The accurate estimation of soil hydraulic parameters (θ_s, α, n, and K_s) of the van Genuchten–Mualem model has attracted considerable attention. In this study, we proposed a new two-step inversion method, which first estimated the hydraulic parameter θ_s using objective function by the final water content, and subsequently estimated the soil hydraulic parameters α, n, and K_s, using a vector-evaluated genetic algorithm and particle swarm optimization (VEGA-PSO) method based on objective functions by cumulative infiltration and infiltration rate. The parameters were inversely estimated for four types of soils (sand, loam, silt, and clay) under an in silico experiment simulating the tension disc infiltration at three initial water content levels. The results indicated that the method is excellent and robust. Because the objective function had multilocal minima in a tiny range near the true values, inverse estimation of the hydraulic parameters was difficult; however, the estimated soil water retention curves and hydraulic conductivity curves were nearly identical to the true curves. In addition, the proposed method was able to estimate the hydraulic parameters accurately despite substantial measurement errors in initial water content, final water content, and cumulative infiltration, proving that the method was feasible and practical for field application.

Reasonable planning of water delivery schedules for canal systems can reduce losses caused by water seepage and improve the utilization efficiency of irrigation water. Empirical methods of water delivery scheduling for canal systems usually cause problems such as insufficient discharge, excessively delayed water delivery, and large losses under given water requirements. In this study, a canal water delivery scheduling model was set up, and a customized algorithm based on particle swarm optimization was proposed. Typical heuristic algorithms often become trapped in local optima and often search inefficiently under numerous constraints; however, the proposed algorithm can overcome these typical problems. The proposed method was evaluated for two typical canal irrigation systems, and the results showed that the algorithm is robust and efficient and can quickly meet the water delivery optimization schedules for canal irrigation systems. Compared with empirical methods, the algorithm reduced the leakage loss of delivered water from 7.29% to 5.40%, and 8.97% to 7.46% for the two tested canal systems. The discharge of the main canal is relatively stable, which can reduce the difficulty of head gate adjustment. The proposed optimization algorithm can provide practical and efficient water delivery schedules for irrigation canal systems.

The numerical simulation of the optimal design of gravity dams is computationally expensive. Therefore, a new optimization procedure is presented in this study to reduce the computational cost for determining the optimal shape of a gravity dam. Optimization was performed using a combination of the genetic algorithm (GA) and an updated Kriging surrogate model (UKSM). First, a Kriging surrogate model (KSM) was constructed with a small sample set. Second, the minimizing the predictor strategy was used to add samples in the region of interest to update the KSM in each updating cycle until the optimization process converged. Third, an existing gravity dam was used to demonstrate the effectiveness of the GA–UKSM. The solution obtained with the GA–UKSM was compared with that obtained using the GA–KSM. The results revealed that the GA–UKSM required only 7.53% of the total number of numerical simulations required by the GA–KSM to achieve similar optimization results. Thus, the GA–UKSM can significantly improve the computational efficiency. The method adopted in this study can be used as a reference for the optimization of the design of gravity dams.

Shape optimization of single-curvature arch dams using the finite element method (FEM) is often computationally expensive. To reduce the computational burden, this study introduces a new optimization method, combining a genetic algorithm with a sequential Kriging surrogate model (GA-SKSM), for determining the optimal shape of a single-curvature arch dam. At the start of genetic optimization, a KSM was constructed using a small sample set. In each iteration of optimization, the minimizing predictor criterion and low confidence bound criterion were used to collect samples from the domain of interest and accumulate them into a small sample set to update the KSM until the optimization process converged. A practical problem involving the optimization of a single-curvature arch dam was solved using the introduced GA-SKSM, and the performance of the method was compared with that of GA-KSM and GA-FEM methods. The results revealed that the GA-SKSM method required only 5.40% and 12.40% of the number of simulations required by the GA-FEM and GA-KSM methods, respectively. The GA-SKSM method can significantly improve computational efficiency and can serve as a reference for effective optimization of the design of single-curvature arch dams.

Accurate inversion of soil hydraulic parameters based on the van Genuchten–Mualem model has received much attention in soil science research. Herein, a hybrid algorithm method using particle swarm optimization and vector-evaluated genetic algorithm was used to invert the parameters θ_s, α, n, and K_s, with the objective functions of infiltration rate, cumulative infiltration, and soil water content. Then, numerical experiments were conducted on four typical soils at three initial water content levels (20, 40, and 60% effective saturation) to verify the accuracy of the inverse method. The results showed that the inversed soil water retention and conductivity curves were approximately the same as the real curves, with the root mean square errors of 0.00101–0.00192 cm³·cm⁻³, 0.00800–0.02519 cm³·cm⁻³, respectively, and both the Nash-Sutcliffe coefficients were approximately 1.0. Additionally, laboratory experiments were also performed to compare with the inversed parameters for verification, within small root mean squared errors and approximately 1.0 Nash–Sutcliffe coefficients. Furthermore, the method can also achieve acceptably accurate parameter inversion even with substantial measurement errors included in the cumulative infiltration, initial water content, and final water content. Thus, the method is effective and robust and found to be practical in field experiments.