Application of Machine-Learning Techniques to Pareto-Optimal Groundwater Management Solutions

Seawater intrusion is a primary water-resources management concern in Santa Barbara, California. To identify optimal water-resources management strategies, a density-dependent solute transport model was coupled with a multi-objective evolutionary algorithm. The objectives were to maximize total pumpage, minimize total seawater intrusion, minimize total drawdown, and minimize the maximum drawdown subject to various constraints such as water-quality and well-capacity constraints. Two climate scenarios (typical and dry) were simulated, resulting in thousands of Pareto-optimal solutions that contain valuable information regarding the underlying simulation model.

To extract the information, we applied supervised and unsupervised machine-learning techniques to the Pareto-optimal solutions. Supervised learning (gradient boosted regression trees) was used to predict objective and constraint values as a function of the decision-variable values, resulting in a very fast, very compact model emulator of the underlying numerical model. Analysis of the results identified key relationships between pumping at extraction wells, concentrations at chloride monitoring wells and the seawater intrusion objective. Simulation output is being added to the dataset, which will improve the predictive ability of the emulator. Unsupervised learning, which included principal-component analysis (PCA), was applied to a dataset composed of values for the objectives, constraints, and decision variables. PCA results indicated that the decision-variable space can be substantially reduced, which indicates that the solution speed of the optimization problem can be greatly increased.