Comparison of Stochastic Programming and Robust Optimization Models for Groundwater Plume Containment

by David W. Watkins, Jr., (S.M.ASCE),
Daene C. McKinney, (A.M.ASCE),



Document Type: Proceeding Paper

Part of: North American Water and Environment Congress & Destructive Water

Abstract: Stochastic optimization models for containing a groundwater contaminant plume through the installation and operation of pumping wells are developed. Two related formulations are presented—stochastic programming with recourse and robust optimization—and their solutions compared. Both models assume a two-stage decision process in which the decision of how many and where to locate wells is made first, and then the pumping rates of the wells are selected upon observing system performance. Both models also allow the decision maker to evaluate the trade off between the expected cost and the risk of gradient violations. However, through the addition of a term representing the risk of cost overruns, robust optimization is likely to be more useful to a risk-averse decision maker. The mixed-integer nonlinear (nonconvex) optimization problems resulting from these formulations are solved using an extension of generalized Benders decomposition (GBD). Computational results show that GBD can find globally optimal solutions even when the nonlinear subproblems are nonconvex, though global opthnality cannot be guaranteed a priori.

Subject Headings: Optimization models | Wells (water) | Risk management | Stochastic processes | Hydrologic models | Groundwater pollution | Plumes | Pumps

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