Treffer: Application of MATLAB and Python optimizers to two case studies involving groundwater flow and contaminant transport modeling

One approach for utilizing geoscience models for management or policy analysis is via a simulation-based optimization framework—where an underlying model is linked with an optimization search algorithm. In this regard, MATLAB and Python are high-level programming languages that implement numerous optimization routines, including gradient-based, heuristic, and direct-search optimizers. The ever-expanding number of available algorithms makes it challenging for practitioners to identify optimizers that deliver good performance when applied to problems of interest. Thus, the primary contribution of this paper is to present a series of numerical experiments that investigated the performance of various MATLAB and Python optimizers. The experiments considered two simulation-based optimization case studies involving groundwater flow and contaminant transport. One case study examined the design of a pump-and-treat system for groundwater remediation, while the other considered least-squares calibration of a model of strontium (Sr) transport. Using these case studies, the performance of 12 different MATLAB and Python optimizers was compared. Overall, the Hooke-Jeeves direct search algorithm yielded the best performance in terms of identifying least-cost and best-fit solutions to the design and calibration problems, respectively. The IFFCO (implicit filtering for constrained optimization) direct search algorithm and the dynamically dimensioned search (DDS) heuristic algorithm also consistently yielded good performance and were up to 80% more efficient than Hooke-Jeeves when applied to the pump-and-treat problem. These results provide empirical evidence that, relative to gradient- and population-based alternatives, direct search algorithms and heuristic variants, such as DDS, are good choices for application to simulation-based optimization problems involving groundwater management.