Simultaneous Stochastic Optimization Research Articles

Adaptive Simultaneous Stochastic Optimization of the Escondida Mining Complex, Chile

AbstractThis paper presents the application of adaptive simultaneous stochastic optimization with a representative branching framework to generate a strategic mining plan for the Escondida mining complex, the world’s largest copper-production operation. This adaptive stochastic optimization considers geological uncertainty while integrating investment and operational alternatives in the production schedule of a mining complex. Mining complexes are comprised of interconnected components affected by multiple sources of uncertainty. Thus, they must be optimized simultaneously in order to maximize their value, manage environmental impacts, and minimize risk. Additionally, due to the extensive lives of assets and the dynamic and uncertain environment in which mining complexes operate, it is not reasonable to assume that the current strategic plan will remain optimal. Thus, an operationally feasible method to embed alternatives in the mine plan is used. The method utilized provides a strategic plan with representative branches for future possible investment decisions. Adaptive decisions are made sequentially over time, activating costs and effects over the model. The optimization process chooses the optimal strategic production plan accordingly, as well as the investments made and their timing. The Escondida mining complex is a multi-element, multi-pit operation with nine different processing destinations. Investment options considered herein are truck and shovel fleet sizing, adding a secondary crusher in one of the plants, and investing in a main crusher assigned to one of the pits. Additionally, operational alternatives at the mine and plant levels are included. The adaptive solution shows a substantial probability that the mine plan might change its design substantially due to geological uncertainty, presenting an increased expected net present value when compared to the previously developed stochastic mathematical programming formulation that does not consider adaptive decisions, thus generating a single static strategic production plan for the related mining complex. Further studies at the Escondida mining complex can consider adoptive solutions integrating capital investments pertinent to climate change issues.

Learning to schedule heuristics for the simultaneous stochastic optimization of mining complexes

The simultaneous stochastic optimization of mining complexes is a large-scale stochastic combinatorial optimization problem that simultaneously manages the extraction of materials from multiple mines and their processing through interconnected facilities to generate a set of final products, while taking into account geological (material supply) uncertainty to manage the associated risk. Existing methods do not offer solutions to such a complex problem in a reasonable time. This work proposes a data-driven framework for heuristic scheduling in a fully self-managed hyper-heuristic to solve the simultaneous stochastic optimization of mining complexes. The proposed learn-to-perturb hyper-heuristic is a multi-neighborhood simulated annealing algorithm that selects the heuristic (perturbation) to be applied in a self-adaptive manner using reinforcement learning to efficiently explore the local search that is best suited to a particular search point. By learning from data that describes the performance of the heuristics, a problem-specific ordering of heuristics that collectively find better solutions faster is obtained. To the best of our knowledge, this research proposes the first data-driven heuristic search tree for mine planning. Results from several instances of two types of large-scale industrial mining complexes show a reduction of up to 80% in execution time and an order of magnitude reduction in primal suboptimality compared to state-of-the-art methods.

Simultaneous stochastic optimization of an open-pit mining complex with preconcentration using reinforcement learning

Simultaneous stochastic optimization of an open-pit mining complex with preconcentration using reinforcement learning

Simultaneous stochastic optimization of mining complexes - mineral value chains: an overview of concepts, examples and comparisons

ABSTRACT This paper overviews the simultaneous stochastic optimisation of mining complexes or mineral value chains where raw materials mined from mineral deposits in an area are transformed into a set of sellable products. The supply of materials extracted from available mines represents a major source of uncertainty and technical risk that needs to be managed, along with market demand. An overview of the main concepts, case studies and comparisons show how the approach manages risk and capitalises on synergies between the components of the mining complex and major differences from conventional methods. Results lead to strategic plans with larger amounts of metal produced from the same mineral resources, a substantially improved ability for operations to meet production forecasts, and a significantly higher net present value.

