Efficient surrogate-based multi-objective optimisation for sustainable island groundwater management

Computational burden, resulting from intensive executions of simulators during optimisation, often hinders the application of the simulation-optimisation (SO) methods for deriving optimal pumping schemes in coastal groundwater management, and impedes conducting sensitivity analysis of optimal pumping strategies to management constraints. For quickly identifying optimal pumping strategies under various constraints, this study develops an efficient framework, where adopting a lower-resolution simulator generates data to build surrogate models with a novel offline training algorithm and then applying a global optimization algorithm to determine optimal solutions according to the surrogate predictions. Traditional offline training approach involves developing surrogates before optimisation, often using training datasets that cover the input space either uniformly or randomly, which can prove inefficient due to potential oversampling of low-gradient areas and under-sampling of high-gradient areas. This study proposes an iterative search algorithm that efficiently selects training points by first scoring each unknown point based on its distance to the closest training point and the gradient of the surrogate estimate and then choosing the input candidate with the maximum score as the next sampling point. The proposed surrogate-based optimisation framework is applied to solve a two-objective groundwater management problem formulated on a three-dimensional island aquifer, using hydrogeological conditions representative of San Salvador Island, Bahamas. The goal is to minimize the operation cost resulting from groundwater pumping and desalination, while maximizing the amount of qualified groundwater supply, subject to constraints on seawater intrusion (SWI) control, expressed in terms of aquifer drawdown and salt mass increase in the aquifer.
Gaussian Process (GP) techniques are employed to construct model surrogates, predicting management objectives and constraint values, alongside quantifying associated uncertainties. By conducting repeated Monte Carlo simulations using these GP models, it becomes possible to ascertain the probability of Pareto optimality for each pumping scheme. Derived optimal pumping schemes are characterized by the Pareto-optimal probabilities and validated by the higher-resolution simulator. Results indicate that the proposed surrogate-based multi-objective optimisation framework can efficiently provide trustable optimal pumping schemes and be used to analyse the sensitivity of optimal groundwater supply cost to the constraints.