The application of 0–1 mixed integer nonlinear programming optimization model based on a surrogate model to identify the groundwater pollution source

Abstract

The optimization model is presently used for the identification of pollution sources and it is based on non-linear programming optimization. The decision variables in this model are continuous, resulting in a weak recognition of integer variables including pollution source location. In addition, as the number of pollution sources increase, so the calculated load increases exponentially and accuracy decreases. Compared with previous studies, this study makes a series of improvements by adopting a 0–1 mixed integer nonlinear programming optimization model to enable the simultaneous identification of both location (integer variable) and the release intensity (continuous variable) of the pollution source. One of the constraints in the optimization model is a simulation component which requires thousands of calls during the calculation process and therefore requires considerable computational load. To avoid this problem, the Kriging surrogate model is established in this study to reduce computational load, while at the same time ensuring the accuracy of the simulation results. The identification result is solved using a genetic algorithm (GA) and represents the real location of the pollution source, while release intensities are close to actual ones with small relative errors. The Kriging surrogate model is based on a 0–1 mixed integer nonlinear programming optimization model and can simultaneously identify both the location and the release intensity of the pollution source with a high degree of accuracy and by using short computational times.