Planning of Groundwater Supply Systems Subject to Uncertainty Using Stochastic Flow Reduced Models and Multi-Objective Evolutionary Optimization

The typical modeling approach to groundwater management relies on the combination of optimization algorithms and subsurface simulation models. In the case of groundwater supply systems, the management problem may be structured into an optimization problem to identify the pumping scheme that minimizes the total cost of the system while complying with a series of technical, economical, and hydrological constraints. Since lack of data on the subsurface system most often reflects upon the development of groundwater flow models that are inherently uncertain, the solution to the groundwater management problem should explicitly consider the tradeoff between cost optimality and the risk of not meeting the management constraints. This work addresses parameter uncertainty following a stochastic simulation (or Monte Carlo) approach, in which a sufficiently large ensemble of parameter scenarios is used to determine representative values selected from the statistical distribution of the management objectives, that is, minimizing cost while minimizing risk. In particular, the cost of the system is estimated as the expected value of the cost distribution sampled through stochastic simulation, while the risk of not meeting the management constraints is quantified as the expected value of the intensity of constraint violation. The solution to the multi-objective optimization problem is addressed by combining a multi-objective evolutionary algorithm with a stochastic model simulating groundwater flow in confined aquifers. Evolutionary algorithms are particularly appropriate in optimization problems characterized by non-linear and discontinuous objective functions and constraints, although they are also computationally demanding and require intensive analyses to tune input parameters that guarantee optimality to the solutions. In order to drastically reduce the otherwise overwhelming computational cost, a novel stochastic flow reduced model is thus developed, which practically allows for averting the direct inclusion of the full simulation model in the optimization loop. The computational efficiency of the proposed framework is such that it can be applied to problems characterized by large numbers of decision variables.