Optimization of high-reliability-based hydrological design problems by robust automatic sampling of critical model realizations

This study demonstrates the high efficiency of the so-called stack-ordering technique for optimizing a groundwater management problem under uncertain conditions. The uncertainty is expressed by multiple equally probable model representations, such as realizations of hydraulic conductivity. During optimization of a well-layout problem for contaminant control, a ranking mechanism is applied that extracts those realizations that appear most critical for the optimization problem. It is shown that this procedure works well for evolutionary optimization algorithms, which are to some extent robust against noisy objective functions. More precisely, differential evolution (DE) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are applied. Stack ordering is comprehensively investigated for a plume management problem at a hypothetical template site based on parameter values measured at and on a geostatistical model developed for the Lauswiesen study site near Tubingen, Germany. The straightforward procedure yields computational savings above 90% in comparison to always evaluating the full set of realizations. This is confirmed by cross testing with four additional validation cases. The results show that both evolutionary algorithms obtain highly reliable near-optimal solutions. DE appears to be the better choice for cases with significant noise caused by small stack sizes. On the other hand, there seems to be a problem-specific threshold for the evaluation stack size above which the CMA-ES achieves solutions with both better fitness and higher reliability.