Objective functions from Bayesian optimization to locate additional drillholes

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.