Abstract The key available information to choose new locations for drilling are the estimated ore grade values and the corresponding uncertainties at the tentative locations. These pieces of information are combined to generate a single objective function. The mathematical form of the objective function should reflect the effect of these values and their relative importance. Traditional objective function use multiplication of these parameters by different powering values. In this study, we develop two novel objective functions from the Bayesian optimization: the probability of improvement (PI), and the expected improvement (EI). These two objective functions seek new drillholes while considering the effect of the used value and their relative importance. Therefore, they can provide a trade-off between exploration and exploitation. All the objective functions have adjustable parameters. These parameters are typically tuned using expert knowledge or heuristic rules. Here, a statistical method based on cross-validation is proposed to adjust the parameters of the traditional and novel objective functions. The performance of the novel objective functions is validated against other ones using a distance based ranking method, in a phosphate deposit. The obtained results demonstrate the robustness of the EI and PI, the newly introduced objective functions from the Bayesian optimization framework.

中文翻译：

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来自贝叶斯优化的目标函数用于定位额外的钻孔

摘要 选择新钻探位置的关键可用信息是估计的矿石品位值和暂定位置的相应不确定性。将这些信息组合起来以生成单个目标函数。目标函数的数学形式应反映这些值的影响及其相对重要性。传统的目标函数使用这些参数乘以不同的幂值。在这项研究中，我们从贝叶斯优化中开发了两个新的目标函数：改进概率 (PI) 和预期改进 (EI)。这两个目标函数在考虑使用值的影响及其相对重要性的同时寻找新的钻孔。因此，它们可以提供探索和开发之间的权衡。所有的目标函数都有可调参数。这些参数通常使用专家知识或启发式规则进行调整。在这里，提出了一种基于交叉验证的统计方法来调整传统和新型目标函数的参数。在磷酸盐矿床中，使用基于距离的排序方法对新目标函数的性能进行了验证。获得的结果证明了 EI 和 PI 的鲁棒性，这是贝叶斯优化框架中新引入的目标函数。在磷酸盐矿床中，使用基于距离的排序方法对新目标函数的性能进行了验证。获得的结果证明了 EI 和 PI 的鲁棒性，这是贝叶斯优化框架中新引入的目标函数。在磷酸盐矿床中，使用基于距离的排序方法对新目标函数的性能进行了验证。获得的结果证明了 EI 和 PI 的鲁棒性，这是贝叶斯优化框架中新引入的目标函数。