Encapsulating the role of solution response space roughness on global optimal solution: application in identification of unknown groundwater pollution sources

A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulation s of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers