## 3 Parametrical Analyses  
In order to investigate the cost and time effective design of cantilever soldier pile retaining wall structures, parametric analysis is presented with the division of two steps. The first step involves the analyses conducted with optimization techniques to show the change effects of design variants, and the second step shows the comparison details of optimization results with finite element software to control the appropriateness of the usage of optimization algorithm to design cantilever soldier piles. For the application of step 1, the HS algorithm is used with the application of beams on elastic soil assumption to evaluate the minimum costs of the cantilever soldier pile retaining walls that are fictionalized according to different project situations in the present study. The design constants and variables of fictionalized cases are given in Table 3. According to the national and international literature studies, manuals, and technical reports, the depth of excavation is assumed to be between 3 and 12 m [16; 37; 38; 39]. At the design stage of retaining piles, it is clear that the designers need the soil parameters, especially the unit weight and the shear strength angle, to determine the lateral earth pressures [3; 4; 5; 6; 7]. It is assumed to embed the pile into a homogenous soil layer that is formed by non-cohesive soils, and the values of the geotechnical parameters are selected from the literature according to the allowable limits [4; 14]. The unit weight of the soil, the internal friction angle, and the ultimate bearing pressure values are taken as variables, and different cases are fictionalized to compare the effects of soil properties on the design of retaining walls and costs. The unit weight of the soil is defined according to the suggestions of [PERSON] [4] and [PERSON] [14]. [PERSON] defined the unit weights of granular soils due to the relative density and internal friction angle values of specimens. The unit weight values are defined as within 14-18 kN/m\({}^{3}\), 17-20 kN/m\({}^{3}\), and 17-22 kN/m\({}^{3}\) for loose, medium, and dense sand, respectively [14]. [PERSON] defined the unit weight of some typical soils in the natural state. 14.5 kN/m\({}^{3}\) is defined for loose uniform sand, and 18 kN/m\({}^{3}\) is defined for dense uniform sand [4]. Correspondingly, the unit weight values of sandy soils are assumed to be between 14 and 20 kN/mto perform parametrical analysis. Shear strength angle values are also identified by the use of the suggestions of [PERSON] and [PERSON]. According to the mentioned boundaries, the shear strength angle is selected between 27\({}^{\circ}\) and 38\({}^{\circ}\) for parametric analyses. Based on the beams on elastic soil assumption, another influencer parameter can be identified as the coefficient of soil reaction to determine the characteristic length of the pile [14; 32]. It is already a big challenge for geotechnical engineers and researchers to determine the reaction of soil in contact with structure. According to this problem, first investigations are made by [PERSON] [40] and a model that assumes the stiffness of the soil, which is considered as the ratio between the contact pressure and the related linear vertical displacement. This relationship can be defined the coefficient of subgrade reaction, \(K_{s}\) with MN/m\({}^{3}\) unit. This theory is governed by a linear-elastic model that models the soil behavior as a group of independent springs. This theory is firstly used to perform analysis for rigid plates, but recently, it has been extended to include the determination of the stresses of flexible structures. The coefficient of the soil reaction can be determined by conducting both laboratory (consolidation, triaxial, California bearing ratio tests) and field tests (plate loading test) or using semi-empirical or empirical [14; 41] equations or selected from tabulated values [14].