

K. Mao, Q. Pan, X. Pang and T. Chai, A novel Lagrangian relaxation approach for the hybrid flowshop scheduling problem in a steelmaking-continuous casting process, European Journal of Operational Research, 236 (2014), 51-60.  doi: 10.1016/j.ejor.2013.11.010.  Google Scholar

[18]

K. Mao, Q. Pan, X. Pang and T. Chai, An effective Lagrangian relaxation approach for rescheduling a steelmaking-continuous casting process, Control Engineering Practice, 30 (2014), 67-77.  doi: 10.1016/j.conengprac.2014.06.003.  Google Scholar

[19]

K. Mao, Q. Pan, X. Pang, T. Chai and P. Luh, An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process, IEEE Transactions on Automation Science and Engineering, 12 (2014), 1-13.  doi: 10.1109/TASE.2014.2332511.  Google Scholar

[20]

H. Missbauer, W. Hauber and W. Werner Stadler, A scheduling system for the steelmaking-continuous casting process: A case study from the steelmaking industry, International Journal of Production Research, 47 (2009), 4147-4172.  doi: 10.1080/00207540801950136.  Google Scholar

[21]

A. Nedic and D. Bertsekas, Incremental Subgradient Methods for Nondifferentiable Optimization, SIAM Journal on Optimization, 12 (2001), 109-138.  doi: 10.1137/S1052623499362111.  Google Scholar

[22]

T. Nishi, Y. Hiranaka and M. Inuiguchi, Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness, Computers and Operations Research, 37 (2010), 189-198.  doi: 10.1016/j.cor.2009.04.008.  Google Scholar

[23]

T. Nishi, Y. Isoya Y and M. Inuiguchi, An integrated column generation and lagrangian relaxation for flowshop scheduling problems, Proceedings of the 2009 IEEE International Conference on Systems, Man and Cybernetics, (2009), 209-304.  doi: 10.1109/ICSMC.2009.5346159.  Google Scholar

[24]

D. Ouelhadj, P. Cowling and S. Petrovic, Utility and stability measures for agent-based dynamic scheduling of steel continuous casting, Journal of Scheduling, 12 (2009), 417-431.  doi: 10.1109/ROBOT.2003.1241592.  Google Scholar

[25]

D. Ouelhadj and S. Petrovic, A survey of dynamic scheduling in manufacturing systems, Journal of Scheduling, 12 (2009), 417-431.  doi: 10.1007/s10951-008-0090-8.  Google Scholar

[26]

D. Ouelhadj, S. Petrovic, P. Cowling and A. Meisels, Inter-agent cooperation and communication for agent-based robust dynamic scheduling in steel production, Advanced Engineering Informatics, 18 (2004), 161-172.  doi: 10.1016/j.aei.2004.10.003.  Google Scholar

[27]

D. Pacciarelli and M. Pranzo, Production scheduling in a steelmaking-continuous casting plant, Computers and Chemical Engineering, 28 (2004), 2823-2835.  doi: 10.1016/j.compchemeng.2004.08.031.  Google Scholar

[28]

Q. Pan, L. Wang, K. Mao, J. Zhao and M. Zhang, An Effective Artificial Bee Colony Algorithm for a Real-World Hybrid Flowshop Problem in Steelmaking Process, IEEE Transactions on Automation Science and Engineering, 10 (2013), 307-322.  doi: 10.1109/TASE.2012.2204874.  Google Scholar

[29]

H. Sherali, G. Choi and C. Tuncbilek, A Variable Target Value Method for Nondifferentiable Optimization, Operation Research Letters, 26 (2000), 1-8.  doi: 10.1016/S0167-6377(99)00063-2.  Google Scholar

[30]

L. Sun, Research on the Optimal Scheduling Method for the productive Process of Steelmaking-Refining-Continuous Casting, Ph. D thesis, Northeastern University in Shenyang, 2015. Google Scholar

[31]

L. Tang, J. Liu, A. Rong and Z. Yang, A review of planning and scheduling systems and methods for integrated steel production, European Journal of Operational Research, 133 (2001), 1-20.  doi: 10.1016/S0377-2217(00)00240-X.  Google Scholar

[32]

