Optimal Charge Planning Model of Steelmaking Based on Multi-Objective Evolutionary Algorithm
Abstract
:1. Introduction
2. Problem Description and Mathematical Model
2.1. Preparing Procedures of Charge Plan
2.2. Mathematical Model of Charge Planning
- (1)
- The number of grouped charges is unknown beforehand.
- (2)
- All contract products are prepared into production in consideration of the stricter requirement of customers on the customization production.
- (3)
- Total weight of a charge can be varied in a certain range.
- (4)
- The steel grades and dimensions of the contract products have been known in advance.
- (5)
- The weight of any production order is less than the furnace capacity, which means the order cannot be split.
- (1)
- Indexes and Parameters:
- M: the number of orders;
- O: the assumed number of charges, and the upper limit of O equals to M;
- j: index of heats (charges), j = 1, 2, …, O;
- i: index of orders, i = 1, 2, …, M;
- di: the due date of order i;
- dej: the earliest due date of orders involved in charge j;
- wi: the weight of order i;
- Vmax: the maximum capacity of steelmaking furnace;
- a: the lower limit coefficient of the total weight of a charge, and Vmin equals to a·Vmax. The value of a depends on the actual production requirements of steel plants and is less than 100%.
- (2)
- Decision Variables:
- xij: binary variable representing whether order i is in charge j (xij = 1) or not (xij = 0);
3. Multi-Objective Evolutionary Algorithm
3.1. Solving Strategy
3.2. Algorithm Design
- p: index of objective function;
- Xq: individual q of the population;
- N: the population size;
- Xpq: the rank of individual q for objective p. The computing method is Xpq = N + 1 − l, where individual q is in position l according to objective p in ascending order;
- k: a constant between 1 and 2, which is used to increase the fitness value of the best individual for a single target;
- Ep(Xq): the single objective fitness of Xq for objective p;
- E(Xq): the fitness of Xq.
3.3. Procedure of TR-MOEA
4. Case Study
4.1. Algorithms Comparison and Parameter Settings
4.2. Results and Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Order No. | Steel Grade | Dimension/mm × mm | Weigh/t | Due Date/d |
---|---|---|---|---|
0056 | 60Si2Mnb | 160 × 160 | 1.250 | 7 |
0012 | 60Si2Mnb | 160 × 160 | 1.250 | 7 |
0119 | 60Si2Mnb | 160 × 160 | 28.747 | 22 |
0089 | 60Si2Mnb | 180 × 180 | 0.625 | 7 |
0015 | 60Si2Mnb | 180 × 180 | 25.622 | 12 |
0016 | 60Si2Mnb | 180 × 180 | 12.499 | 12 |
0017 | SUP9b | 160 × 160 | 11.249 | 12 |
0100 | SUP9b | 160 × 160 | 6.874 | 17 |
0080 | SUP9b | 180 × 180 | 0.625 | 17 |
… … | … … | … … | … … | … … |
Parameters | Values |
---|---|
Population size (N) | 40 |
Generation (G) | 120 |
Lower limit coefficient of the total weight in a charge (a) | 95% |
Size of non-inferior solution set Q (n) | 8 |
Recombination probability | 80% |
Methods | Difference in the Due Dates/d·t | Open Order Amount/t | Penalty Value/¥ | Computation Time/s |
---|---|---|---|---|
TR-MOEA | 1971.645 | 31.340 | 5105.645 | 108 |
1659.185 | 31.975 | 4856.685 | ||
1240.480 | 33.208 | 4561.280 | ||
1131.105 | 37.572 | 4888.305 | ||
1012.380 | 41.943 | 5215.680 | ||
GA | 2275.370 | 30.518 | 5227.170 | 112 |
MPGA | 2149.665 | 30.345 | 5184.165 | 99 |
Manual | 2265.358 | 35.470 | 5812.358 | 2512 |
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Yang, J.; Wang, B.; Zou, C.; Li, X.; Li, T.; Liu, Q. Optimal Charge Planning Model of Steelmaking Based on Multi-Objective Evolutionary Algorithm. Metals 2018, 8, 483. https://doi.org/10.3390/met8070483
Yang J, Wang B, Zou C, Li X, Li T, Liu Q. Optimal Charge Planning Model of Steelmaking Based on Multi-Objective Evolutionary Algorithm. Metals. 2018; 8(7):483. https://doi.org/10.3390/met8070483
Chicago/Turabian StyleYang, Jianping, Bailin Wang, Caoyun Zou, Xiang Li, Tieke Li, and Qing Liu. 2018. "Optimal Charge Planning Model of Steelmaking Based on Multi-Objective Evolutionary Algorithm" Metals 8, no. 7: 483. https://doi.org/10.3390/met8070483