A mixed-integer non-linear programming with surrogate model for optimal remediation design of NAPLs contaminated aquifer

Abstract

A mixed-integer non-linear programming (MINLP) with surrogate model was introduced to derive the optimal surfactant enhanced aquifer remediation (SEAR) process (remediation cost minimisation and removal rate maximisation) at a nitrobenzene-contaminated site. First, a 3D multi-phase flow simulation model was developed to simulate the SEAR process; using a radial basis function artificial neural network (RBFANN), the surrogate model was built which was an approximation of the simulation model; a MINLP was built to identify the optimal remediation strategies and genetic algorithm (GA) and penalty function were combined to solve the model; at last, the optimal remediation strategies were obtained. The approximation result of RBFANN was compared with that of back-propagation artificial neural network (BPANN), mean absolute error, mean relative error and coefficient of determination of the developed RBFANN model were 0.01, 2.27% and 0.85 respectively, which indicated much higher approximation accuracy than BPANN. The MINLP with surrogate model is a powerful tool for non-aqueous phase liquids (NAPLs) contaminated site remediation optimisation problem and it can greatly improve computational efficiency.