L. Tang, P. Luh, J. Liu and L. Fang, Steelmaking process scheduling using Lagrangian relaxation, International Journal of Production Research, 40 (2002), 55-70.   Google Scholar

[33]

L. Tang, G. Wang and Z. Chen, Integrated charge batching and casting width selection at Baosteel, Operations Research, 62 (2014), 772-787.  doi: 10.1287/opre.2014.1278.  Google Scholar

[34]

L. Tang, Y. Zhao and J. Liu, An Improved Differential Evolution Algorithm for Practical Dynamic Scheduling in Steelmaking-continuous Casting Production, IEEE Transactions on Evolutionary Computation, 18 (2014), 209-213.  doi: 10.1109/TEVC.2013.2250977.  Google Scholar

[35]

G. Vieira, J. Hermann and E. Lin, Rescheduling manufacturing systems: a framework of strategies, policies and methods, Journal of Scheduling, 6 (2003), 36-92.  doi: 10.1023/A:1022235519958.  Google Scholar

[36]

R. Xiong, Y. Fan and C. Wu, A dynamic job shop scheduling method based on Lagrangian relaxation, Tsinghua Science and Technology, 4 (1999), 1297-1302.   Google Scholar

[37]

H. Xuan and L. Tang, Scheduling a hybrid flowshop with batch production at the last stage, Computers and Operations Research, 34 (2007), 2718-2733.  doi: 10.1016/j.cor.2005.10.014.  Google Scholar

[38]

S. Yu and Q. Pan, A Rescheduling Method for Operation Time Delay Disturbance in Steelmaking and Continuous Casting Production Process, International Journal of Iron and Steel Research, 19 (2012), 33-41.  doi: 10.1016/S1006-706X(13)60029-1.  Google Scholar

[39]

H. Zhong, X Dong and H. Shi, Research on the load balancing scheduling problem of reentrant hybrid flowshops, Chinese High Technology Letters, 25 (2015), 70-81.   Google Scholar

[40]

H. Zhong, Y Zhu and S. Lin, A dynamic co-evolution compact genetic algorithm for E/T problem, The 17th IFAC Symposium on System Identification, (2015), 1433-1437.   Google Scholar

Figure 1.  Steelmaking-continuous casting process
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Connection between started operations and statuses of an operatio
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Illustration of the four performance indexes for the revised scheduling of SCC
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  The results obtained by SSLRA
Cast vs. charge(SLLRA)LBUBGap (%) Time (s)
2 vs.59374569836724.70299.5
2 vs.61182728139889215.45313.3
2 vs.71497377173291313.59327.8
2 vs.81837244225238618.43323.7
3 vs.51923113218372511.93309.4
3 vs.6248775327112458.24355.2
3 vs.73294573369024510.72377.2
3 vs.83999272529474224.47466.1
4 vs.5310002332748485.34378.5
4 vs.6413474945912349.94449.2
4 vs.75368271754542228.85598.4
4 vs.86650012908276526.78739.6
5 vs.5464882351193749.19504.7
5 vs.66168391999811638.30663.2
5 vs.781029271192475332.052199.5
5 vs.8103737521358372123.637824
Average4106654753257017.601008.08
Table Options

Download as excel

Cast vs. charge(SLLRA)LBUBGap (%) Time (s)
2 vs.59374569836724.70299.5
2 vs.61182728139889215.45313.3
2 vs.71497377173291313.59327.8
2 vs.81837244225238618.43323.7
3 vs.51923113218372511.93309.4
3 vs.6248775327112458.24355.2
3 vs.73294573369024510.72377.2
3 vs.83999272529474224.47466.1
4 vs.5310002332748485.34378.5
4 vs.6413474945912349.94449.2
4 vs.75368271754542228.85598.4
4 vs.86650012908276526.78739.6
5 vs.5464882351193749.19504.7
5 vs.66168391999811638.30663.2
5 vs.781029271192475332.052199.5
5 vs.8103737521358372123.637824
Average4106654753257017.601008.08
Table 2.  The results obtained by DCSLA
Cast vs. charge(DCSLA)LBUBGap (%) Time (s)
2 vs.59374569541511.751.6
2 vs.6118272812946218.642.2
2 vs.7149737715198471.483.2
2 vs.8183724419976368.031.9
3 vs.5192311320037434.022
3 vs.6248775325056320.713.2
3 vs.7329457333494251.641.5
3 vs.8399927241864434.471.5
4 vs.5310002331538461.712.1
4 vs.6413474942004741.562.7
4 vs.7536827154383621.293.8
4 vs.8665001267394361.333.1
5 vs.5464882347536282.202.4
5 vs.6616839163745223.233.9
5 vs.78102927919373611.865.9
5 vs.810373752113764638.818.8
Average410665443151223.923.11
Table Options

