Estimation or simulation of soil properties? An optimization problem with conflicting criteria

Both estimation and simulation approaches are formulated as the selection of a set of attribute values that are optimal for criteria that are typically conflicting. Estimation amounts to minimize local criteria such as a local error variance, whereas stochastic simulation aims to reproduce global Ž . statistics such as the histogram or semivariogram. A simulated annealing SA algorithm is presented to generate maps of optimal values: an initial random image is gradually perturbed so as to minimize a weighted combination of three components that measure deviations from local or global features of interest. The approach is illustrated using an environmental data set related to soil contamination by zinc. A validation set shows that, depending on the relative weight given to local and global constraints, the final maps have properties ranging from estimation to simulation Ž . in terms of mean square error MSE of prediction and extent of the space of uncertainty. Ž Combination of both types of constraints leads to better performances smaller proportions of misclassified locations, smaller prediction errors for the average proportion of contaminated . locations within remediation units than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. q 2000 Elsevier Science B.V. All rights reserved.