Solution of a Well-Field Design Problem with Implicit Filtering

Abstract

Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.

Developing portfolios of water supply transfers

“…IFFCO's combination of stencil-based sampling and gradient-based optimization is most effective when the function to be minimized is a smooth surface with low-amplitude perturbations. Such problems are common in a number of applications, and while implicit filtering has not been applied to water resource management problems, it has been successfully employed in some related settings, including the design of groundwater remediation systems [Battermann et al, 2002;Fowler et al, 2004].…”

A decision making framework with MODFLOW-FMP2 via optimization: Determining trade-offs in crop selection

“…Moreover, imposing a wider range of hydrological or conjunctive use constraints, e.g., limiting values of hydraulic head at pumping wells near critical features of the domain, should be enforced to better understand the underlying models. Previous work (Fowler et al, 2004(Fowler et al, , 2008 highlighted the influence these types of constraints have on optimization landscapes, leading to non-convexities and discontinuous feasible regions and further supporting the use of evolutionary algorithms as a global search tool.…”

“…The result shows small plateaus in the optimization landscapes and large regions with minimal changes in water usage. These properties create local minima that can trap gradient based methods or stencil based methods when a sufficiently small increment is used (Fowler et al, 2004(Fowler et al, , 2008. Fig.…”

Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions.

“…In order to test the effectiveness of the MFO approach, we compare results for the HC problem included in the set of community problems proposed in [27]. For the simple domain of this problem, the FBHC formulation has been shown to be sufficient [12]. However, it should be noted that other approaches are needed for more realistic domains [1].…”