## 1 Introduction  
The addition of a wrapped face to reinforced soil embankments is a novelty in reinforcement structures. The end of the reinforcement material is folded back and wrapped around the embankment at the surface of the slope. The lateral soil pressure is transmitted to the soil through reinforcement strips, anchoring the structure. It has advantages, namely it is light weight, has strong adaptability, and has good seismic resistance; it occupies a small amount of land; and saves on building materials; among other things [1]. In recent years, China has attached great importance to reducing carbon emissions, and reinforced soil embankments with wrapped faces can be utilized in the gaps in geogrid grass planting, giving the effect of greening and landscaping, and can also reduce carbon emissions [2]; this is a considerable development. This soil reinforcement structure has been used more frequently, as the number of deeply excavated and highly filled embankments has increased [3, 4]. Scholars have investigated the mechanical properties and stability of these structures using theoretical analysis [5, 6], laboratory tests [7, 8, 9], field monitoring [10, 11], and numerical simulations [12, 13]. However, due to the complex interaction mechanisms between the geogrid and the soil, determining the impact of the reinforcement parameterson slope stability remains challenging [14]. Consequently, further research is necessary to select design parameters that meet the requirements of engineering practice. [PERSON] et al. [14] used an orthogonal experimental design to analyze the sensitivity of factors affecting the reinforced slope's stability and to assess the reinforcement performance. They proposed that slope engineering should make use of materials with high cohesiveness and large internal friction angles. The nonlinear finite element program ABAQUS was utilized by [PERSON] et al. [15] to evaluate the impact of the quantity of the reinforcement layers, the reinforcement material modulus, the soft foundation modulus, the fill height, and the thickness of the soft soil layers, demonstrating that reinforcement inhibited lateral displacement and improved slope stability. The length and horizontal spacing of the reinforcing strips, as well as the internal friction angle and cohesiveness of the fill, were examined by [PERSON] et al. [16] with regard to their impact on slope stability. The stability index of reinforced soil embankments was analyzed by [PERSON] et al. [17] using the Monte Carlo method. They found that higher cohesion, the internal friction angle, the tensile strength of the reinforcement material, and the soil-reinforcement friction coefficient, improved the stability. [PERSON] et al. [18] employed a sequential quadratic programming algorithm based on indoor model tests to develop a mathematical model aimed at optimizing the reinforcement deployment scheme for reinforced soil-retaining walls. The objective was to minimize the amount of reinforcement strips, while ensuring no damage occurred. Although numerous studies have been conducted on reinforced soil structures, previous optimal designs have often overlooked the interaction between various design parameters. Furthermore, these studies primarily focused on stability as the main optimization objective, with less emphasis on economic factors. To achieve efficient and accurate optimal design parameters for reinforced soil embankments that ensure both safety and cost effectiveness, this paper leverages the reconstruction project involving Xianhu Road in Yiling District, Yichang City. The design parameters considered include the wrapping thickness, slope rate, elastic modulus of the filler, reinforcement strip length, modulus of elasticity of the reinforcement strip, and the interfacial friction angle. Constraints are set for the maximum lateral displacement, maximum vertical displacement, maximum XZ direction stress, maximum shear strain increment, and the factor of safety. The objective is to minimize the embankment cost per meter.