Optimal location of additional exploratory drillholes using afuzzy-artificial bee colony algorithm
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ORIGINAL PAPER
Optimal location of additional exploratory drillholes using a fuzzy-artificial bee colony algorithm Bahram Jafrasteh1 · Nader Fathianpour1
Received: 21 April 2016 / Accepted: 8 March 2017 © Saudi Society for Geosciences 2017
Abstract In most research studies, the problem of locating additional drillhole is simplified, and the ore body is considered as a 2d object. In this study, location of additional drillholes are optimized by considering the third dimension of the ore body, the azimuth and the dip of additional drill holes. A new objective function is defined to address the effect of rock type in locating new drillholes. The optimization problem is solved using a novel fuzzy-artificial bee colony algorithm, called FABC. The parameters of the FABC algorithm is dynamically adjusted using a designed fuzzy inference system with three performance measures as inputs and two outputs. The comparison performance with state-of-the-art optimization algorithm, using a nonparametric hypothesis test, indicates higher performance of the FABC algorithm. The results indicate significantly a decrease of kriging variance by introducing additional drillholes. Keywords Ore grade estimation · Additional drillholes · Fuzzy-artificial bee colony algorithm · Rock types
Introduction Due to straightforward influence on mining costs and improving ore reserve estimation, locating new drillholes is
Bahram Jafrasteh
[email protected] Nader Fathianpour [email protected] 1
Department of Mining Engineering, Isfahan University of Technology, Isfahan 8415683111, Iran
one of the most important problems in the mining industry. In the past century, geostatistical methods have been applied to characterize the spatial variation of regional variables for classification, simulation, designing optimal sampling strategies, and ore reserve estimation. Over the past 30 years, kriging, as a best linear unbiased estimator (BLUE), has been applied to estimate ore grade value in various deposits. Kriging unbiasedness plus its optimality in a minimum mean square error sense have made it “BLUE” (Olea 2000). An empirical semivariogram of data as a part of structural analysis is calculated and a model is fitted to the semivariogram in order to be used in kriging calculations. As one of the main advantages of the kriging method, the weights of observations are calculated according to the form of related semivariogram. Ordinary kriging (OK) as a variant of kriging is widely applied to estimate ore grade value and obtain kriging variance. Kriging variance highly depends on the model parameters of related variogram and sampling strategy. The kriging variance can be a guide to extra sampling measurements. Sabourin (1977) proposed a method for classifying local tonnage quantities using a constant parameter multiplied by the distribution variance of the blocks (Sabourin 1984). The constant differs for measured, indicated and inferred resources. In (McBratney et al. 1981; McBratney and Webster 1981), researchers plotted a graph of maximum kri
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