Download as excel

Cast vs. charge(DCSLA)LBUBGap (%) Time (s)
2 vs.59374569541511.751.6
2 vs.6118272812946218.642.2
2 vs.7149737715198471.483.2
2 vs.8183724419976368.031.9
3 vs.5192311320037434.022
3 vs.6248775325056320.713.2
3 vs.7329457333494251.641.5
3 vs.8399927241864434.471.5
4 vs.5310002331538461.712.1
4 vs.6413474942004741.562.7
4 vs.7536827154383621.293.8
4 vs.8665001267394361.333.1
5 vs.5464882347536282.202.4
5 vs.6616839163745223.233.9
5 vs.78102927919373611.865.9
5 vs.810373752113764638.818.8
Average410665443151223.923.11
Table 3.  Computational results of DCSLA for SCC rescheduling
ETEventsEV-1 (s)EV-2 (s)EV-3 (min)DG (%) Time (s)IN
1R1-T2-M1002212.9476.63162
2R1-T3-M1001511.8566.31115
3R1-T1-M2001613.6475.92141
4R1-T2-M2001913.0958.7128
5R1-T3-M2002111.5544.76103
6R1-T1-M300188.68121.91196
7R1-T2-M3001112.97134.73187
8R1-T3-M3001011.3283.66165
9R2-T2-M100197.749.3263
10R2-T3-M100128.318.6960
11R2-T1-M200169.2212.8152
12R2-T2-M200197.939.3361
13R2-T3-M200228.888.8968
14R2-T1-M300149.1215.959
15R2-T2-M300168.457.6342
16R2-T3-M300118.678.6974
Average0016.3110.2746.49104
(ET: Event Type, IN: Number of Iterations, DG: Duality Gap, EV: Evaluation Values)
Table Options

Download as excel

ETEventsEV-1 (s)EV-2 (s)EV-3 (min)DG (%) Time (s)IN
1R1-T2-M1002212.9476.63162
2R1-T3-M1001511.8566.31115
3R1-T1-M2001613.6475.92141
4R1-T2-M2001913.0958.7128
5R1-T3-M2002111.5544.76103
6R1-T1-M300188.68121.91196
7R1-T2-M3001112.97134.73187
8R1-T3-M3001011.3283.66165
9R2-T2-M100197.749.3263
10R2-T3-M100128.318.6960
11R2-T1-M200169.2212.8152
12R2-T2-M200197.939.3361
13R2-T3-M200228.888.8968
14R2-T1-M300149.1215.959
15R2-T2-M300168.457.6342
16R2-T3-M300118.678.6974
Average0016.3110.2746.49104
(ET: Event Type, IN: Number of Iterations, DG: Duality Gap, EV: Evaluation Values)
[1]

Mostafa Abouei Ardakan, A. Kourank Beheshti, S. Hamid Mirmohammadi, Hamed Davari Ardakani. A hybrid meta-heuristic algorithm to minimize the number of tardy jobs in a dynamic two-machine flow shop problem. Numerical Algebra, Control & Optimization, 2017, 7 (4) : 465-480. doi: 10.3934/naco.2017029
[2]

Xiangyu Gao, Yong Sun. A new heuristic algorithm for laser antimissile strategy optimization. Journal of Industrial & Management Optimization, 2012, 8 (2) : 457-468. doi: 10.3934/jimo.2012.8.457
[3]

Chia-Huang Wu, Kuo-Hsiung Wang, Jau-Chuan Ke, Jyh-Bin Ke. A heuristic algorithm for the optimization of M/M/$s$ queue with multiple working vacations. Journal of Industrial & Management Optimization, 2012, 8 (1) : 1-17. doi: 10.3934/jimo.2012.8.1
[4]

