Using a Combination of Genetic Algorithm and the Grid Search Method to Determine Optimum Cutoff Grades of Multiple Metal Deposits

One of the most difficult problems in mining operation is how to determine optimum cutoff grades of ores at different periods over the lifespan of the mine that will maximize the net present value (NPV) of the mine. Maximizing the NPV of a mining operation, subject to different constraints is a non-linear programming problem. These problems can often be solved by the use of gradient methods, direct search methods or intelligent optimization methods. In this paper, a hybrid genetic algorithm combined with the grid search method is used to find the optimum cutoff grades of multiple metal deposits that will maximize the NPV. At first, the solution space is determined by using the grid search method, then the optimum cutoff grades are determined accurately by the use of genetic algorithm. The result of a sensitivity analysis of the problem shows that when crossover probability ranges between 55 to 70%, and mutation probability is between 8 to 11%, and population size greater than 35 individuals; the optimum cutoff grades can be determined with high accuracy while keeping the computational time relatively low.     

Optimal extraction sequence modeling for open pit mining operation considering the dynamic cutoff grade

The cutoff grade problem is an important research challenge and vital optimization task in the yearly operational planning of open pit mines due to its combinatorial nature. Because of it's influenced by the economic parameters, the capacities of stages in the mining operation, mining sequence, and grade distribution of the deposit. Essentially, it asserts that the dynamic cutoff grade at any given period is a function of the ore availability and the needs of the mill at that period. Consequently, cutoff grades strategy and extraction sequence should be considered, simultaneously. Due to its goal, various attempts have been made to develop a computerized procedure for the extraction sequence of open pit mine. None of the resulting approaches appear to enjoy wide acceptance because of it's the numerous associated variables. A new model is proposed to overcome this shortcoming. This model solves the problem in the three steps: 1) the actual economic loss associated with each type of processing for each block, 2) the probabilities distribution and average grade for each type processing is computed from independent realization, and 3) each block with its expected economic loss is developed as a binary integer programming model. Using this model, the optimum extraction sequences in each period are identified based on the optimum processing decisions. A case study is presented to illustrate the applicability of the model developed. Results showed that the extraction sequences obtained using the suggested model will be realistic and practical. This model allows for the solution of very large problem in reasonable time with very high solution quality in terms of optimal net present value.     

Methods for Calculation of Optimal Cutoff Grades in Complex Ore Deposits

The cutoff grade of valuable components delimits the complex ore reserves suitable for efficient mining. The cutoff grade optimization is conducted to maximize the net present value of products in mining projects. The investigations were realized by using the equivalent grade method, iterated grid search method, genetic algorithm, and golden section search. The software presented ensures the calculation of the optimal production with melting considered and the cutoff grades over the life of mine.     

边界品位的动态规划优化模型及算法

在分析边界品位优化现有方法存在问题的基础上,提出边界品位动态规划优化模型以及算法步骤。该模型考虑矿体的开采顺序和矿床不同区段的品位分布,实现了地下开采边界品位在时间和空间上的动态结合。基于建立的数学模型,开发了相应的计算机应用系统,并在非洲某铜矿进行了应用。     

基于Whittle的露天境界动态优化研究

开采境界圈定是露天矿山开采设计的基础，境界优化结果的优劣直接制约着矿山的整体发展效益。露天开采过程中面对的是复杂多变的地质岩体、无序的品位分布、多变的经济参数等一系列非线性动态问题，现有的主流境界优化方法未能有效考虑该类问题。为实现对露天矿山境界优化的经济动态评估以及矿山剥采均衡，将露天境界优化与地质品位、矿体赋存状态相结合，根据地质数据库采用SURPAC软件建立了矿体三维实体模型和块段品位模型。借助境界动态优化分析软件Whittle，并根据某矿山实际情况，将浮动圆锥法和LG图论法相结合，在一定的技术、经济指标条件下，生成了一系列不同价格对应的露天境界优化方案。根据矿山设计生产规模，对各个境界方案进行进度计划排产，同时考虑了资金的时间价值，引入贴现率指标，获得了各个方案的最大净现值，确定净现值最大的方案为最优方案。研究表明：该方案的提出，实现了动态条件下该矿山露天境界的高效动态优化，为露天矿山开采境界优化提供了新思路。     

金铜矿床品位指标的综合评价研究

通过对影响矿山经营效果的多种因素综合分析，采用系统建模法和模糊综合评判方法，对某金铜矿的边界品位、工业品位及相关的主要技术指标进行了多目标优化研究。结果表明，优化后该矿的总利润和净现值有了明显的提高，说明将该矿的品位指标进行优化是合理的。     

放矿截止品位动态优化方法研究及应用

放矿截止品位的确定合理与否关系到矿山的综合效益,随着开采活动、市场经济指标的动态变化,有必要对截止品位进行动态优化计算。结合鲁矿集团下属两矿山的最优截止品位的研究,综合考虑矿产品价格、采选成本、地质品位、采选工艺等因素对于截止品位的影响,以最大盈利值为原则建立了截止品位动态优化模型,并通过黄金分割法求得了最优值。其结果为矿山生产决策提供了重要的理论依据。     

