Constrained optimization of spatial sampling using continuous simulated annealing

Spatial sampling is an important issue in environmental studies because the sample configuration influences both costs and effectiveness of a survey. Practical sampling constraints and available pre-information can help to optimize the sampling scheme. In this paper, spatial simulated annealing (SSA) is presented as a method to optimize spatial environmental sampling schemes. Sampling schemes are optimized at the point-level, taking into account sampling constraints and preliminary observations. Two optimization criteria have been used. The first optimizes even spreading of the points over a region, whereas the second optimizes variogram estimation using a proposed criterion from the literature. For several examples it is shown that SSA is superior to conventional methods of designing sampling schemes. Improvements up to 30% occur for the first criterion, and an almost complete solution is found for the second criterion, Spatial simulated annealing is especially useful in studies with many sampling constraints, It is flexible in implementing additional, quantitative criteria.