Comprehensive Utilization of Mineral Resources: Optimal Blending of Polymetallic Ore Using an Improved NSGA-III Algorithm
Abstract
:1. Introduction
- (1)
- A multi-objective ore blending mathematical model for the polymetallic mineral is established. The grade of several metals and the grindability of the ore are considered objectives. The oxidation rate and harmful substances that affect the recovery rate of the mineral beneficiation are considered the constraints. These factors are not considered by the existing traditional ore blending model, but they are a confirmed impact on beneficiation [11,14].
- (2)
- A novel algorithm is proposed. To solve the multi-objective ore blending mathematical model, a novel algorithm is proposed based on the NSGA-III algorithm which is improved by using a mating pool mechanism, a general normalization process, and the reference-point generation method, named as constrained NSGA-III algorithm based on a matching mechanism (CM-NSGA-III).
- (3)
- The model and CM-NSGA-III are applied to obtain a daily ore blending plan for a large open-pit mine in China. We analyze the overall situation of the calculated target values, the target demand of each unloading point, and the finally obtained planning. The results show that the CM-NSGA-III scheme can obtain a satisfactory ore blending plan.
2. Literature Review of Ore Blending
3. Mathematical Model of Polymetallic Ore Blending Schedule Problem
3.1. Problem Assumption and Description
- In a mining face (or a loading point), the various components in the geology are uniform distribution. We can get the average value of each component through laboratory tests and calculations. The type of rock at a mining face (or a loading point) is unique.
- The implementation of the ore blending is strictly in accordance with the ore blending schedule.
- The relationship between the beneficiation recovery rate and the homogeneous ore has been established by laboratory tests. As long as the ore is blended to the required quality, the best beneficiation recovery rate can be obtained.
3.2. Mathematical Formulation of Polymetallic Ore Blending Schedule Problem
4. The Proposed CM-NSGA-III Algorithm
4.1. The Framework of the Proposed CM-NSGA-III Algorithm
Algorithm 1. Framework of CM-NSGA-III |
Input: N (population size) Output: approximated Pareto-optimal front
Repeat ∪ and i = i + 1 until || ≥ N, Last front to be included: if || = N then, , break else
Normalize objectives: = Normalization () Association: () = Associate (W, ) %: closest reference point, d: distance between s and π(s) Compute niche count: , j ∈ W Choose K members one at a time from to construct : Niching (K, , π, d, W, , ) Transformation reference point set W: W = Reference-Point-Transformation (W) end if |
4.2. ASF Mating-Pool Scheme and Normalization
4.2.1. ASF Mating-Pool Scheme
Algorithm 2. ASF Mating-Pool () |
%: the maximum ASF value of solution i,
|
4.2.2. Normalization
4.3. Reference-Point Generation and Transformation
4.4. Constraints Handling
5. Case Study
5.1. The Situation of the Polymetallic Open-Pit Mine and Experimental Data
5.2. Parameter Settings and Experimental Environment
5.3. Results
5.4. Discussion
6. Conclusions
- There is a conflict between the various metals in the ore when the associated metal ores are blended, i.e., for the grade of one metal in the blended ore to meet its beneficiation grade, the grade of the other metal in the ore will deviate from its beneficiation grade. So, the blending of associated ores is a multi-objective optimization problem, and it cannot be converted into a single-objective optimization problem by assigning weights to each objective. If it is transformed into a single-objective optimization problem, the optimal result will be a Pareto local optimum solution.
- Through the experiment, compared with the NSGA-III algorithm, the result obtained by the CM-NSGA-III algorithm is better. It shows that the CM-NSGA-III algorithm has better optimization solving performance. Moreover, the proposed model and algorithm can provide different optimal ore blending schemes available for the production of the mine and ensure a relatively minimal deviation from the required target by testing on the case.
