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<p>The design of an underground mine is a critical stage with a huge impact in its economic value. Such design encompasses the stopes and the developments to access them. The current approach is optimizing the first with the goal of maximizing economic value and designing the developments later, for the optimized stopes. Unfortunately, this sequential approach may not lead to a global optimum, because it needs to assume a <i>constant cost model</i> (CCM) with a fixed cost per ton which cannot account for shared infrastructure or transportation distances that are independent of the stope tonnages. In fact, the <i>input cost</i> (cost per ton used for optimizing the stopes) may be different from the <i>output cost</i> (cost per ton estimated after the stopes and developments are designed). In this paper, we analyze the impact of using the CCM and propose a <i>decomposed cost model</i> (DCM) coupled with a reinforcement learning algorithm (RL) that can jointly optimize the stopes and the developments. We tested the more accurate cost model and the algorithm in several scenarios. The first result shows that the gap between the input cost and the output cost may be substantial and therefore lead to very different reserve estimations. However, we also show that if the cost is updated iteratively, then the solutions converge for different initial cost estimations. Concretely in our case study, we tried an initial cost of 100$/t and of 130$/t. Both converged to 117.19$/t. A second result compared the performance of a commercial package with the proposed RL algorithm when using a CCM with a cost equal to the limit obtained before. The stopes obtained with the RL algorithm contain about 14% more gold than the commercial package, thus validating the optimization algorithm. Finally, a third experiment evaluated the impact of moving from the CCM to the DCM (both with the RL algorithm). In this case, the change of cost model produced an increase in reserves of 8%, or about 23% from the commercial package. These results highlight the impact of the cost model in the estimation of reserves and the potential of using machine learning techniques to overcome the limitations of current optimization models.</p>

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Maximizing Underground Mine Reserves Through a More Accurate Cost Model and the Application of Machine Learning

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Santiago Valencia,
  • Nelson Morales Varela,
  • Michel Gamache

摘要

The design of an underground mine is a critical stage with a huge impact in its economic value. Such design encompasses the stopes and the developments to access them. The current approach is optimizing the first with the goal of maximizing economic value and designing the developments later, for the optimized stopes. Unfortunately, this sequential approach may not lead to a global optimum, because it needs to assume a constant cost model (CCM) with a fixed cost per ton which cannot account for shared infrastructure or transportation distances that are independent of the stope tonnages. In fact, the input cost (cost per ton used for optimizing the stopes) may be different from the output cost (cost per ton estimated after the stopes and developments are designed). In this paper, we analyze the impact of using the CCM and propose a decomposed cost model (DCM) coupled with a reinforcement learning algorithm (RL) that can jointly optimize the stopes and the developments. We tested the more accurate cost model and the algorithm in several scenarios. The first result shows that the gap between the input cost and the output cost may be substantial and therefore lead to very different reserve estimations. However, we also show that if the cost is updated iteratively, then the solutions converge for different initial cost estimations. Concretely in our case study, we tried an initial cost of 100$/t and of 130$/t. Both converged to 117.19$/t. A second result compared the performance of a commercial package with the proposed RL algorithm when using a CCM with a cost equal to the limit obtained before. The stopes obtained with the RL algorithm contain about 14% more gold than the commercial package, thus validating the optimization algorithm. Finally, a third experiment evaluated the impact of moving from the CCM to the DCM (both with the RL algorithm). In this case, the change of cost model produced an increase in reserves of 8%, or about 23% from the commercial package. These results highlight the impact of the cost model in the estimation of reserves and the potential of using machine learning techniques to overcome the limitations of current optimization models.