A Data-Driven Approach for the Simultaneous Stochastic Optimization of Mining Complexes

The simultaneous stochastic optimization of mining complexes (SSOMC) is a large-scale stochastic combinatorial optimization problem that simultaneously manages the extraction of materials from multiple mines and their processing using interconnected facilities to generate a set of finished products while taking into account geological uncertainty to manage the associated risk. To address the need for self-managed solution approaches that are able to tackle large-scale instances without resorting to aggregation, this work proposes a data-driven framework for heuristic scheduling in a fully self-managed hyper-heuristic to solve the SSOMC. The proposed hyper-heuristic selects the heuristic (perturbation) to be applied in a self-adaptive manner using state-of-the-art reinforcement learning methods to efficiently explore which local search is best suited for a particular search point. Experiments on real-world mining complexes show a significant reduction in the computational time by 30–45%.

Geometallurgical prediction models of processing plant indicators for stochastic mine production scheduling

This article presents a new geometallurgical framework that builds empirical prediction models of key performance indicators of the processing plant and integrates them into a simultaneous stochastic optimization model for mine production scheduling. The prediction models are created by tracking blended rock properties and matching them with observed responses from the operating processing plant. Several applied case studies in a gold mining complex are presented building prediction models of ball mill throughput, steel ball consumptions, and reagent consumptions from collected data in a gold leaching operation. Finally, the integration of these geometallurgical prediction models into stochastic mine production scheduling is demonstrated to monetize the gained insights. Compared with conventional planning, the resulting mine plans increase yearly profit and are more likely to align with production targets.

Learning to Schedule Heuristics for the Simultaneous Stochastic Optimization of Mining Complexes

Learning to Schedule Heuristics for the Simultaneous Stochastic Optimization of Mining Complexes

Simultaneous Stochastic Optimization of a Mining Complex with Preconcentration Using Reinforcement Learning

Simultaneous Stochastic Optimization of a Mining Complex with Preconcentration Using Reinforcement Learning

Simultaneous production scheduling and transportation optimization from mines to port under uncertain material supply

Industrial mining complexes can be optimized using simultaneous stochastic optimization (SSO), which manages the risks associated with meeting production targets while capitalizing on the synergies that exist between the various components of the related mineral value chain. This paper introduces an extension of past SSO approaches for the long-term, allowing to simultaneously optimize the schedule of the production and the mines-to-port transportation of mining complexes under uncertain material supply. The inclusion of mine-to-port transportation scheduling facilitates the analysis of the mines-to-port equipment usage, while generating suitable mine production schedules. The proposed stochastic mathematical program formulation is applied to a two-mine, single-port iron ore mining complex. In doing so, it is shown that the related model is capable of producing optimal production schedules, minimizing deviations from products requirements, and delineating the yearly use of the mine-to-port transportation equipment.

An Application of Simultaneous Stochastic Optimization at a Large Open-Pit Gold Mining Complex under Supply Uncertainty

The simultaneous stochastic optimization of mining complexes optimizes various components of the related mineral value chain jointly while considering material supply (geological) uncertainty. As a result, the optimization process capitalizes on the synergies between the components of the system while not only quantifying and considering geological uncertainty, but also producing strategic mine plans, maximizing the net present value. This paper presents an application of simultaneous stochastic optimization at a large gold mining complex. The complex contains three open-pit mines, three stockpiles, a waste dump, and a processing facility. Material hardness management is integrated at the processing facility. The case study generated production schedules for each mineral deposit considered, as well as an overall assessment of the project and related forecasts. It resulted in an 18 year life-of-asset and identified the semi-autogenous grinder (SAG) mill as the bottleneck of the operation.

Simultaneous stochastic optimization of production sequence and dynamic cut-off grades in an open pit mining operation

An open pit mining operation is a complex system that constitutes several components or processes. An optimal production sequence that defines timing of extraction and a dynamic cut-off grade policy that defines the supply of materials from sources to destinations within the system are crucial to the success of an operation. In current practice, separate sequencing and cut-off grade models achieve these important milestones as part of strategic planning. This paper presents a mathematical model that derives the optimal extraction sequence and cut-off grade policy simultaneously considering grade uncertainty and stockpiling. A framework of genetic, maximum flow and cut-off grade algorithms solves this complex non-linear problem. An application of the method at realistic copper and gold mining operations reveals the value (up to 29% increase in discounted value) of stockpiling as well as risk quantification under uncertainty.