- When the quality of the ore is not strictly required, i.e., it is allowed to fluctuate within a certain range, the method proposed in this paper can provide a theoretical basis for determining the fluctuation range of various metals in the ore.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Nwaila, G.T.; Ghorbani, Y.; Becker, M.; Frimmel, H.E.; Petersen, J.; Zhang, S. Geometallurgical Approach for Implications of Ore Blending on Cyanide Leaching and Adsorption Behavior of Witwatersrand Gold Ores, South Africa. Nat. Resour. Res. 2020, 29, 1007–1030. [Google Scholar] [CrossRef]
- Sotoudeh, F.; Nehring, M.; Kizil, M.; Knights, P.; Mousavi, A. Production scheduling optimisation for sublevel stoping mines using mathematical programming: A review of literature and future directions. Resour. Policy 2020, 68, 101809. [Google Scholar] [CrossRef]
- Yu, S.; Zhu, K.; He, Y. A hybrid intelligent optimization method for multiple metal grades optimization. Neural Comput. Appl. 2012, 21, 1391–1402. [Google Scholar] [CrossRef]
- Githiria, J.; Musingwini, C. A stochastic cut-off grade optimization model to incorporate uncertainty for improved project value. J. South Afr. Inst. Min. Metall. 2019, 119, 217–228. [Google Scholar] [CrossRef]
- Khan, A.; Asad, M.W.A. An optimal cut-off grade policy under diverse stockpile handling strategies in open-pit mining operations. Int. J. Min. Reclam. Environ. 2021, 35, 141–151. [Google Scholar] [CrossRef]
- Chanda, E.K.C.; Dagdelen, K. Optimal blending of mine production using goal programming and interactive graphics systems. Int. J. Surf. Min. Reclam. Environ. 1995, 9, 203–208. [Google Scholar] [CrossRef]
- Prasojo, T.S.; Yulianto, A.; Hindarto, A.; Parinussa, B.; Arifien, A. Ore Blending as Mine Scheduling Strategy to Accommodate Resources Conservation at Pakal Nickel Mine, PT ANTAM (Persero) Tbk. Procedia Earth Planet. Sci. 2013, 6, 24–29. [Google Scholar] [CrossRef]
- Danish, A.A.K.; Khan, A.; Muhammad, K.; Ahmad, W.; Salman, S. A simulated annealing based approach for open pit mine production scheduling with stockpiling option. Resour. Policy 2021, 71, 102016. [Google Scholar] [CrossRef]
- Armstrong, M.; Lagos, T.; Emery, X.; Homem-de-Mello, T.; Lagos, G.; Sauré, D. Adaptive open-pit mining planning under geological uncertainty. Resour. Policy 2021, 72, 102086. [Google Scholar] [CrossRef]
- Van Tonder, E.; Deglon, D.A.; Napier-Munn, T.J. The effect of ore blends on the mineral processing of platinum ores. Miner. Eng. 2010, 23, 621–626. [Google Scholar] [CrossRef] [Green Version]
- Bicak, O. A technique to determine ore variability in a sulphide ore. Miner. Eng. 2019, 142, 105927. [Google Scholar] [CrossRef]
- Liu, B.; Zhang, D.; Gao, X. A Method of Ore Blending Based on the Quality of Beneficiation and Its Application in a Concentrator. Appl. Sci. 2021, 11, 5092. [Google Scholar] [CrossRef]
- Kumral, M. Solution of Ore Blending Problem by Stochastic Approach. In Proceedings of the 10th International Mining Congress and Exhibition of Turkey-IMCET; Available online: https://www.maden.org.tr/resimler/ekler/18c255f89434eab_ek.pdf (accessed on 23 August 2022).
- Mkurazhizha, H. The Effects of Ore Blending on Comminution Behaviour and Product Quality in a Grinding Circuit-Svappavaara (LKAB) Case Study. Master’s Thesis, Luleå University of Technology, Luleå, Sweden, 2018. [Google Scholar]
- Kumral, M. Application of chance-constrained programming based on multi-objective simulated annealing to solve a mineral blending problem. Eng. Optimiz. 2003, 35, 661–673. [Google Scholar] [CrossRef]
