Joint simulation through orthogonal factors generated by the L-SHADE optimization method

Abstract Due to its better results over the traditional co-simulation methods, joint simulation of variables through orthogonal factors has gained popularity. In this approach, practitioners transform variables into orthogonal factors, simulate them independently, and back-transform the results into the initial space. It is unlikely to generate spatially uncorrelated factors at more than two lags. Therefore, the idea of simultaneous diagonalization have become the topic of so many studies. Some approaches have used the Jacobi transformation to replace a multivariate minimization problem with a sequence of univariate problems. However, these studies do not pay attention to the interruption of the previously minimized univariate problems while solving the new one. Therefore, this study aimed to minimize the objective function by considering all the univariate problems at once using the L-SHADE optimization method. The proposed method was applied to the Meiduk porphyry copper deposit to generate the L-SHADE factors. L-SHADE was efficient due to high speed of convergence and giving logical answer. Comparison among the L-SHADE factors and those of principal component analysis and Min/max autocorrelation factors showed better performance of the L-SHADE method such that the cross-variograms of the L-SHADE factors did not show noticeable spatial pattern and generally had smaller values. Sequential simulation was used to produce fifty equiprobable realizations from the L-SHADE factors. The proposed approach could reproduce the means, variances, correlation coefficients, cumulative distributions, and auto/cross-variograms of the variables in the simulations. Therefore, the simulations were reliable to be used in long-term production planning. A weighted multi-objective model using binary integer variables was developed to find the best possible production plan among different production scheduling alternatives developed based on the simulations. Different weighting scenarios were considered to investigate the impacts of economic (net present value), resources (ore extraction), and environmental (waste removal) objectives on stakeholder interests.