My research focuses on using operations research and advanced analytical methods such as mathematical modeling, optimization, discrete event/continuous simulation, and intelligent agents to arrive optimal or near-optimal solutions to complex, large-scale mine planning/operations decision-making problems.
Development of new optimization techniques and uncertainty quantification for mine planning and design plays a vital role in reducing environmental footprint and financial risk of mining projects. Deviations from optimal plans in mega mining projects will result in huge financial losses, delayed reclamation, and resource sterilization.
My research interests focuses on two areas of research with the general goal of reducing the mining environmental impact.
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Risk Based Mine Planning and Mineral Processing Design Integration,
using
o Discrete optimization
o Stochastic programming
o Multi-objective optimization
o Intelligent multi-agent systems
o Heuristics and meta-heuristics
●
Simulation Optimization of Mining Systems, using
o Discrete event simulation
o Continuous simulation
o Stochastic modeling
My research activities are conducted through the industrial research consortium, Mining Optimization Laboratory (MOL) at the School of Mining and Petroleum Engineering at the University of Alberta.
The objective of the research group is to focus on creative, far-sighted fundamental research addressing industry applicative needs. MOL carries out research projects with clear objectives, scope, deliverables, and timelines with focus on two major areas:
● Applications of Operations Research in Mining Planning and Design.
● Simulation / Optimization of Mining Systems.
For more information please visit the MOL website at: www.ualberta.ca/mol
● Large-Scale Open Pit Production Scheduling Framework using Mixed Integer Linear Programming.
● Intelligent 3D Algorithm for Optimal Long-Term Open Pit Planning.
● Continuous Time Open Pit Simulator
● Open Pit Modified Geometrical Models
● Economic Pit Expansion Model
● Object Oriented Analysis, Design, and Implementation of Intelligent Planning Framework
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Development of a mixed integer linear programming (MILP) formulation for open pit production scheduling optimization. We developed, implemented, and tested practical MILP models for open pit production scheduling in TOMLAB/CPLEX environment. The MILP formulation of open pit production scheduling becomes intractable because of the size of the problem. To reduce the number of continuous and binary variables in the model, we aggregated blocks into larger units, referred to as mining-cuts using clustering algorithms. We presented two MILP formulations at two different levels of granularity: (i) controlled processing at block level and mining at mining-cut level; and (ii) controlled processing and mining both at mining-cut level. Details of the numerical modelling techniques and implementation stages were also presented. The main objective of this research was to highlight the considerable achievable economic gains that are possible through production scheduling optimization. Also, we aimed at improving the practicality and performance of the MILP production scheduling formulations. We verified and validated the MILP production scheduler by a comparative case study against one of the standard industry tools — Whittle strategic mine planning software. The input parameters and the mining strategies in Whittle and MILP scheduler were inspected cautiously to make sure an unbiased comparative study was undertaken. The goal was to maximize the NPV at a discount rate of 10%, while assuring a constant uniform feed to the processing plant. We aimed at generating a practical schedule taking into account the minimum operational room required, the number of active benches in each period, the number of benches added to the pit in each period, uniformity of processing plant feed, and variability of the stripping ratio. The difference between the cumulative discounted cash flow of the MILP scheduler and the Whittle Milawa alanced results is $50.4 million dollars. This is a substantial amount considering the relatively small size of the open pit. Production scheduling optimization techniques are still not widely used in the mining industry. There is a need to improve the practicality and performance of the current production scheduling optimization tools used in mining industry. Also, to gain more common recognition in industry, there is a need to highlight the considerable achievable economic gains that are possible through production scheduling optimization. Further focused research is underway to develop and test different clustering techniques that would generate an optimized clustering approach for the mining-cuts. Also the next step is to extend the mixed integer linear programming framework into stochastic mathematical programming domain to address the grade uncertainty issue.
● Development of Intelligent 3D Algorithm for Optimal Long-Term Open Pit Planning.
The major shortcomings of the current mine planning and optimization techniques can be summarized as: (i) inability to solve large industrial problems; (ii) limitation in dealing with stochastic processes and random variables governing mining operations; (iii) inadequacy in referencing time aspect of the final pit limit optimization problem. These deficiencies can cause an open pit mining operation severely in terms of dollars, time, strategic and tactical plans. The researcher developed and implemented the intelligent open pit optimal production simulator (IOPS) based on reinforcement learning to address these problems. Q-learning as the core of IOPS engine learns optimal plans from experience in the form of sample simulation episodes of the open pit push-backs. Unlike the current algorithms IOPS has the capability of dealing with the mine planning parameters as stochastic variables. The verification and validation of the research through case studies of operating mines demonstrated remarkable improvement on the expected net present value of the mining investments, comparing to the results of the standard tools used in industry. The intelligent simulator leads to net present values 5-8% better than the conventional methods. This research endeavor was a ground-breaking effort employing artificial intelligence in order to provide knowledge and novel understandings into mine planning domain. The research enormously contributes to the body of knowledge on intelligent open pit mine planning and design. The research has formulated robust mathematical models and comprehensive algorithms, expanding the frontiers of open pit planning and optimization paradigm. The models developed enables step-changes in planning and management of mines. The algorithms and models developed have the potential to be the fundamental of the next generation of commercial mine design software packages based on intelligent agents.