- Askari-Nasab, H.; Pourrahimian, Y.; Ben-Awuah, E.; Kalantari, S. Mixed integer linear programming formulations for open pit production scheduling. J. Min. Sci. 2011, 47, 338–359. [Google Scholar] [CrossRef]
- Blom, M.L.; Burt, C.N.; Pearce, A.R.; Stuckey, P.J. A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines. INFORMS J. Comput. 2014, 26, 658–676. [Google Scholar] [CrossRef]
- Onuaguluchi, O.; Eren, O. Recycling of copper tailings as an additive in cement mortars. Constr. Build. Mater. 2012, 37, 723–727. [Google Scholar] [CrossRef]
- Ma, L.; Liu, C.D.; Bi, Y.L.; Peng, S.P.; Jiang, K.S.; Zhang, H.; Luo, Q.; Xue, F.; Xu, T.X.; Li, T.X.; et al. Experimental Study on Impermeability Law of Aquiclude Reconstructed by Mudstone of External Dump in Arid Zone. Adv. Civ. Eng. 2021, 2021, 5561794. [Google Scholar] [CrossRef]
- Singh, V.; Biswas, A.; Tripathy, S.K.; Chatterjee, S.; Chakerborthy, T.K. Smart ore blending methodology for ferromanganese production process. Ironmak. Steelmak. 2016, 43, 481–487. [Google Scholar] [CrossRef]
- Liu, X.; Liu, C.; Wang, B.; Ye, F. Optimization of iron ore blending in the COREX shaft furnace. J. S. Afr. Inst. Min. Metall. 2019, 119, 445–452. [Google Scholar] [CrossRef]
- Xu, T.J.; Yang, P.; Liu, Z.Q. Mine Ore Blending Planning and Management Based on the Fuzzy Multi-objective Optimization Algorithm. In Proceedings of the 2008 International Seminar on Business and Information Management, Wuhan, China, 19 December 2008. [Google Scholar]
- Gholamnejad, J.; Azimi, A.; Teymouri, M. Application of stochastic programming for iron ore quality control. J. Min. Environ. 2018, 9, 331–338. [Google Scholar]
- Ulger, N.E.; Ozer, U.; Akkaya, U.G. Determination of quality of a quartzite deposit, model of pre-blending, and the developing software-boss. J. Min. Sci. 2011, 47, 483–492. [Google Scholar] [CrossRef]
- Gholamnejad, J.; Kasmaee, S. Optimum blending of iron ore from Choghart stockpiles by using goal programming. J. Cent. South Univ. 2012, 19, 1081–1085. [Google Scholar] [CrossRef]
- Letelier, O.R.; Espinoza, D.; Goycoolea, M.; Moreno, E.; Munoz, G. Production Scheduling for Strategic Open Pit Mine Planning: A Mixed-Integer Programming Approach. Oper. Res. 2020, 68, 1425–1444. [Google Scholar] [CrossRef]
- Singh, G.; Garcia-Flores, R.; Ernst, A.; Welgama, P.; Zhang, M.M.; Munday, K. Medium-Term Rail Scheduling for an Iron Ore Mining Company. Interfaces 2014, 44, 222–240. [Google Scholar] [CrossRef]
- Blom, M.L.; Pearce, A.R.; Stuckey, P.J. A Decomposition-Based Algorithm for the Scheduling of Open-Pit Networks Over Multiple Time Periods. Manag. Sci. 2016, 62, 3059–3084. [Google Scholar] [CrossRef]
- Moreno, E.; Rezakhah, M.; Newman, A.; Ferreira, F. Linear models for stockpiling in open-pit mine production scheduling problems. Eur. J. Oper. Res. 2017, 260, 212–221. [Google Scholar] [CrossRef]
- Jamshidi, M.; Osanloo, M. Reliability analysis of production schedule in multi-element deposits under grade-tonnage uncertainty with multi-destinations for the run of mine material. Int. J. Min. Sci. Technol. 2019, 29, 483–489. [Google Scholar] [CrossRef]
- Rezakhah, M.; Moreno, E.; Newman, A. Practical performance of an open pit mine scheduling model considering blending and stockpiling. Comput. Oper. Res. 2020, 115, 12. [Google Scholar] [CrossRef]
- Samatova, L.A.; Shepeta, E.D.; Gvozdev, V.I. Poor scheelite ores from Primorye deposits: Mineralogy and processing characteristics and dressing flowsheets. J. Min. Sci. 2012, 48, 565–573. [Google Scholar] [CrossRef]
- Gu, Q.; Lu, C.; Guo, J.; Jing, S. Dynamic management system of ore blending in an open pit mine based on GIS/GPS/GPRS. Min. Sci. Technol. 2010, 20, 132–137. [Google Scholar] [CrossRef]
