Multi-objective optimization in variably saturated fluid flow

Abstract

A general purpose multi-objective inverse modeling strategy was developed and implemented to quantify fluid flow parameters in variably saturated porous materials. The strategy combines a robust and mass-conservative numerical simulator of the flow equation with an optimization algorithm and an experimental data set to estimate the parameters. The numerical simulator of the direct problem shows excellent agreement with a reference solution and conserves global mass with near perfection. An adaptive method was proposed in which the sensitivity matrix was calculated by one-sided finite difference approximation at the early stages of the optimization and the more accurate two-sided differentiation as the search approaches the minimum. A combined termination criterium was developed to stop the inverse code at the solution. The results of the multi-objective optimization were compared with those of single-objective minimization. While single-objective optimization generates reasonable results for either the fluid pressure head profile or the fluid content data, the proposed multi-objective optimization shows excellent agreement with both profiles simultaneously.