Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model

Presidential address: Optimization in underground mine planning-developments and opportunities.

Presidential address presented at the The Southern African Institute of Mining and Metallurgy Annual General Meeting on 11 August 2016.The application of mining-specific and generic optimization techniques in the mining industry is deeply rooted in the discipline of operations research (OR). OR has its origins in the British Royal Air Force and Army around the early 1930s. Its development continued during and after World War II. The application of OR techniques to optimization in the mining industry started to emerge in the early 1960s. Since then, optimization techniques have been applied to solve widely different mine planning problems. Mine planning plays an important role in the mine value chain as operations are measured against planned targets in order to evaluate operational performance. An optimized mine plan is expected to be sufficiently robust to ensure that actual outcomes are close or equal to planned targets, provided that variances due to poor performance are minimal. Despite the proliferation of optimization techniques in mine planning, optimization in underground mine planning is less extensively developed and applied than in open pit mine planning. This is due to the fact that optimization in underground mine planning is far more complex than open pit optimization. Optimization in underground mine planning has been executed in four broad areas, namely: development layouts, stope envelopes, production scheduling, and equipment selection and utilization. This paper highlights commonly applied optimization techniques, explores developments and opportunities, and makes a case for integrated three-dimensional (3D) stochastic optimization, in underground mine planning.MvdH201

Production scheduling and mine fleet assignment using integer programming

Production Scheduling, extraction sequence of mining blocks in different production periods to maximize profit over the life of the mine and subjected to different constraints, is an important aspect of any mining activity. Mine production scheduling problem can be solved using various approaches, but the best approach is one which can give an optimal result. Production scheduling solely cannot result in a proper planning thus, fleet assignment problem needs to be incorporated into production scheduling problem to have a realistic mine plan. Proper fleet assignment ensures that the fleet is not under or over utilized. Fleet assignment problem is integer type programming since, size of fleet cannot be a floating number. In this thesis, production scheduling and fleet assignment problem are solved using branch and cut algorithm. Production schedule for 4736 blocks from a case study of coal mine is done with a production period of 5 years. Solution time for solving the production scheduling problem was 48.14 hours with an NPV value of Rs 4.45938x1011. Short terms production scheduling is done for one year and the NPV value obtained was Rs 7.59796x1010 with a solution time of 57.539 minutes. Fleet assignment is done for first year and is observed that the size of dumper fleet can be reduced to 30 thus saving huge amount of initial capital investment

Evaluating the efficiency of the genetic algorithm in designing the ultimate pit limit of open-pit mines

The large-scale open-pit mine production planning problem is an NP-hard issue. That is, it cannot be solved in a reasonable computational time. To solve this problem, various methods, including metaheuristic methods, have been proposed to reduce the computation time. One of these methods is the genetic algorithm (GA) which can provide near-optimal solutions to the problem in a shorter time. This paper aims to evaluate the efficiency of the GA technique based on the pit values and computational times compared with other methods of designing the ultimate pit limit (UPL). In other words, in addition to GA evaluation in UPL design, other proposed methods for UPL design are also compared. Determining the UPL of an open-pit mine is the first step in production planning. UPL solver selects blocks whose total economic value is maximum while meeting the slope constraints. In this regard, various methods have been proposed, which can be classified into three general categories: Operational Research (OR), heuristic, and metaheuristic. The GA, categorized as a metaheuristic method, Linear Programming (LP) model as an OR method, and Floating Cone (FC) algorithm as a heuristic method, have been employed to determine the UPL of open-pit mines. Since the LP method provides the exact answer, consider the basics. Then the results of GA were validated based on the results of LP and compared with the results of FC. This paper used the Marvin mine block model with characteristics of 53271 blocks and eight levels as a case study. Comparing the UPL value's three ways revealed that the LP model received the highest value by comparing the value obtained from GA and the FC algorithm's lowest value. However, the GA provided the results in a shorter time than LP, which is more critical in large-scale production planning problems. By performing the sensitivity analysis in the GA on the two parameters, crossover and mutation probability, the GA's UPL value was modified to 20940. Its UPL value is only 8% less than LP's UPL value

An adaptive neighborhood search algorithm for optimizing stochastic mining complexes