- Marques, D.M.; Costa, J.F.C.L. An algorithm to simulate ore grade variability in blending and homogenization piles. Int. J. Miner. Process. 2013, 120, 48–55. [Google Scholar] [CrossRef]
- Zhao, S.; Lu, T.F.; Koch, B.; Hurdsman, A. Automatic quality estimation in blending using a 3D stockpile management model. Adv. Eng. Inform. 2015, 29, 680–695. [Google Scholar] [CrossRef]
- Ilic, D.; Lavrinec, A.; Orozovic, O. Simulation and analysis of blending in a conveyor transfer system. Miner. Eng. 2020, 157, 11. [Google Scholar] [CrossRef]
- Ma, L.; Lai, X.P.; Zhang, J.G.; Xiao, S.S.; Zhang, L.M.; Tu, Y.H. Blast-Casting Mechanism and Parameter Optimization of a Benched Deep-Hole in an Opencast Coal Mine. Shock Vib. 2020, 2020, 1396483. [Google Scholar] [CrossRef]
- Ma, L.; Zhang, J.G.; Xu, C.; Lai, X.P.; Luo, Q.; Liu, C.D.; Li, K.M. Comprehensive Evaluation of Blast Casting Results Based on Unascertained Measurement and Intuitionistic Fuzzy Set. Shock Vib. 2021, 2021, 8864618. [Google Scholar] [CrossRef]
- Deb, K.; Jain, H. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints. IEEE Trans. Evol. Comput. 2014, 18, 577–601. [Google Scholar] [CrossRef]
- Jain, H.; Deb, K. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach. IEEE Trans. Evol. Comput. 2014, 18, 602–622. [Google Scholar] [CrossRef]
- He, Z.; Yen, G.G. Many-Objective Evolutionary Algorithms Based on Coordinated Selection Strategy. IEEE Trans. Evol. Comput. 2017, 21, 220–233. [Google Scholar] [CrossRef]
- Yuan, Y.; Xu, H.; Wang, B.; Zhang, B.; Yao, X. Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers. IEEE Trans. Evol. Comput. 2016, 20, 180–198. [Google Scholar] [CrossRef]
- Jiang, S.; Yang, S. A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization. IEEE Trans. Evol. Comput. 2017, 21, 329–346. [Google Scholar] [CrossRef]
- Tian, Y.; Cheng, R.; Zhang, X.; Jin, Y. PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]. IEEE Comput. Intell. Mag. 2017, 12, 73–87. [Google Scholar] [CrossRef] [Green Version]
- Hou, J.; Li, G.Q.; Wang, H.; Hu, N.L. Genetic algorithm to simultaneously optimise stope sequencing and equipment dispatching in underground short-term mine planning under time uncertainty. Int. J. Min. Reclam. Environ. 2020, 34, 307–325. [Google Scholar] [CrossRef]
- Yang, H.; Hu, N.L.; Xu, Z.; Chen, L. A Real-Time Ore Proportioning System in a Large Open-Pit Copper-Molybdenum Mine. Appl. Mech. Mater. 2013, 336–338, 2124–2129. [Google Scholar] [CrossRef]
Capacity at the j-th unloading point (crushing station or stockpiling station). | |
Production capacity of each shovel in each production cycle. | |
Transportation capability of each truck in each production cycle. | |
Ore grade of the k-th metal at the i-th loading point (or mining face). | |
Target ore grade of the k-th metal at the j-th crushing station. | |
Percentage of the s-th harmful substance. | |
Percentage of the s-th harmful substance at the i-th loading point (or mining face). | |
The number of metal species. | |
The number of loading points (or mining faces). | |
The number of crushing stations. | |
The number of stockpiling stations. | |
The number of shovels in the open-pit mine. | |
The number of trucks in the open-pit mine. | |
Oxidation rate at the i-th loading points (or mining faces). | |
Allowable oxidation rate at the j-th unloading points (crushing station or stockpiling station). | |
The minimum required production of the i-th ore loading point (or mining face). | |
The maximum quantity of ore at the i-th ore loading point (or mining face). | |
The number of types of rock. | |
