Abstract
Mineral value chains, also known as mining complexes, involve mining, processing, stockpiling, waste management and transportation activities. Their optimization is typically partitioned into separate stages, considered sequentially. An integrated stochastic optimization of these stages has been shown to increase the net present value of the related mining projects and operations, reduce risk in meeting production targets, and lead to more robust and coordinated schedules. However, it entails solving a larger and more complex stochastic optimization problem than separately optimizing individual components of a mineral value chain does. To tackle this complex optimization problem, a new matheuristic that integrates components from exact algorithms (relaxation and decomposition), machine learning techniques (reinforcement learning and artificial neural networks), and heuristics (local improvement and randomized search) is proposed. A general mathematical formulation that serves as the basis for the proposed methodology is also introduced, and results of computational experiments are presented.
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Notes
Note that, in this paper, it is assumed that the recovery factor at the first-stage and intermediate facilities is equal to 1, while it is smaller than 1 in the last-stage facilities. Different values for the recovery factor can be easily accommodated without any added conceptual difficulties.
Note that upper bound on the flow from \(i\) to \(j\) cannot be defined as \(\overline{{Y}_{ij}^{s}}=min\{{\sum }_{g\in {\mathcal{G}}_{i}}{w}_{g}^{s}, \overline{{C}_{i}}, \overline{{C}_{j}}\}\) because the capacity constraints are modelled as soft constraints (cf. constraints (27)–(29)), and thus the flow on arc \((i,j)\) might exceed the facilities’ capacity.
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Acknowledgements
The work in this paper was funded by NSERC CRDPJ 411270-10, NSERC Discovery Grant 239019-06, and the industry members of the COSMO Stochastic Mine Planning Laboratory: AngloGold Ashanti, Barrick, BHP, De Beers, Kinross, Newmont, and Vale. This support is gratefully acknowledged. The authors would like to thank two anonymous referees for their valuable comments and suggestions that helped improve the paper.
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Lamghari, A., Dimitrakopoulos, R. & Senécal, R. A matheuristic approach for optimizing mineral value chains under uncertainty. Optim Eng 23, 1139–1164 (2022). https://doi.org/10.1007/s11081-021-09629-9
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DOI: https://doi.org/10.1007/s11081-021-09629-9