Bi-objective Extraction-injection Optimization Modeling for Saltwater Intrusion Control Considering Surrogate Model Uncertainty

Data-driven machine learning surrogates are used to substitute complex groundwater numerical simulation models within optimization algorithms to reduce computational burden for large-scale aquifer management. The traditional surrogate-assisted simulation–optimization modeling has been limited due to uncertainty persisting in surrogate model predictions. More advanced methods are imperative to reduce impact of uncertainties from surrogate models on solution optimality. In this regard, we propose an ensemble surrogate-based simulation–optimization methodology for optimal saltwater intrusion (SWI) control through accounting for uncertainty induced by surrogate models. The optimization model includes two conflicting objectives: minimizing total groundwater pumping and injection rate from an extraction-injection horizontal well system while reducing chloride concentration at monitoring locations below a certain level as much as possible. Three types of machine learning surrogates including artificial neural network, random forest and support vector machine were established to replace a high-fidelity physically based saltwater intrusion model. Optimal Latin hypercube design combined with parallel computing on high performance computing (HPC) was performed to generate input–output data of pumping and injection schedules and resulting salinity levels. An innovative Bayesian set pair analysis approach was presented to derive posterior model weights by considering both training and testing data. The newly constructed individual and ensemble machine learning surrogates were then coupled with a bi-objective optimization model to obtain Pareto-optimal extraction-injection strategies in a deep “2000-foot” sand of the Baton Rouge area, Louisiana, where the optimization was solved using a multi-objective genetic algorithm NSGA-II. Results showed that individual and ensemble surrogate models were accurate enough for salinity prediction. Through comparing the Pareto-optimal solutions, the ensemble surrogate-based modeling was confirmed to provide more reliable and conservative strategies for alleviating saltwater intrusion threat while considerably reducing computational cost. The improved Bayesian set pair analysis approach proved to be robust to integrate multiple models by quantifying model uncertainty.