Pareto-based efficient stochastic simulation–optimization for robust and reliable groundwater management

Abstract

Summary Simulation–optimization methods are used to develop optimal solutions for a variety of groundwater management problems. The true optimality of these solutions is often dependent on the reliability of the simulation model. Therefore, where model predictions are uncertain due to parameter uncertainty, this should be accounted for within the optimization formulation to ensure that solutions are robust and reliable. In this study, we present a stochastic multi-objective formulation of the otherwise single objective groundwater optimization problem by considering minimization of prediction uncertainty as an additional objective. The proposed method is illustrated by applying to an injection bore field design problem. The primary objective of optimization is maximization of the total volume of water injected into a confined aquifer, subject to the constraints that the resulting increases in hydraulic head in a set of control bores are below specified target levels. Both bore locations and injection rates were considered as optimization variables. Prediction uncertainty is estimated using stacks of uncertain parameters and is explicitly minimized to produce robust and reliable solutions. Reliability analysis using post-optimization Monte Carlo analysis proved that while a stochastic single objective optimization failed to provide reliable solutions with a stack size of 50, the proposed method resulted in many robust solutions with high reliability close to 1.0. Results of the comparison indicate potential gains in efficiency of the stochastic multi-objective formulation to identify robust and reliable groundwater management strategies.