A quantum-inspired tensor network method for constrained combinatorial optimization problems

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum inspired algorithm for general locally constrained combinatorial optimization problems by encoding the constraints directly into a tensor network state. The optimal solution can be efficiently solved by borrowing the imaginary time evolution from a quantum many-body system. We demonstrate our algorithm with the open-pit mining problem numerically. Our computational results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems

Development and evaluation of models for assessing geochemical pollution sources with multiple reactive chemical species for sustainable use of aquifer systems: source characterization and monitoring network design

Michael designed a groundwater flow and reactive transport optimization model. He applied this model to characterize contaminant sources in Australia's first large scale uranium mine site in the Northern Territory. He identified the contamination sources to the groundwater system in the area. His findings will assist planning actions and steps needed to implement the mitigation strategy of this contaminated aquifer

Stochastic optimization of strategic mine planning of a hypothetical copper deposit through a parametrizable algorithm

To perform a surface mine planning it is necessary to start from an initial evaluation of the mineral resource. The open pit schedule evaluation is a key step in the process of planning the extraction activities of a mining company. Traditional approaches applied to define the ultimate pit limit consider a single estimated model, which deviates from a real assessment of the mineral asset. Over the recent years, new approaches were proposed, so that the benefits of departing from deterministic world view, where every variable are static and modeled from an arithmetic average, to a stochastic evaluation which allows understanding the risk associated to the open pit long term mine planning. Exact optimization approaches were studied due the major roll of mine planning to financial analytics, however the implications associated with these methods are considered and a metaheuristic approach is proposed to solve the case of study.Resumen: Para realizar la planificación de una mina de superficie es necesario partir de una evaluación inicial del recurso mineral. La evaluación del secuenciamiento de una mina a cielo abierto es un paso clave en el proceso de planeación de las actividades de extracción de una empresa minera. Los enfoques tradicionales aplicados para definir el límite máximo de la fosa consideran un único modelo estimado, que se desvía de una evaluación real del activo mineral. En los últimos años, se propusieron nuevos enfoques, de modo que los beneficios de apartarse de la visión del mundo determinística, donde cada variable es estática y modelada desde un promedio aritmético, hasta una evaluación estocástica que permite comprender el riesgo asociado a la planificación minera a largo plazo. Los enfoques de optimización exacta se estudiaron debido a el rol crucial de la planificación minera en los analísis financieros, sin embargo se consideran las implicaciones asociadas con estos métodos y se propone un enfoque metaheurístico para resolver el caso de estudio.Maestrí

Open Pit Production Scheduling applying Meta Heuristic approach

Production scheduling of a mine is required for effective and economic operations of a mine. Here we are trying to perform production scheduling of mining of mineral blocks under some specific constraints to maximize the profit. The large number of variables and inequalities involved in the process makes it nearly impossible to solve using classical optimization techniques. The techniques and softwares available take a huge amount of time to produce optimized solutions. In this project Genetic Algorithm, a metaheuristic algorithm, has been considered to perform the optimization. The solution provided may not be optimized but will be very nearly optimized and will take significantly lesser time. It starts from a random solution performing several crossovers, mutations and eliminations to reach the optimized solution. A study was carried out in an open pit iron ore mine. The NPV of the mine was found to be a cumulative of over 551 million $. The average stripping ratio was calculated to be 1.72 over the period of 4 years. The computational time required to solve the problem was 31 mins

Evaluation of methods for stope design in mining and potential of improvement by pre-investigations

The importance of stope design for mine planning is considerable. Therefore, stope design and its challenges have been in the focus of research for the past 50 years. Empirical, numerical and analytical methods for stope design have been developed over the past decades in order to improve this process. This thesis is assessing which areas for improvement there still are and which problems are still only unsatisfactorily solved. After establishing background knowledge about the importance of stope design for mine planning and evaluating the factors influencing stope design, the focus is laid on the development of stope design methods in the past, as well as current research related to the topic, to create a comprehensive overview of recent and future developments. This is done by means of a literature review and research analysis. On the other side, the mining industry´s needs and challenges related to stope design are assessed, by means of survey, mine visit and interview. The insights gained in both parts are compared and checked for potential harmonies and disharmonies. Finally, from those conclusions practical recommendations for the GAGS-project are extracted and consecutively presented. In stope design research the focus and dominance of empirical methods has slowly shifted towards more research being conducted in the area of numerical and analytical methods. It can also be concluded that numerical methods and personal expertise are far more important for stope design within industry than commonly assumed. It was identified that in order to improve stope design, it is desired to increase the amount of geotechnical data acquired, the software improved, and stope design integrated within the general mine planning process. Additionally, interesting insights were gained by an in-depth analysis of survey responses, for example, the outstanding importance of the cut-off grade for stope design within gold mining operations. In order to allow for an optimal acceptance of novel geotechnical methods for stope design, the acquired data should be implementable into stope design within three days, preferably be compatible or implemented within a software and allow for stope design to be integrated into general mine planning. To promote the benefits a comprehensive scientific case-study demonstrating the realized benefits should be performed

