Multi-objective optimization of spatial sampling

The optimization of spatial sampling by simulated annealing has been demonstrated and applied for a range of objective functions. In practice more than one objective function may be important for sampling, and there may be complex trade-offs between them. In this paper it is shown how a multi-objective optimization algorithm can be applied to a spatial sampling problem. This generates a set of solutions which is non-dominated (no one solution does better than any other on all objective functions). These solutions represent different feasible trade-offs between the objective functions, and a subset might be practically acceptable. The algorithm is applied to a hypothetical example of sampling for a regional mean with the variance of the mean and the total distance travelled between sample points as the two objective functions. The solutions represent a transition of sample arrays from a loose grid to a tight loop. The potential to develop this approach and apply it to other spatial sampling problems is discussed.