Comparison of particle swarm optimization and simulated annealing for locating additional boreholes considering combined variance minimization

One of the most important stages in complementary exploration is optimal designing the additional drilling pattern or defining the optimum number and location of additional boreholes. Quite a lot research has been carried out in this regard in which for most of the proposed algorithms, kriging variance minimization as a criterion for uncertainty assessment is defined as objective function and the problem could be solved through optimization methods. Although kriging variance implementation is known to have many advantages in objective function definition, it is not sensitive to local variability. As a result, the only factors evaluated for locating the additional boreholes are initial data configuration and variogram model parameters and the effects of local variability are omitted. In this paper, with the goal of considering the local variability in boundaries uncertainty assessment, the application of combined variance is investigated to define the objective function. Thus in order to verify the applicability of the proposed objective function, it is used to locate the additional boreholes in Esfordi phosphate mine through the implementation of metaheuristic optimization methods such as simulated annealing and particle swarm optimization. Comparison of results from the proposed objective function and conventional methods indicates that the new changes imposed on the objective function has caused the algorithm output to be sensitive to the variations of grade, domain's boundaries and the thickness of mineralization domain. The comparison between the results of different optimization algorithms proved that for the presented case the application of particle swarm optimization is more appropriate than simulated annealing. Definition of new objective function for locating additional boreholes.Application of metaheuristic methods for objective function minimization.Comparison of results from proposed objective function to conventional ones.Validation of algorithm in Esphordi phosphate mine.

[1]  J. Boisvert,et al.  Mineral resource classification : a comparison of new and existing techniques by , 2014 .

[2]  A. Journel.  Nonparametric estimation of spatial distributions , 1983 .

[3]  K. Juang,et al.  Using sequential indicator simulation to assess the uncertainty of delineating heavy-metal contaminated soils. , 2004, Environmental pollution.

[4]  Oy Leuangthong,et al.  On the Use of MultiGaussian Kriging for Grade Domaining in Mineral Resource Characterization , 2012 .

[5]  M. Safa,et al.  Optimally Locating Additional Drill holes to Increase the Accuracy of Ore/Waste Classification , 2015 .

[6]  Patrick Siarry,et al.  A comparative study of various meta-heuristic techniques applied to the multilevel thresholding problem , 2010, Eng. Appl. Artif. Intell..

[7]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[8]  F. Torab,et al.  Magnetite-apatite deposits of the Bafq district, Central Iran: apatite geochemistry and monazite geochronology , 2007, Mineralogical Magazine.

[9]  R. Romer,et al.  Uranium–lead ages of apatite from iron oxide ores of the Bafq District, East-Central Iran , 2011 .

[10]  Kalyan Saikia,et al.  Exploration drilling optimisation using geostatistics: a case in Jharia Coalfield, India , 2006 .

[11]  Yan Zhou,et al.  Application of the PSO-SVM model for coal mine safety assessment , 2012, 2012 8th International Conference on Natural Computation.

[12]  Ardeshir Hezarkhani,et al.  Additional Exploratory Boreholes Optimization Based on Three-Dimensional Model of Ore Deposit , 2009 .

[13]  D. Giaouris,et al.  Comparison of particle swarm and simulated annealing algorithms for induction motor fault identification , 2009, 2009 7th IEEE International Conference on Industrial Informatics.

[14]  Oswald Marinoni,et al.  Improving geological models using a combined ordinary–indicator kriging approach , 2003 .

[15]  João Felipe C. L. Costa,et al.  Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution , 2004 .

[16]  K. Osburn,et al.  Enhanced geological modelling of the Upper Elsburg reefs and VCR to optimize mechanized mine planning at South Deep Gold Mine , 2014 .

[17]  Andre G. Journel,et al.  Geostatistics: Models and tools for the earth sciences , 1986 .

[18]  J. Basterrechea,et al.  Comparison of Different Heuristic Optimization Methods for Near-Field Antenna Measurements , 2007, IEEE Transactions on Antennas and Propagation.

[19]  J. Yamamoto.  An Alternative Measure of the Reliability of Ordinary Kriging Estimates , 2000 .

[20]  Asif Khan,et al.  Application of Particle Swarm Optimization to the Open Pit Mine Scheduling Problem , 2015 .

[21]  Ardeshir Hezarkhani,et al.  A Simulated Annealing-Based Algorithm to Locate Additional Drillholes for Maximizing the Realistic Value of Information , 2013, Natural Resources Research.

[22]  Clayton V. Deutsch,et al.  Correcting for negative weights in ordinary kriging , 1996 .

