Surrogate assisted multi-objective robust optimization for groundwater monitoring network design

The robust optimization of groundwater quality monitoring network is subject to many conflicting objectives and high level of uncertainty in hydraulic conductivity. This study develops a two-stage stochastic optimization framework including the uncertainty quantification using a cheap-to-evaluate surrogate model and an improved epsilon multi-objective noisy memetic algorithm (epsilon-MONMA) for monitoring network design. The surrogate model based on sparse polynomial chaos expansion (PCE) is constructed to replace expensive simulation model in the uncertainty quantification of concentrations at the pre-defined monitoring locations for reducing huge computational cost. Additionally, the scenario discovery strategy using sparse PCE model is applied to filter a typical scenario set and the centroid of contaminant plume is used as the diversity metric, which avoids enumerating all possible contamination plumes caused by the uncertain K-field in the optimization. The proposed algorithm is then employed to solve stochastic management model to achieve robust monitoring design, indicating the insensitivity of monitoring design to plume uncertainty no matter which of the many possible scenarios becomes the true distribution of contamination under the true K-field. A synthetic aquifer considering uncertainty in hydraulic conductivity is designed to optimize monitoring network design. The Pareto-optimal solutions to the synthetic example are achieved under three of plume scenario sets defined at deterministic scenario (Scenario A0), Monte Carlo based scenario discovery (Scenario A1) and surrogate assisted scenario discovery (Scenario A2), respectively. Comprehensive analysis demonstrates that the monitoring design based on Scenario A2 outperforms either of the two designs based on Scenarios A0 and A1 in terms of the improvement of robustness of designs evaluated against the typical scenario set. Meanwhile, the performance of monitoring network deteriorates as the uncertainty of plume (noisy strength) increases, indicating the significance of reducing parameter uncertainty in groundwater monitoring design. The research findings show that the developed stochastic optimization framework is a computationally efficient and promising tool for multi-objective design of groundwater monitoring network under uncertainty.