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

Liangliang Sun; Fangjun Luan; Yu Ying; Kun Mao

doi:10.3934/jimo.2016081

Article Contents

2017, Volume 13, Issue 3: 1431-1448. Doi: 10.3934/jimo.2016081

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

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
* Corresponding author:Liangliang Sun

Received: December 31, 2014

Published: September 2017

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.

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Steelmaking-continuous casting process

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

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

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Table 1. The results obtained by SSLRA

Cast vs. charge(SLLRA)	LB	UB	Gap (%)	Time (s)
2 vs.5	937456	983672	4.70	299.5
2 vs.6	1182728	1398892	15.45	313.3
2 vs.7	1497377	1732913	13.59	327.8
2 vs.8	1837244	2252386	18.43	323.7
3 vs.5	1923113	2183725	11.93	309.4
3 vs.6	2487753	2711245	8.24	355.2
3 vs.7	3294573	3690245	10.72	377.2
3 vs.8	3999272	5294742	24.47	466.1
4 vs.5	3100023	3274848	5.34	378.5
4 vs.6	4134749	4591234	9.94	449.2
4 vs.7	5368271	7545422	28.85	598.4
4 vs.8	6650012	9082765	26.78	739.6
5 vs.5	4648823	5119374	9.19	504.7
5 vs.6	6168391	9998116	38.30	663.2
5 vs.7	8102927	11924753	32.05	2199.5
5 vs.8	10373752	13583721	23.63	7824
Average	4106654	7532570	17.60	1008.08

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Table 2. The results obtained by DCSLA

Cast vs. charge(DCSLA)	LB	UB	Gap (%)	Time (s)
2 vs.5	937456	954151	1.75	1.6
2 vs.6	1182728	1294621	8.64	2.2
2 vs.7	1497377	1519847	1.48	3.2
2 vs.8	1837244	1997636	8.03	1.9
3 vs.5	1923113	2003743	4.02	2
3 vs.6	2487753	2505632	0.71	3.2
3 vs.7	3294573	3349425	1.64	1.5
3 vs.8	3999272	4186443	4.47	1.5
4 vs.5	3100023	3153846	1.71	2.1
4 vs.6	4134749	4200474	1.56	2.7
4 vs.7	5368271	5438362	1.29	3.8
4 vs.8	6650012	6739436	1.33	3.1
5 vs.5	4648823	4753628	2.20	2.4
5 vs.6	6168391	6374522	3.23	3.9
5 vs.7	8102927	9193736	11.86	5.9
5 vs.8	10373752	11376463	8.81	8.8
Average	4106654	4315122	3.92	3.11

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Table 3. Computational results of DCSLA for SCC rescheduling

ET	Events	EV-1 (s)	EV-2 (s)	EV-3 (min)	DG (%)	Time (s)	IN
1	R1-T2-M1	0	0	22	12.94	76.63	162
2	R1-T3-M1	0	0	15	11.85	66.31	115
3	R1-T1-M2	0	0	16	13.64	75.92	141
4	R1-T2-M2	0	0	19	13.09	58.7	128
5	R1-T3-M2	0	0	21	11.55	44.76	103
6	R1-T1-M3	0	0	18	8.68	121.91	196
7	R1-T2-M3	0	0	11	12.97	134.73	187
8	R1-T3-M3	0	0	10	11.32	83.66	165
9	R2-T2-M1	0	0	19	7.74	9.32	63
10	R2-T3-M1	0	0	12	8.31	8.69	60
11	R2-T1-M2	0	0	16	9.22	12.81	52
12	R2-T2-M2	0	0	19	7.93	9.33	61
13	R2-T3-M2	0	0	22	8.88	8.89	68
14	R2-T1-M3	0	0	14	9.12	15.9	59
15	R2-T2-M3	0	0	16	8.45	7.63	42
16	R2-T3-M3	0	0	11	8.67	8.69	74
Average		0	0	16.31	10.27	46.49	104
(ET: Event Type, IN: Number of Iterations, DG: Duality Gap, EV: Evaluation Values)

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