Random Forest-Based Multi-Objective Optimization Design Method of Relief Wells for Levee Safety

Relief well designs mainly focus on conventional parameters such as well diameter and well spacing by engineering experience, lacking rigorous analysis. The impact of wellhead elevation remains unclear. This paper proposes a multi-objective optimization method for determining the design parameters (i.e., the wellhead elevation and number of wells) of relief wells. MODFLOW is used to develop a three-dimensional transient seepage numerical model of the levee. The design parameters of relief wells are optimized by balancing the safety factor and the economic cost by non-dominated sorting genetic algorithm-II (NSGA-II). To remove computational burden within NSGA-II, random forest (RF) is used to establish an intelligent surrogate model for evaluating the hydraulic characteristics of levees. The final optimal design parameters are determined by entropy weight and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Finally, the proposed approaches are illustrated using the Wuhan Yangtze River Levee, China. Results show that compared with the empirical approach, the optimal design parameters obtained by the proposed approaches can not only meet the safety threshold for the levee, but also reduce the costs by 15%. The importance of wellhead elevation on the hydraulic gradient is about six times that of the number of wells.