Les métaheuristiques sont très utilisées dans le domaine de l'optimisation discrète. Elles permettent d’obtenir une solution de bonne qualité en un temps raisonnable, pour des problèmes qui sont de grande taille, complexes, et difficiles à résoudre. Souvent, les métaheuristiques ont beaucoup de paramètres que l’utilisateur doit ajuster manuellement pour un problème donné. L'objectif d'une métaheuristique adaptative est de permettre l'ajustement automatique de certains paramètres par la méthode, en se basant sur l’instance à résoudre. La métaheuristique adaptative, en utilisant les connaissances préalables dans la compréhension du problème, des notions de l'apprentissage machine et des domaines associés, crée une méthode plus générale et automatique pour résoudre des problèmes. L’optimisation globale des complexes miniers vise à établir les mouvements des matériaux dans les mines et les flux de traitement afin de maximiser la valeur économique du système. Souvent, en raison du grand nombre de variables entières dans le modèle, de la présence de contraintes complexes et de contraintes non-linéaires, il devient prohibitif de résoudre ces modèles en utilisant les optimiseurs disponibles dans l’industrie. Par conséquent, les métaheuristiques sont souvent utilisées pour l’optimisation de complexes miniers. Ce mémoire améliore un procédé de recuit simulé développé par Goodfellow & Dimitrakopoulos (2016) pour l’optimisation stochastique des complexes miniers stochastiques. La méthode développée par les auteurs nécessite beaucoup de paramètres pour fonctionner. Un de ceux-ci est de savoir comment la méthode de recuit simulé cherche dans le voisinage local de solutions. Ce mémoire implémente une méthode adaptative de recherche dans le voisinage pour améliorer la qualité d'une solution. Les résultats numériques montrent une augmentation jusqu'à 10% de la valeur de la fonction économique.Metaheuristics are a useful tool within the field of discrete optimization that allow for large, complex, and difficult optimization problems to achieve a solution with a good quality in a reasonable amount of time. Often metaheuristics have many parameters that require a user to manually define and tune for a given problem. An adaptive metaheuristic aims to remove some parameters from being tuned or defined by the end user by allowing the method to specify and/or adapt a parameter or set of parameters based on the problem. The adaptive metaheuristic, using advancements in understanding of the problem being solved, machine learning, and related fields, aims to provide this more generalized and automatic toolkit for solving problems. Global optimization of mining complexes aims to schedule material movement in mines and processing streams to maximize the economic value of the system. Often due to the large number of integer variables within the model, complicated constraints, and non-linear constraints, it becomes prohibitive to solve these models using commercially available optimizers. Therefore, metaheuristics are often employed in solving mining complexes. This thesis builds upon a simulated annealing method developed by Goodfellow & Dimitrakopoulos (2016) to optimize the stochastic global mining complex. The method outlined by the authors requires many parameters to be defined to operate. One of these is how the simulated annealing algorithm searches the local neighborhood of solutions. This thesis illustrates and implements an adaptive way of searching the neighborhood for increasing the quality of a solution. Numerical results show up to a 10% increase in objective function value

Improving Confidence in Evolutionary Mine Scheduling via Uncertainty Discounting

Mine planning is a complex task that involves many uncertainties. During early stage feasibility, available mineral resources can only be estimated based on limited sampling of ore grades from sparse drilling, leading to large uncertainty in under-sampled parts of the deposit. Planning the extraction schedule of ore over the life of a mine is crucial for its economic viability. We introduce a new approach for determining an "optimal schedule under uncertainty" that provides probabilistic bounds on the profits obtained in each period. This treatment of uncertainty within an economic framework reduces previously difficult-to-use models of variability into actionable insights. The new method discounts profits based on uncertainty within an evolutionary algorithm, sacrificing economic optimality of a single geological model for improving the downside risk over an ensemble of equally likely models. We provide experimental studies using Maptek's mine planning software Evolution. Our results show that our new approach is successful for effectively making use of uncertainty information in the mine planning process

Optimised decision-making under grade uncertainty in surface mining

Mining schedule optimisation often ignores geological and economic risks in favour of simplistic deterministic methods. In this thesis a scenario optimisation approach is developed which uses MILP optimisation results from multiple conditional simulations of geological data to derive a unique solution. The research also generated an interpretive framework which incorporates the use of the Coefficient of Variation allowing the assessment of various optimisation results in order to find the solution with the most attractive risk-return ratio

Quantification of uncertainty of geometallurgical variables for mine planning optimisation

Interest in geometallurgy has increased significantly over the past 15 years or so because of the benefits it brings to mine planning and operation. Its use and integration into design, planning and operation is becoming increasingly critical especially in the context of declining ore grades and increasing mining and processing costs. This thesis, comprising four papers, offers methodologies and methods to quantify geometallurgical uncertainty and enrich the block model with geometallurgical variables, which contribute to improved optimisation of mining operations. This enhanced block model is termed a geometallurgical block model. Bootstrapped non-linear regression models by projection pursuit were built to predict grindability indices and recovery, and quantify model uncertainty. These models are useful for populating the geometallurgical block model with response attributes. New multi-objective optimisation formulations for block caving mining were formulated and solved by a meta-heuristics solver focussing on maximising the project revenue and, at the same time, minimising several risk measures. A novel clustering method, which is able to use both continuous and categorical attributes and incorporate expert knowledge, was also developed for geometallurgical domaining which characterises the deposit according to its metallurgical response. The concept of geometallurgical dilution was formulated and used for optimising production scheduling in an open-pit case study.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

Controlling short-term deviations from production targets by blending geological confidence classes of reporting standards

Meeting short-term production targets is desired by many companies, since this would enable them to finetune the processing operation,meet budget plans and obey contract requirements. Recently stochastic optimization solutions have been developed requiring geostatistical simulations as input. The significant value added has been demonstrated, however, an operational implementation of such approaches for day-to-day use is complex and seems currently difficult as it requires expert knowledge and extensive computational capacity. To control the short-term deviations, a new fast metaheuristic scheduler is developed that blends Geological Confidence Classes (GCC’s) from resource reporting standards. For the scheduler, a new penalty function is developed to schedule for a target blend of GCC’s and a new method is developed to enforce smooth mining patterns in three dimensions. The metaheuristic solver uses a Genetic Algorithm and an Ant Colony Optimization algorithm to efficiently converge towards the Pareto optimum. To establish an optimal blend of GCC’s, a methodology is developed which creates a range of equally probable scenarios of deviations from production targets for different blends of GCC’s. A least-squares estimate can be fitted to these scenarios at the required level of confidence to determine the optimal blend for a maximum allowed deviation. An historical world class gold deposit is used to show that the monthly and quarterly deviations can be controlled by blending GCC’s. Furthermore, the case study shows the possibility to establish an optimal blend of GCC’s by using the developed methodology. The scheduler proofs to be able to efficiently create and evaluate schedules to blend the GCC’s for this case study. For a maximum quarterly deviation of 15% at a 90% confidence level, the established optimal blend is 59% ore tonnage classified as measured resources. For the monthly deviations, a maximum of 15% is too low and cannot be met at a 90% confidence level