● Development of Continuous Time Open Pit Simulator
Current mine production planning, scheduling, and allocation of resources are based on mathematical programming models. In practice, the optimized solution can not be attained without examining all possible combinations and permutations of the extraction sequence. Operations research methods have limited applications in large-scale surface mining operations, because the number of variables becomes too large. The researcher developed and implemented the continuous-time simulation algorithm to address these problems. The researcher simulated the dynamics of open pit geometry and the subsequent material movement as a continuous system described by time-dependent differential equations. The continuous-time open pit production simulator (COPS), was developed and implemented in MATLAB. Discrete open pit production simulator (DOPS), mimics the stochastic dynamic expansion of an open pit using discrete incremental push-backs in different directions. The interactions of economic pit expansion model with DOPS returns the operation’s net present value following the simulated schedule. The simulation is run for sufficient iterations to find the practical sequence of extraction among all realizations, which results in the highest NPV. COPS models the dynamics of open pit geometry and the subsequent materials movement as a continuous system described by time-dependent partial differential equations. Function approximation of the discrete simulated push-backs generated by DOPS, provides the means to convert the set of PDEs to a system of ODEs. Numerical integration yields the trajectory of the pit geometry over time with the respective volume of materials transferred and the NPV of the mining operation. A case study of an iron ore deposit with 114 000 blocks was carried out to verify and validate the model. The continuous simulation yielded an NPV of $449 million over a 21-year of mine life at a discount rate of 10% per annum, whereas the conventional methods yielded an NPV of $336 million. The continuous-time simulator, in conjunction with the stochastic simulation models and intelligent agents provide a powerful tool for optimizing the scheduling process, while addressing the random field and dynamic processes in open pit mine planning.
● Development of Open Pit Modified Geometrical Models
Ore and waste extraction from an open pit mine takes place on different elevations. The pit expands horizontally and vertically towards the final pit limits. The main long-term objective is to meet quantity and quality targets of production in order to maximize the market value of the mining venture. There is therefore a need for models that capture the evolution of the open pit geometry as the pit expands through time and space. Previous research has provided a basis for using the solid geometry of an elliptical frustum to model the open pit expansion process. The assumption underlying the elliptical frustum causes a considerable error in volume computations. To reduce this error, a more accurate, modified elliptical frustum model was presented by the researcher. The modified geometry consists of four quadrants of elliptical frustums, which are appended along the major and minor axes of the top ellipsoid. This model divides the open pit into four sections, north-west, north-east, south-west, and south-east. Each area is defined by the major and minor axes of the respective top ellipsoid. The overall stable pit slope is defined for each region according to the rock slope stability and geo-mechanical studies. This is a pioneering effort at modeling open pit geometry with modified elliptical frustum with five variables. The new model reduces considerable error in volume calculations. It also facilitates the process of saving the long term plan as incremental changes in the dimensions of the major and minor axes of the elliptical frustum rather than saving all the block coordinates for different scenarios. The improvement in accuracy, reporting the volumes of ore and waste transferred during operation has been between 9-13%.
● Development of Economic Pit Expansion Model
A useful planning model must be able to relate the dynamics of the open pit with the geological and economic block model. Such a model must yield grade of ore, stockpile, and contaminant materials. It must also provide the amount of ore and waste moved on a bench-by-bench basis, as well as, the economics of the pushback design for each period of the mining operations. The researcher has developed the economic pit expansion model, which fits the modified open pit geometrical model on the economic block model, and it returns the pit monetary value, average grade of ore, waste, and stockpile material at any desired period of production. The procedure starts searching the economic block model level by level. In each level, the distance between the center of the ellipse and the center of the current block is compared to the length of the radii of the ellipse. Afterward, a decision is made as to whether or not the block is inside the frustum. The procedure finally returns the volume of ore, waste, stockpile material, and their respective grades, and the monetary value of the suggested pushback.
● Object Oriented Analysis, Design, and Implementation of Intelligent Planning Framework
Prototype software packages are one of the ways of disseminating knowledge into practical applications in long-term. The researcher analyzed, designed, and implemented the algorithms and models of the intelligent open pit optimal simulator (IOPS) as a graphical user interface (GUI). The Java Reinforcement Learning Library, JavaRL, (Kerr et al., 2003) was chosen as the core of the IOPS application implementation. Java programming language version 1.4.2 (Sun Microsystems, 1994-2006) and MATLAB version 7.04 (MathWorks, 2005) were selected as the platform for programming. The IOPS graphical user interface was implemented using IntelliJ IDE (JetBrains, 2000-2006). The graphical user interface facilitates the interaction of the end users with the reinforcement learning kernel of the software. The user can simply set the parameters of the design such as: block dimensions, model framework origin, stable slope angles, final pit limit dimensions, minimum mining width, yearly production targets, and the input block-model file. The IOPS engine is based on three basic objects: agents, environments, and simulations. The intelligent learning agent interacts with the economic block model as the environment. The simulation manages the interaction between the agent and the environment and collects data. The numerical reward is a number representing a push-back’s cash flow, the actions and states are instances of classes derived from the abstract classes respectively.