A robust mixed integer linear programming framework for underground cut-and-fill mining production scheduling

ABSTRACT

A review of general optimization studies that have been proposed for underground mining shows that previous works lack flexibility, operability and practicality in relation to cut-and-fill mining production scheduling. This paper presents a robust mixed integer linear programming (MILP) formulation for underground cut-and-fill mining. The objective function of the model is to maximize the net present value (NPV) of the operation while meeting all mining and processing operational and technical constraints. The MILP model features stope development and extraction sequencing constraints, mining and processing tonnage fluctuation constraints, and extraction duration and active levels control constraints. These features make the model more practical and expandable. The MILP model is verified and validated with two case studies from an existing mine and the results are compared with the actual mining strategy. The comparison shows a 9% to 17% improved NPV in both case studies resulting from mining higher grades and processing less tonnes thereby generating a better cash flow.     

复杂多金属露天矿山最终境界动态综合优化

为了将矿岩时间属性准确加入到复杂多金属露采矿山境界优化过程中, 提出了基于矿床块体模型的动态综合优化方法。采用当量品位的方式将多金属元素转化为综合当量品位并对矿床块模型进行经济参数赋值, 运用L-G图论法通过矿石售价折扣的方式获得一系列静态方案, 研究分析了复杂矿山的开采工艺并对各方案编排进度计划, 统计计算各方案年现金流, 经贴现获得净现值(NPV), 综合分析各方案NPV及资源回收情况确定最优方案, 实现复杂多金属露天矿山最终境界的动态综合优化圈定。基于生产进度计划的境界动态优化方法与矿山实际生产紧密结合, 其优化结果可为矿山设计及未来生产提供更好的基础支撑, 为露采矿山最优境界寻找开辟了一条新的途径。     

露天矿山开采境界动态优化圈定

按不同边界品位对矿床模型进行优化参数属性赋值,形成一系列静态价值模型,运用动锥法及L-G法进行初步优化,获得一系列静态境界方案,通过编排进度计划等方式将时间属性植入矿床块体模型,计算不同境界方案的年现金流,经贴现获得净现值(NPV),综合比较各方案NPV及资源回收情况确定最终方案。以某大型露天铜矿为例,利用矿业软件Surpac及进度计划软件Min-esched实现了最终境界的动态优化圈定,结果显示,原静态最优方案为不可行方案,而动态优化最终方案在经济效益上占绝对优势。     

市场经济下金属露天矿边界品位的优化与控制

随着我国经济体制的转变，我国矿物产成品逐渐与国际矿物市场接轨，这导致矿物产成品价格随着市场供需关系的变化而波动。在此情况下，金属露天矿存在着如何有效控制开采边界品位，以争取最大经济效益问题。为此，建立了生产金属产品全过程即与采、选、冶相关的边界品位优化模型，讨论了不同条件下的边界品位控制策略。     

Optimal mill cut-off grade modeling in the mineral deposits via MIP: Haftcheshmeh copper deposit

Cut-off grade play a critical role in defining tonnages mined and processed, average grade of mill feed, cash flows, mine life time, and all major characteristics of a mineral deposit. Simply, the cut-off grade is the lowest grade at which material is considered ore and is processed to create a concentrated commodity product. Essentially, it asserts that the mill cut-off grade is a function of the ore availability and the needs of the mill. The focus of this paper is upon one of these long time-scale decisions: whether to process the extracted material, or to waste it. Consequently, an effort is made for the development of a model for optimization of mill cut-off grade which considers grade blending of mineral deposit. A new mixed integer programming (MIP) model is proposed to deal with this objective and with this model determined the mill cut-off grade of Haftcheshmeh Copper deposit. The results show the obtained mill cutoff grade from proposed model generates the optimum average grade. Therefore, generated net value (NV) from this model is nearer to reality.     

矿山经营参数整体动态优化系统的研究

将矿山采矿、选矿全过程作为模型，结合最先进的采、选工艺、设备技术，以矿山经营整体经济效益最优化为目标建立了矿山经营参数整体动态优化模型，并结合实际，以边界品位、损失率、贫化率、出矿截止品位、干选选比、甩废石矿石品位、选矿比、精矿品位为变量，对弓长岭矿业公司矿山经营系统进行了整体优化，其优化结果不仅提供了各参数的控制指标，而且可年增加经济效益6882．8万元。     

沙溪铜矿开采边界品位动态优化方法

边界品位对矿山而言是一个尤其重要的决策参数。我国的边界品位指标制定于计划经济时期,随着我国市场经济的不断完善,现行的矿产工业指标越来越不能适应采矿工业的发展。沙溪铜矿具有埋藏深、储量大、品位低等特点,如何实现经济合理开采,其中首要解决的便是边界品位的问题。鉴于此,提出以铜品位0.1%为边界圈定矿化域、进行地质统计学估值得到矿化域模型,从而得到矿石储量、平均品位与边界品位的关系的方法,随后提出以最大净现值为目标的边界品位动态优化数学模型和算法。最后,应用所提方法优化了沙溪铜矿边界品位,与原初步设计结果相比,使得矿山服务年限、回收金属量、总现金流量、总净现值都得到了显著提高。该方法对我国大量的储量大、品位低的地下矿床经济开采具有借鉴意义。     