[23]  John C. Davis,et al.  Boundary assessment under uncertainty: A case study , 1993 .

[24]  H. P. Knudsen,et al.  Advanced geostatistics in ore reserve estimation and mine planning (practitioner's guide). [Disjunctive Kriging technique] , 1977 .

[25]  Ying Wang,et al.  Coal mine safety production forewarning based on improved BP neural network , 2015 .

[26]  H. Z. Hu,et al.  Mapping an uncertainty zone between interpolated types of a categorical variable , 2012, Comput. Geosci..

[27]  João Felipe Coimbra Leite Costa,et al.  Additional Samples: Where They Should Be Located , 2001 .

[28]  Ardeshir Hezarkhani,et al.  Optimally locating additional drill holes in three dimensions using grade and simulated annealing , 2012, Journal of the Geological Society of India.

[29]  Haiyu Gao,et al.  The updated kriging variance and optimal sample design , 1996 .

[30]  Donald E. Scheck,et al.  Optimum locations for exploratory drill holes , 1983 .

[31]  A. D. S. Gillies,et al.  Review of the Applications of Geostatistics in the Coal Industry , 1989 .

[32]  R. Reese.  Geostatistics for Environmental Scientists , 2001 .

[33]  Asif Khan,et al.  Production Scheduling of Open Pit Mines Using Particle Swarm Optimization Algorithm , 2014, Adv. Oper. Res..

[34]  Ferenc Szidarovszky,et al.  Multiobjective observation network design for regionalized variables , 1983 .

[35]  S. Soltani,et al.  Use of genetic algorithm in optimally locating additional drill holes , 2011 .

[36]  Esperanza García Gonzalo,et al.  PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case , 2010 .

[37]  S. Dreiss,et al.  Hydrostratigraphic interpretation using indicator geostatistics , 1989 .

[38]  Roussos Dimitrakopoulos,et al.  Algorithmic integration of geological uncertainty in pushback designs for complex multiprocess open pit mines , 2013 .

[39]  Aminaton Marto,et al.  Prediction of airblast-overpressure induced by blasting using a hybrid artificial neural network and particle swarm optimization , 2014 .

[40]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[41]  J. C. Koppe,et al.  Comparative analysis of the resource classification techniques: case study of the Conceição Mine, Brazil , 2010 .

[42]  Gary Froyland,et al.  The Value of Additional Drilling to Open Pit Mining Projects , 2018 .

[43]  R. Olea.  Geostatistics for Natural Resources Evaluation By Pierre Goovaerts, Oxford University Press, Applied Geostatistics Series, 1997, 483 p., hardcover, $65 (U.S.), ISBN 0-19-511538-4 , 1999 .

[44]  Jacques A. Ferland,et al.  Application of a Particle Swarm Algorithm to the Capacitated Open Pit Mining Problem , 2007 .

[45]  A. Mileham,et al.  Applications of particle swarm optimisationin integrated process planning and scheduling , 2009 .

[46]  Mark Gershon,et al.  Application of a new approach for drillholes location optimization , 1988 .

[47]  Ebrahim Ghasemi,et al.  Particle swarm optimization approach for forecasting backbreak induced by bench blasting , 2016, Neural Computing and Applications.

[48]  J. Yamamoto,et al.  Quantification of Uncertainty in Ore-Reserve Estimation: Applications to Chapada Copper Deposit, State of Goiás, Brazil , 1999 .

[49]  Alfred Stein,et al.  Deriving Optimal Exploration Target Zones on Mineral Prospectivity Maps , 2009 .

[50]  F. D. van der Meer.  A comparison of convential classification methods and a new indicator kriging based method using high - spectral resolution images, AVIRIS , 1992 .

[51]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[52]  Taher Niknam,et al.  An efficient hybrid evolutionary optimization algorithm based on PSO and SA for clustering , 2009 .

[53]  Alastair J. Sinclair,et al.  Applied Mineral Inventory Estimation , 2006 .

[54]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[55]  W. W. Bartley,et al.  Evolutionary Epistemology, Rationality, and the Sociology of Knowledge , 1987 .

[56]  G.B.M. Heuvelink,et al.  Is the ordinary kriging variance a proper measure of interpolation error , 2002 .

[57]  A. E. Tercan.  ASSESSMENT OF BOUNDARY UNCERTAINTY IN A COAL DEPOSIT BY MEANS OF PROBABILITY KRIGING , 1998 .

[58]  Julián M. Ortiz,et al.  Parallel implementation of simulated annealing to reproduce multiple-point statistics , 2011, Comput. Geosci..