Optimization of Underground Stope with Network Flow Method

RÉSUMÉ La thèse présente une série d'algorithmes originaux visant à optimiser la géometrie de chantiers souterrains en 3D, typiquement pour la méthode d'abattage par sous-niveaux (ou méthode des longs trous). Les algorithmes proposés s'inspirent des méthodes efficaces d'optimisation ayant été développées pour les mines à ciel ouvert. La clé de l'adaptation de cette methode pour la méthode des longs trous est de reconnaître que la cheminée verticale (ou monterie), servant à initier un chantier, joue un rôle similaire à la surface dans les mines à ciel ouvert. Un système de coordonnées cylindriques est défini autour de la monterie. Les valeurs économiques des blocs dans ce système sont determinées à partir des données en forage. Les angles limites pour le toit et le plancher sont contrôlés par les liens entre les blocs en coupe verticale. La longueur de chantier est contrôle dans le plan horizontal, à l'aide de deux paramètres : 1) R, la distance horizontale maximale entre un bloc et la cheminée et 2) yR, la largeur minimale de l'enveloppe créée pour exploiter le bloc se trouvant à cette distance maximale. La hauteur du chantier est déterminée par l'extension de la monterie, laquelle limite aussi les liens dans le plan vertical. L'ensemble des liens et des blocs constitue un réseau. Le réseau est complété par deux noeuds fictifs, la source et le puits. En maximisant le flux partant de la source vers le puits, on identifie le chantier optimal. Le chantier obtenu est optimal cependant conditionnellement à la monterie étudiée (localisation et extension), la discrétisation adoptee et les liens représentant les contraintes de pentes. Le problème revient alors à determiner les paramètres de la monterie qui maximisent le profit. Pour ce faire, on utilise une méthode de type génétique permettant d'explorer des solutions variées et surtout de s'échapper d'optimums locaux. La méthode est appliquée sur plusieurs gisements et les résultats sont comparés à ceux de la méthode du chantier flottant ("floating stope"). La méthode proposée démontre sa supériorité sur ces exemples.----------ABSTRACT The dissertation presents a series of algorithms to optimize the underground stope geometry in 3D, typically for sublevel stoping method or longhole stoping. The proposed algorithms are based on network flow method, an effective technique applied in open pit optimization. The key to adapt this method to underground mining is to recognize that the vertical raise to initiate a stope plays a similar role to the surface in open pit mining. Accordingly, a cylindrical coordinate system starting from the raise is introduced to redefine a ore block model. This facilitate the manipulation of geometric constraints. The slope limits of hanging wall and footwall are controlled by the links between the blocks in vertical section. The width of stope is controlled in horizontal plane, by defining two parameters: 1) R, the maximum distance to mine a block from raise, and 2) yR, the minimum width of envelope created to mine the farthest block. The height of stope is defined by the raise extension which limits the links in the vertical section. The blocks and links constitute a network ow graph. Solving the graph with efficient maximum ow method yields an optimal stope conditional to the specified raise. This is the core of proposed methods, an optimal stope generator for given raise parameters. With the stope generator, the global optimization of raise parameters produces a global optimal stope. The algorithm using a single raise is suitable for the relatively small sub-vertical ore bodies. It is shown to provide better results than floating stope algorithm in several scenarios tested

Solution procedures for block selection and sequencing in flat-bedded potash underground mines

Phosphates, and especially potash, play an essential role in the increase in crop yields. Potash is mined in Germany in underground mines using a conventional drill-and-blast technique. The most commercially valuable mineral contained in potash is the potassium chloride that is separated from the potash in aboveground processing plants. The processing plants perform economically best if the amount of potassium contained in the output is equal to a specific value, the so-called optimal operating point. Therefore, quality-oriented extraction plays a decisive role in reducing processing costs. In this paper, we mathematically formulate a block selection and sequencing problem with a quality-oriented objective function that aims at an even extraction of potash regarding the potassium content. We, thereby, have to observe some precedence relations, maximum and minimum limits of the output, and a quality tolerance range within a given planning horizon. We model the problem as a mixed-integer nonlinear program which is then linearized. We show that our problem is NP-hard in the strong sense with the result that a MILP-solver cannot find feasible solutions for the most challenging problem instances at hand. Accordingly, we develop a problem-specific constructive heuristic that finds feasible solutions for each of our test instances. A comprehensive experimental performance analysis shows that a sophisticated combination of the proposed heuristic with the mathematical program improves the feasible solutions achieved by the heuristic, on average, by 92.5%