Optimization of the sampling design for multiobjective soil mapping using the multiple path SSA (MP-SSA) method

Spatial sampling is important for soil surveys and mapping, and the optimization of the sampling design is a hot topic. Most often in soil sampling, multiple purposes are usually involved and corresponding objectives need to be optimized as much as possible. In such cases, balanced optimization is needed to produce the best compromised solutions that reach the maximum common interest, but not to generate a well-spread Pareto front. To solve this problem, the multiple path spatial simulated annealing (MP-SSA) was developed by extending the classic SSA. It can synchronously optimize multiobjective functions of different types and magnitudes by setting one annealing path for each objective, and designing a voting and annealing mechanism. To illustrate the difference and performance for MP-SSA, it was compared with the archived multiobjective simulated annealing (AMOSA) and Non-dominated Sorting Genetic Algorithm II (NSGA-II), both aiming at generating well-spread Pareto front, in two case studies with hypothetical data and actual soil heavy metal data. The results show that the MP-SSA is more efficient in generating the best compromised solutions, and is an efficient and promising tool for balanced multiobjective optimization for spatial sampling design when all objectives need to be optimized as much as possible.