Distance function modeling in optimally locating additional boreholes

The optimal locating of additional boreholes is complicated and very time consuming. Some methods such as metaheuristic algorithms, calculation parallelism, and reducing the time of objective function calculation could be used to increase the calculation speed; among these methods, the latter is preferred due to its extensive influence on the optimization of time. The main reasons that make the objective function calculation cumbersome are mentioned hereafter, and according to their priority: (1) excessive quantity of blocks in the geological block model, and (2) inverting the matrix of average semivariogram between samples is a time consuming operation. The present study aims to decrease the calculation time by reducing the number of blocks without considering their size increment that affects accuracy. To achieve this purpose, the objective function is calculated according to the block model of uncertainty zone, which is defined by using the recently introduced distance function to investigate uncertainty in mineralized domain boundaries. In order to evaluate the performance of the present approach on reducing the calculation time as well as the precision in locating additional boreholes, the results from particle swarm optimization as a metaheuristic algorithm are compared by considering two different scenarios of combined variance reduction on the basis of a three-dimensional geological block model and an uncertainty block model. The comparative results show that using the uncertainty block model reduces the calculation time by one-third, and the proposed locations of the boreholes are more consistent to the study's aim, which is to reduce the boundary's uncertainty.