Abstract
Complex geographical spatial sampling usually encounters various multi-objective optimization problems, for which effective multi-objective optimization algorithms are much needed to help advance the field. To improve the computational efficiency of the multi-objective optimization process, the archived multi-objective simulated annealing (AMOSA)-II method is proposed as an improved parallelized multi-objective optimization method for complex geographical spatial sampling. Based on the AMOSA method, multiple Markov chains are used to extend the traditional single Markov chain; multi-core parallelization technology is employed based on multi-Markov chains. The tabu-archive constraint is designed to avoid repeated searches for optimal solutions. Two cases were investigated: one with six typical traditional test problems, and the other for soil spatial sampling optimization applications. Six performance indices of the two cases were analyzed—computational time, convergence, purity, spacing, min-spacing and displacement. The results revealed that AMOSA-II performed better which was more effective in obtaining preferable optimal solutions compared with AMOSA and NSGA-II. AMOSA-II can be treated as a feasible means to apply in other complex geographical spatial sampling optimizations.
Highlights
In complex geographical spaces, spatial sampling scenarios are commonly involved in various sampling purposes and different monitoring factors, which leads to the diversity and complexity of sampling objectives
The lower convergence indices and higher purity indices for all optimal solution set sizes illustrate that the optimal solutions obtained by archived multi-objective simulated annealing (AMOSA)-II are much more convergent than those obtained by AMOSA and NSGA-II
This indicates that the optimal solutions generated by AMOSA-II are much more convergent and more diverse than those generated by AMOSA and NSGA-II
Summary
Spatial sampling scenarios are commonly involved in various sampling purposes and different monitoring factors, which leads to the diversity and complexity of sampling objectives. The basic spatial sampling purposes mainly include estimation, interpolation, inspection, classification and detection [1]. These sampling purposes are always combined based on different situations—such as for the estimation of variogram parameters and mapping accuracy, or for population mean estimation and interpolation; multi-objective spatial sampling problems are derived from such multiple sampling purposes [2,3]. When multiple sampling purposes are combined with multiple sampling factors, such multi-objective spatial sampling problems become a lot more complex
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