Optimal design of groundwater pollution monitoring network based on a back-propagation neural network surrogate model and grey wolf optimizer algorithm under uncertainty.

In the optimal design of groundwater pollution monitoring network (GPMN), the uncertainty of the simulation model always affects the reliability of the monitoring network design when applying simulation-optimization methods. To address this issue, in the present study, we focused on the uncertainty of the pollution source intensity and hydraulic conductivity. In particular, we utilized simulation-optimization and Monte Carlo methods to determine the optimal layout scheme for monitoring wells under these uncertainty conditions. However, there is often a substantial computational load incurred due to multiple calls to the simulation model. Hence, we employed a back-propagation neural network (BPNN) to develop a surrogate model, which could substantially reduce the computational load. We considered the dynamic pollution plume migration process in the optimal design of the GPMN. Consequently, we formulated a long-term GPMN optimization model under uncertainty conditions with the aim of maximizing the pollution monitoring accuracy for each yearly period. The spatial moment method was used to measure the approximation degree between the pollution plume interpolated for the monitoring network and the actual plume, which could effectively evaluate the superior monitoring accuracy. Traditional methods are easily trapped in local optima when solving the optimization model. To overcome this limitation, we used the grey wolf optimizer (GWO) algorithm. The GWO algorithm has been found to be effective in avoiding local optima and in exploring the search space more effectively, especially when dealing with complex optimization problems. A hypothetical example was designed for evaluating the effectiveness of our method. The results indicated that the BPNN surrogate model could effectively fit the input-output relationship from the simulation model, as well as significantly reduce the computational load. The GWO algorithm effectively solved the optimization model and improved the solution accuracy. The pollution plume distribution in each monitoring yearly period could be accurately characterized by the optimized monitoring network. Thus, combining the simulation-optimization method with the Monte Carlo method effectively addressed the optimal monitoring network design problem under uncertainty.