The number of loading points (or mining face) of the r-th type of rock. | |
The minimum production of the j-th crushing station. | |
The minimum ore transportation volume from the i-th loading point (or mining face) to the j-th unloading point (crushing station or stockpiling station) | |
Target percentage of the r-th type of rock at the j-th crushing station. | |
Quantity from the i-th loading point (or mining face) to the j-th unloading point (crushing station or stockpiling station). |
Loading Point | Ore Quantity (ton) | Mo Grade (%) | W Grade (%) | Cu Grade (%) | Oxidation Rate (%) | Rock Type |
---|---|---|---|---|---|---|
No. 1 | 6000 | 0.083 | 0.118 | 0.006 | 0.204 | skarn |
No. 2 | 3500 | 0.098 | 0.034 | 0.010 | 0.058 | skarn |
No. 3 | 4800 | 0.170 | 0.134 | 0.017 | 0.094 | skarn |
No. 4 | 5000 | 0.055 | 0.017 | 0.006 | 0.046 | halleflinta |
No. 5 | 6000 | 0.087 | 0.157 | 0.010 | 0.250 | skarn |
No. 6 | 5500 | 0.114 | 0.092 | 0.010 | 0.074 | gillebackite |
No. 7 | 6000 | 0.095 | 0.081 | 0.015 | 0.080 | skarn |
No. 8 | 4000 | 0.066 | 0.069 | 0.017 | 0.197 | skarn |
No. 9 | 4600 | 0.095 | 0.081 | 0.015 | 0.080 | skarn |
No. 10 | 5000 | 0.075 | 0.021 | 0.009 | 0.028 | halleflinta |
No. 11 | 8400 | 0.118 | 0.157 | 0.021 | 0.220 | skarn |
No. 12 | 6800 | 0.093 | 0.177 | 0.020 | 0.283 | skarn |
No. 13 | 7000 | 0.066 | 0.086 | 0.017 | 0.197 | skarn |
No. 14 | 6000 | 0.069 | 0.079 | 0.009 | 0.157 | gillebackite |
Unloading Point | Capacity | Mo Grade (%) | W Grade (%) | Cu Grade (%) | Upper Oxidation Rate (%) | |
---|---|---|---|---|---|---|
Lower | Upper | |||||
1# | 4150 | 4400 | 0.085 | 0.065 | 0.011 | 0.1 |
2# | 5950 | 6200 | 0.095 | 0.103 | 0.013 | 0.147 |
3# | 6550 | 7200 | 0.095 | 0.103 | 0.013 | 0.147 |
4# | 3400 | 4000 | 0.088 | 0.068 | 0.011 | 0.104 |
Parameters | NSGA-III | CM-NSGA-III |
---|---|---|
Initial population size | n = 84 | n = 84 |
Reference points | H = 78 | H = 81 |
Maximum iterations | gen = 100,000 | gen = 100,000 |
Decision variable | D = 56 | D = 56 |
Crossover probability | = 1 | = 1 |
Mutation probability | ||
Distribution index | η = 20 | η = 20 |
Unloading Point | Loading Point (ton) | Total | Ore Grade (%) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | Mo | W | Cu | ||
1# | 0 | 494 | 0 | 309 | 0 | 658 | 0 | 0 | 0 | 1728 | 0 | 750 | 0 | 311 | 4249 | 0.0850 | 0.0650 | 0.0110 |
2# | 947 | 310 | 303 | 0 | 0 | 795 | 315 | 0 | 570 | 483 | 678 | 653 | 389 | 662 | 6105 | 0.0956 | 0.1025 | 0.0130 |
3# | 623 | 301 | 785 | 710 | 513 | 436 | 965 | 310 | 0 | 0 | 616 | 472 | 311 | 729 | 6771 | 0.0956 | 0.1013 | 0.0130 |
4# | 537 | 1067 | 0 | 332 | 0 | 0 | 555 | 0 | 308 | 380 | 0 | 303 | 0 | 0 | 3480 | 0.0879 | 0.0680 | 0.0110 |
Total | 2107 | 2171 | 1088 | 1351 | 513 | 1889 | 1835 | 310 | 877 | 2591 | 1294 | 2178 | 701 | 1701 | 20,605 | - | - | - |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Chen, L.; Gu, Q.; Wang, R.; Feng, Z.; Zhang, C. Comprehensive Utilization of Mineral Resources: Optimal Blending of Polymetallic Ore Using an Improved NSGA-III Algorithm. Sustainability 2022, 14, 10766. https://doi.org/10.3390/su141710766
Chen L, Gu Q, Wang R, Feng Z, Zhang C. Comprehensive Utilization of Mineral Resources: Optimal Blending of Polymetallic Ore Using an Improved NSGA-III Algorithm. Sustainability. 2022; 14(17):10766. https://doi.org/10.3390/su141710766
Chicago/Turabian StyleChen, Lu, Qinghua Gu, Rui Wang, Zhidong Feng, and Chao Zhang. 2022. "Comprehensive Utilization of Mineral Resources: Optimal Blending of Polymetallic Ore Using an Improved NSGA-III Algorithm" Sustainability 14, no. 17: 10766. https://doi.org/10.3390/su141710766