# Inverse Modeling of Seepage Parameters Based on an Improved Gray Wolf Optimizer
## 1 Introduction
It has been extensively adopted in various fields due to its simple structure, fewer parameters, and easy coding implementation. However, it tends to converge to locally optimal solutions. In addition, suboptimal values could result from completely randomized initial populations. Therefore, strategies of improvement are proposed as necessary. Generally, there are three main strategies to improve the GWO, including adjustments of initial populations, convergence factor, and formula of a location update [30]. [PERSON] et al. [31] combined the concept of opposition with GWO, initially providing a uniform population for the algorithm. [PERSON] et al. [32] introduced the theory of good point set to population initialization, which improved the homogeneity of the population. Based on this, [PERSON] et al. [33] considered the dynamics of the iterative process and proposed an equation of the convergence factor based on the number of iterations. This exponential function simulates the iterative process and balances the local and global search to a certain extent. [PERSON] et al. [34] described the decay process of the parameter by an exponential function, which leads to improved accuracy for GWO. [PERSON] et al. [35] applied the spiral property from the whale optimization algorithm (WOA) to the GWO, which solves the premature convergence in the evolutionary algorithm. [PERSON] et al. [36] introduced variational operators to update the location of the individual in GWO and improved the algorithm's performance. [PERSON] and [PERSON] [37] adopted a random wandering strategy to enhance the accuracy of the algorithm. A great deal of research has been conducted on the improvement of GWO. However, local and global search, along with homogenization and randomization, cannot be relatively balanced by these improvements. GWO based on these strategies is still limited in terms of efficiency and accuracy. Therefore, there remains potential for improvement across these dimensions. Based on the evolution of the GWO, three strategies are proposed to ensure the accuracy and efficiency of the algorithm. Initial populations of semi-uniform and semi-random were proposed for rational initialization. A polynomial-based nonlinear convergence factor was applied to maintain a balance between global and local search. Weighting factors based on Euclidean norms and hierarchy were given to dynamically update the wolves' positions for jumping out of the local optimum at the late stage of the iterative search [38; 39]. The Improved Gray Wolf Optimizer (IGWO) has been proven to be effective through numerical experiments. This algorithm was applied for the inversion model of the Kakiwa Dam located in Sichuan Province, China. The fitness function is constructed by measurements of piezometers and measuring weir. The finite element method was used to simulate the seepage process under the assumption of steady flow. The free tetrahedral grid is used to construct the two-dimensional mesh of the dam. The finite element calculation is carried out in COMSOL Multiphysics, while the iterative control and data extraction are implemented in MATLAB. The objective hydraulic conductivity and the corresponding fitness value were determined when the maximum number of iterations was achieved. The seepage field at the dam site was also presented.