Adaptive simultaneous stochastic optimization of a gold mining complex: A case study

Adaptive simultaneous stochastic optimization of a gold mining complex: A case study

Simultaneous stochastic optimization of an open pit gold mining complex with supply and market uncertainty

ABSTRACTA mining complex can include multiple mines, stockpiles, waste dumps and processing facilities. Traditional optimization approaches are often based on sequential optimization of the various components in the mining complex leading to suboptimal solutions. They also do not account for uncertainty in critical inputs, resulting in misleading forecasts. This paper presents an application of a stochastic framework that simultaneously optimizes mining, destination and processing decisions for a multi-pit, multi-processor gold mining complex. The framework accounts for supply and market uncertainty via stochastic orebody and commodity price simulations as inputs to a unified optimization model. The case study notably assesses the impacts of integrating market uncertainty as input that influences all components of the production schedule. Additionally, cut-off grade decisions are determined by the simultaneous optimization process, considering material variability and operating constraints while reducing the number of a-priori decisions to be made. This approach generates solutions that capitalize on the synergies between extraction sequencing, cut-off grade optimization, blending and processing while managing and quantifying risk in strategic plans, which ultimately leads to more metal production and higher net present values.

Effects of High-Order Simulations on the Simultaneous Stochastic Optimization of Mining Complexes

A mining complex is composed of mines, mineral processing streams, stockpiles, and waste facilities, which culminate with generated products that are delivered to customers. The supply uncertainty and variability of materials extracted from the mines, which flow through a mining complex to generate products, can be quantified through geostatistical simulations and can be used as inputs to the simultaneous optimization of mining complexes. A critical aspect to consider is that mineral deposits are characterized by spatially complex, non-Gaussian geological properties and multiple-point connectivity of high-grades, features that are not captured by conventional second-order simulation methods. This paper investigates the benefits of simultaneously optimizing a mining complex where the simulations of the mineral deposit are generated by a high-order, direct-block simulation approach. The optimized life-of-mine (LOM) production schedule is compared to a case in which the same setting is optimized by having the related simulations generated using a second-order simulation method. The comparison shows that the incorporation of simulations that reproduce the spatial connectivity of high-grades results in a more informed LOM production schedule. The sequence of extraction is driven by the spatial connectivity of high-grades, resulting in a mill throughput with better material quality and reduced waste extraction. Furthermore, the discounted cash-flow increases by more than 5% as compared to the case in which the second-order simulations are used.

Application of simultaneous stochastic optimization with geometallurgical decisions at a copper–gold mining complex

ABSTRACTSimultaneous stochastic optimization of mining complexes aims to optimize its different components in a single optimization model under grade, geometallurgical and material type uncertainty. The single optimization model capitalizes on synergies between the different components and the quantified variability and uncertainty of the materials mined, to better meet production targets while maximizing the net present value (NPV) of a mining complex. Integrating uncertainty and decisions about geometallurgical aspects of materials in the optimization model assists in achieving higher and more stable throughput with comminution circuits. This paper introduces an approach to integrate uncertainty and decisions about two non-additive geometallurgical properties, semi-autogenous power index and bond work index in the simultaneous stochastic optimization model. An application of the proposed approach at a large copper–gold mining complex indicates higher chances of meeting the different production targets, substantial increase in metal production and a 19.3% increase in NPV compared to the conventional plan.

Simultaneous stochastic optimization of production scheduling at Twin Creeks Mining Complex, Nevada

Simultaneous stochastic optimization of production scheduling at Twin Creeks Mining Complex, Nevada

Simultaneous Stochastic Optimization of Mining Complexes and Mineral Value Chains