Chuanhao Guo, Erfang Shan, Wenli Yan. A superlinearly convergent hybrid algorithm for solving nonlinear programming. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1009-1024. doi: 10.3934/jimo.2016059
[5]

Débora A. F. Albanez, Maicon J. Benvenutti. Continuous data assimilation algorithm for simplified Bardina model. Evolution Equations & Control Theory, 2018, 7 (1) : 33-52. doi: 10.3934/eect.2018002
[6]

Ya Liu, Zhaojin Li. Dynamic-programming-based heuristic for multi-objective operating theater planning. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020145
[7]

Mao Chen, Xiangyang Tang, Zhizhong Zeng, Sanya Liu. An efficient heuristic algorithm for two-dimensional rectangular packing problem with central rectangle. Journal of Industrial & Management Optimization, 2020, 16 (1) : 495-510. doi: 10.3934/jimo.2018164
[8]

Andrew E.B. Lim, John B. Moore. A path following algorithm for infinite quadratic programming on a Hilbert space. Discrete & Continuous Dynamical Systems, 1998, 4 (4) : 653-670. doi: 10.3934/dcds.1998.4.653
[9]

Zhiqing Meng, Qiying Hu, Chuangyin Dang. A penalty function algorithm with objective parameters for nonlinear mathematical programming. Journal of Industrial & Management Optimization, 2009, 5 (3) : 585-601. doi: 10.3934/jimo.2009.5.585
[10]

Abdel-Rahman Hedar, Alaa Fahim. Filter-based genetic algorithm for mixed variable programming. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 99-116. doi: 10.3934/naco.2011.1.99
[11]

Paul B. Hermanns, Nguyen Van Thoai. Global optimization algorithm for solving bilevel programming problems with quadratic lower levels. Journal of Industrial & Management Optimization, 2010, 6 (1) : 177-196. doi: 10.3934/jimo.2010.6.177
[12]

Gianni Di Pillo, Giampaolo Liuzzi, Stefano Lucidi. A primal-dual algorithm for nonlinear programming exploiting negative curvature directions. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 509-528. doi: 10.3934/naco.2011.1.509
[13]

Rong Hu, Ya-Ping Fang. A parametric simplex algorithm for biobjective piecewise linear programming problems. Journal of Industrial & Management Optimization, 2017, 13 (2) : 573-586. doi: 10.3934/jimo.2016032
[14]

Yunsai Chen, Zhao Yang, Liang Ma, Peng Li, Yongjie Pang, Xin Zhao, Wenyi Yang. Efficient extraction algorithm for local fuzzy features of dynamic images. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1311-1325. doi: 10.3934/dcdss.2019090
[15]

Binghai Zhou, Yuanrui Lei, Shi Zong. Lagrangian relaxation algorithm for the truck scheduling problem with products time window constraint in multi-door cross-dock. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021151
[16]

Jian Gu, Xiantao Xiao, Liwei Zhang. A subgradient-based convex approximations method for DC programming and its applications. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1349-1366. doi: 10.3934/jimo.2016.12.1349
[17]

Zhi Guo Feng, Kok Lay Teo, Volker Rehbock. A smoothing approach for semi-infinite programming with projected Newton-type algorithm. Journal of Industrial & Management Optimization, 2009, 5 (1) : 141-151. doi: 10.3934/jimo.2009.5.141
[18]

Soodabeh Asadi, Hossein Mansouri. A Mehrotra type predictor-corrector interior-point algorithm for linear programming. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 147-156. doi: 10.3934/naco.2019011
[19]

Shaojun Zhang, Zhong Wan. Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive. Journal of Industrial & Management Optimization, 2012, 8 (2) : 493-505. doi: 10.3934/jimo.2012.8.493
[20]

Chenchen Wu, Dachuan Xu, Xin-Yuan Zhao. An improved approximation algorithm for the $2$-catalog segmentation problem using semidefinite programming relaxation. Journal of Industrial & Management Optimization, 2012, 8 (1) : 117-126. doi: 10.3934/jimo.2012.8.117

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (290)
  • HTML views (448)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy