Comparison of Three Multiobjective Optimization Algorithms for Inverse Modeling of Vadose Zone Hydraulic Properties

Inverse modeling has become increasingly popular for estimating effective hydraulic properties across a range of spatial scales. In recent years, many different algorithms have been developed to solve complex multiobjective optimization problems. In this study, we compared the efficiency of the Nondominated Sorting Genetic Algorithm (NSGA-II), the Multiobjective Shuffled Complex Evolution Metropolis algorithm (MOSCEM-UA), and AMALGAM, a multialgorithm genetically adaptive search method for multiobjective estimation of soil hydraulic parameters. In our analyses, we implemented the HYDRUS-1D model and used observed pressure head data at three different depths from the Spydia experimental field site in New Zealand. Our optimization problem was posed in a multiobjective context by simultaneously using three complementary RMSE criteria at each depth. We analyzed the trade-off between these criteria and the adherent Pareto uncertainty. The results demonstrate that all three algorithms were able to find a good approximation of the Pareto set of solutions, but differed in the rate of convergence to this distribution. Small differences in performance of the various algorithms were observed because of the relative high dimension of the optimization problem in combination with the presence of multiple local optimal solutions within the three-objective search space. The Pareto parameter sets yielded satisfactory results when simulating the transient tensiometric pressure at predetermined observation points in the investigated vadose zone profile. The overall best parameter set was found by AMALGAM with RMSE values of 0.14, 0.11, and 0.17 m at the 0.4-, 1.0-, and 2.6-m depths, respectively. In contrast, the fit errors were substantially higher at these respective depths, with RMSE values ranging from 0.87 to 1.49 m, when using soil hydraulic parameters derived from laboratory analysis of small vadose zone cores.