2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
TB2 - Optimization of industrial mining complexes under uncertainty II
May 17, 2022 03:30 PM – 05:10 PM
Location: Trudeau Corporation (green)
Chaired by Roussos Dimitrakopoulos
03:30 PM - 03:55 PM
Coordination Of Drills in Open-Pit Mines: Constraint Programming Formulations
We introduce a vehicle routing and scheduling type of problem where (1) the underlying graph dynamically changes as nodes are visited, (2) the availability of the tasks that are to be performed depends on the position of the vehicles and (3) the relative positions of the vehicles with respect to each other are constrained. This problem arises in open-pit mines when trying to coordinate multiple electrical drills that operate in the same area. This problem is interesting because solving it is a key step towards automating the drilling machines. In order to solve this problem we propose a constraint programming (CP) model. We also propose a second CP model in order to solve an extension of this problem where we consider the case where two groups of drilling machines are placed at opposite sides of the drilling area; the goal being -in both cases- the minimization of the makespan. In order to accelerate the solving process we develop a heuristic algorithm that constructs a feasible solution to the problem which we use as a starting point.
03:55 PM - 04:20 PM
A Probabilistic Sequential Approach to predict the Blastability Index in an open mine pit
The Blastability Index (BI) is a quantitative measure of the blastability of a rock mass. This index is a function of the hardness of the rock and depends on mechanical and geological variables. We are interested in predicting the blastability index for all the coordinates (x,y,z) of a deposit. An approach is proposed based on the assumption that at the beginning no information is known about the blastability index. The developed model should be able to be adjusted as information is collected during drilling. We also want to determine at what point we can have good estimates. Ideally, tests on different drilling patterns should be carried out on different types of deposits. The developed model must adopt a sequential learning. The data are observed as sequence of observed holes. Probabilistic supervised learning approaches can be used. Among these approaches, we mention the Gaussian processes which are very similar to Kriging in geostatistics. Our purpose is to explore the Gaussian Processes literature to build a sequential real time prediction system. The goal is to be able to adaptability update the model in real time when new upcoming observation of newly drilled hole arrives. Approximations methods such as sparse Gaussian Process would be investigated to see if they provide faster training time.
keywords: Gaussian Processes, Sparse Gaussian Processes, Deep Gaussian Processes, Bayesian Inference, Variational Inference, MCMC Sampling.
04:20 PM - 04:45 PM
Neural Networks meet Optimization: Computational Efficiency for Simultaneous Stochastic Optimization of Mineral Value Chains
Mineral value chains include the joint modelling of mines, processing facilities, waste management facilities, and transportation. The traditional mine planning process usually consists of the optimization of each stage separately and sequentially. Such sequential optimization approaches neglect the synergies among different components in a mining complex and thus fail to capture these synergies, leading to an inferior net present value (NPV) of mining projects. Simultaneous stochastic optimization of the entire mineral value chain has been shown to increase the NPV of a mining project while reducing the risk of not meeting production targets by producing a more coordinated schedule and destination policy. However, simultaneous stochastic optimizations of large and complex mineral value chains are computationally expensive. To tackle this computational efficiency issue, this presentation proposes a metaheuristic that combines heuristics, mathematical programming techniques, and machine learning that utilizes artificial neural networks as a surrogate. In this presentation, the general framework of the algorithm is introduced with the exploration of different inputs. The result of the numerical case study is presented with a comparison to the algorithm without the neural network to evaluate the efficiencies.