Recent developments in modelling and optimization approaches for the production of mineral and energy resources have resulted in new simultaneous stochastic optimization frameworks and related digital technologies. A mining complex is a type of value chain whereby raw materials (minerals) extracted from various mineral deposits are transformed into a set of sellable products, using the available processing streams. The supply of materials extracted from a group of mines represents a major source of uncertainty in mining operations and mineral value chains. The simultaneous stochastic optimization of mining complexes, presented herein, aims to address major limitations of past approaches by modelling and optimizing several interrelated aspects of the mineral value chain in a single model. This single optimization model integrates material extraction from a set of sources along with their uncertainty, the related risk management, blending, stockpiling, non-linear transformations that occur in the available processing streams, the utilization of processing streams, and, finally, the transportation of products to customers. Uncertainty in materials extracted from the related mineral deposits of a mining complex is represented by a group of stochastic simulations. This paper presents a two-stage stochastic mixed integer nonlinear programming formulation for modelling and optimizing a mining complex, along with a metaheuristic-based solver that facilitates the practical optimization of exceptionally large mathematical formulations. The distinct advantages of the approach presented herein are demonstrated through two case studies, where the stochastic framework is compared to past approaches that ignore uncertainty. Results demonstrate major improvements in both meeting forecasted production targets and net present value. Concepts and methods presented in this paper for the simultaneous stochastic optimization for mining complexes may be adopted and applied to the optimization of smart oil fields.

Estimation of subsurface geomodels by multi-objective stochastic optimization

We present a new method to estimate subsurface geomodels using a multi-objective stochastic search technique that allows a variety of direct and indirect measurements to simultaneously constrain the earth model. Inherent uncertainties and noise in real data measurements may result in conflicting geological and geophysical datasets for a given area; a realistic earth model can then only be produced by combining the datasets in a defined optimal manner. One approach to solving this problem is by joint inversion of the various geological and/or geophysical datasets, and estimating an optimal model by optimizing a weighted linear combination of several separate objective functions which compare simulated and observed datasets. In the present work, we consider the joint inversion of multiple datasets for geomodel estimation, as a multi-objective optimization problem in which separate objective functions for each subset of the observed data are defined, followed by an unweighted simultaneous stochastic optimization to find the set of best compromise model solutions that fits the defined objectives, along the so-called “Pareto front”. We demonstrate that geostatistically constrained initializations of the algorithm improves convergence speed and produces superior geomodel solutions. We apply our method to a 3D reservoir lithofacies model estimation problem which is constrained by a set of geological and geophysical data measurements and attributes, and assess the sensitivity of the resulting geomodels to changes in the parameters of the stochastic optimization algorithm and the presence of realistic seismic noise conditions.

A Computable Equilibrium Model for the Study of Political Economy

Theory: The need for the development and use of a concept of joint, political-economic equilibrium is increasingly recognized by students of democracy and markets. Yet, to date, no adequate theoretical and methodological synthesis of this kind has been produced. The few works which have attempted it suffer from a lack of theoretical balance between economic and political theory; unrealistic, temporally aggregated conceptions of political-economic equilibrium; failure to incorporate theoretically meaningful stochastic elements of economic and political processes; and the absence of a coherent methodology for gauging the empirical power of political-economic models. Methods: In the spirit of the AJPS workshop, it is shown how these problems can be solved. An improved model is built, one which fuses a branch of real business cycle theory and the theory of presidential approval. This model produces a notion of computable political-economic equilibrium that provides for market clearing and simultaneous stochastic optimization by economic and political agents. Then, using data analysis techniques developed in parallel by real business cycle theorists (Hansen and Heckman 1996; Kydland and Prescott 1990, 1996; Lucas 1987; Prescott 1986a, 1986b, 1991; Sims 1996) and political methodologists (Brady 1996; Jackson 1995), the model is parameterized for the United States. More specifically, on the basis of estimates from economics and political science and some numerical experimentation, certain of its parameters are set so that, when simulated, the model mimics the United States political economy in the 1980s. Results: The parameterized model is used to study some important counterfactuals. The first is the impact of increased approval volatility on political-economic equilibration. Such volatility is expected in view of America's likely involvement in the post Cold War era's increasing number of low intensity international conflicts. The second is the impact of presidents pursuing relatively high-nonminimum winning-levels of approval. This kind of behavior is attributed to certain presidents along with the claim that it has harmful effects on markets and hence on various facets of social welfare. The former