International Irrigation Center
Four alternative simulation/optimization models useful for computing optimal sustained-yield (steady-state) groundwater pumping strategies are compared in terms of formulation, solution procedure, accuracy, and computational efficiency. The different models require different computer processing time and memory. For the aquifer tested system, if more than 10% of the cells have pumping as a decision variable, a fully linearized embedding model will require less computer memory than any other model. All the models address linear and nonlinear steady-state flow in multilayer, unconfined/confined aquifers. They also address several types of nonsmooth external flows. Newly presented are a response matrix model solving external flows described by nonsmooth functions through cycling, and a fully nonlinear embedding model that directly achieves an optimal solution without cycling. Models are tested using a hypothetical three-layer (unconfined/confined) aquifer system (3 layers x 15 rows x 15 columns = 675 cells) . Empirically, globally optimal solutions seem to be obtained. All the models compute the same optimal pumping even if their optimizations are begun using vastly different initial guesses. This addresses a common concern that the solutions to nonlinear problems are not necessarily globally optimal.
Takahashi S. and R.C. Peralta. 1992. Optimizing perennial groundwater yield planning for nonlinear systems: approach comparison. International Irrigation Center Report IIC-92/2. Utah State Univ., Logan, Utah. 58 p.