## 2 Design and Methodology  
The design of retaining structures consists of the integrated analysis of two different fields such as geotechnical and structural engineering, as before mentioned. In addition to these design issues, the cost of the structural system is the identifier parameter of the design process to select the applicable type. However, it is hard to acquire both the safety and economy simultaneously saving time and labor by the usage of traditional design methods [28]. Therefore, in recent studies, the techniques that allow saving time and cost have been used in the design process of retaining structures. In this regard, [PERSON] et al. used optimization algorithms with a single objective optimistic model using the m-method of piles in a row design and discussed the wall displacement via cost [29]. [PERSON] and [PERSON] used genetic algorithm to optimize the design parameters of the retaining pile system [30]. In a similar vein, within the present study, optimization of the cantilever soldier pile retaining walls has been investigated with the use of harmony search algorithm but differentiated from the reference studies, the design rules of the pile system is defined with the beams on elastic soil assumption. Besides this, the present study is differentiated from other studies by the type of selected design variants (project necessities, soil properties, and environmental conditions), by used design rules (beam on elastic soil assumption), and by the applied comparison procedure (comparisons with a well-known commercial geotechnical analysis software). Therefore, the design procedures of cantilever soldier piles based on the mentioned method are described step by step to detail all these differences. The cross-section of a simple cantilever soldier pile wall is given in Figure 1a. In Figure 1a, the symbols \(h\), \(d\), \(L\), and \(D\) represent the excavation depth, embedment depth, and total length of the pile and the diameter of the pile, respectively. The stability of soldier pile walls relies upon the mobilization of earth pressures on both sides of the wall stem [8; 9]. Active and passive stresses which are generated according to this earth pressures are shown in Figure 1b according to the beam on elastic soil assumption. Rankine Earth Pressure Theory is used to calculate lateral earth coefficients. \(q_{a}\) describes the external load that is affecting the soldier pile at the active side of the wall. \(q_{a}\) is converted to lateral load (\(P_{q\mu}\)) by the use of active lateral earth coefficient of natural soil conditions. \(P_{a}\) and \(P_{p}\) define the lateral soil reaction forces of the active and passive side, respectively. Within this paper, cantilever soldier piles are assumed to behave similar to beams on elastic soil and the piles are considered to constitute a continuous wall system by locating tangent. Depending on the continuous elastic support assumption, the soil is described by an elastic continuum [18; 19; 20; 21], and the reaction of the soil at a specified section of a pile is only dependent on the deformation of that part and not on the deflections of pile above and below it [20; 22; 31]. For this reason, it is assumed that the calculation of the embedment depth and pivot point location is only dependent  
Figure 1: The cross-section of a cantilever soldier pile (**a**); Distribution of earth pressure along the pile (**b**); Continuous elastic support assumption (**c**,**d**). on the equilibrium of forces, which are activated through the penetrated part of the pile in the soil. The main important feature supplied by using soil as a continuum medium is that input variables can be directly related to measurable and realistic soil properties such as the stiffness and strength of the material [5]. The representative parameters of the flexural rigidity and characteristic length of the pile are \(EI\) and \(l_{0}\), respectively.