基于控制理论的露天矿边际品位最优化

基于控制理论提出了一个露天矿边际品位最优化新方法。比现有的边际分析技术在数学形式方面更推进了一步，而且对一种重要的品位分布形式－－指数分布的优化问题，可以获得品位函数的解析解。它还可以为更为复杂的边际品位问题研究（如价格波动问题）提供建模工具。最后给出了一个应用分析案例。     

基于DIMINE软件系统的露天矿境界优化研究

露天境界优化是露天矿设计和生产经营管理的重要环节,而最终境界优化是一项需要综合考虑矿山资源状况、开采技术条件、矿产品销售价格、矿石开采及处理成本等多种因素,实现经济效益最大化的复杂工作。目前,三维可视化矿床模拟技术和露天境界优化方法的完美结合使其工序更为简化,并可获得良好的动态效果。以广西平果铝土矿为研究对象,借助DIMINE软件系统建立了该露天矿山的三维实体模型,更加准确、直观地反映了矿床与工程实体的形态及其空间分布关系。针对所建的矿体模型进行了品位估值、储量计算等工作,并基于Le-rchs-Grossmann优化方法(L-G法)对该铝土矿进行露天境界优化研究,参照采矿手册及工程经验,确定合理的露天境界优化参数,得出了该矿山露天开采的最优经济境界。结果可用来指导该矿山前期的资源开发和投资决策,并为后期安排生产计划和实时调度控制提供可靠的依据。     

Long Term Production Scheduling Optimisation for a Surface Mining Operation: An Application of MineMax™ Scheduling Software

Since long term production scheduling deals with movement of ore and waste during the life of a mine, it has a significant effect on the cash flow of a mining operation. Therefore, mine planners often seek to optimise the production schedule with respect to a given criterion. The most commonly used criterion in long term scheduling optimisation is to maximise net present value (NPV). The process involves sequencing of ore blocks or parcels to be mined in each period over the life of the mine subject to precedence and other physical constraints imposed by the mining system. The complexity of mine production scheduling in practice entails a computer solution using mathematical programming as the optimisation technique. Linear and mixed integer programming techniques have been used to optimise long term production schedules but most of the computer programs based on these make overly simplifying assumptions and lack the flexibility to handle practical considerations of mine scheduling. MineMax? scheduling software is applied to long term scheduling for a multielement surface mining operation. MineMax uses mixed integer programming with the branch and bound algorithm as solution strategy. The system allows the planner to generate a mine production schedule in the same manner as manual scheduling, but making use of the interactivity in planning data input, in-built optimisation algorithm and the speed of the personal computer. This study involves investigation into the effects of reblocking and grade intervals on the mining schedule, specifically, the material movement, milling grade and the cash flow over the life of the mine.     

Using equivalent grade factors to find the optimum cut-off grades of multiple metal deposits

One of the most important aspects of mine design is to determine the optimum cut-off grades. Material grading above and below the cut-off is directed to different destinations. Optimization of cut-off grade is now an accepted principle for open pit planning studies. The most commonly criteria used in cut-off grade optimization is to maximize net present value. Lane formulated the concept of cut-off grade optimization for single metal deposit but this method cannot be use in multiple metal deposits. Because in single metal deposits six points are possible candidates for the optimum cut-off grade, in multiple metal deposits an infinite number of points are possible candidates for the optimum cut-off grades. The objective function evaluation of these infinite points is impossible. In this paper, the equivalent grade factor is used to find optimum cut-off grade of multiple metal deposits. First, the objective function is defined for multiple metal deposits and then objective function is converted to one variable function by using equivalent factors. The optimum equivalent cut-off grade of main metal can be found by the optimization techniques such as the Lane algorithm or elimination methods. At final step, the optimum cut-off grades will be determined by interpolation of grade-tonnage distribution of deposit.     

安徽某矿山边界品位动态优化研究

基于盈亏平衡法的思路,推导出边界品位动态优化数学模型.该模型可以根据市场价格的变动,动态确定最低工业品位.这一动态优化方法以安徽某铜矿山为研究对象,先根据当前市场价格,得到最低工业品位,然后在品位区间0.1％～0.4％间按0.05％间距计算各品位矿体储量,采用贴现现金流法对矿山价值进行详细估算,估算结果验证了优化模型的临界值,并以最大累计净现值为指标确定最优开采边界品位.     

缓倾斜中厚矿体无底柱分段崩落法合理回采工艺研究

缓倾斜中厚矿体条件下的无底柱分段崩落法矿山普遍存在矿石损失和贫化严重等突出问题,是矿山急待解决的问题。通过试验研究和大顶山矿区的现场试验,研究结果表明,对于缓倾斜矿体条件下采用"垂直分区"、"组合放矿"新工艺并通过优化炮孔布置与优化切割爆破参数等技术措施,可以在较好地解决缓倾斜矿体条件下无底柱分段崩落法矿石损失和贫化严重的问题,可明显提高矿山生产的经济效益。