**4. Methodology**

As previously mentioned, although many studies have been implemented to optimize the retaining wall design, no studies have been conducted so far investigating the effect of various methods of determining the parameters of the soil ultimate bearing capacity on the design optimization of these structures. The current study deals with this issue and, in particular, the effect of using the methods developed by Meyerhof, Hansen, and Vesic (respectively abbreviated as MM, HM, and VM hereafter) on the cost of the retaining wall. For this purpose, a database containing discrete values of the

mentioned variables (*X*1 to *X*8 and *R*1 to *R*4) was generated. Then, the PSO algorithm was used to solve the optimum design problem defined above. All the process of optimum design was implemented via a code written in MATLAB [18]. The flowchart of the design optimization process is shown in Figure 4. The next section investigates the effects of the above three methods on the optimum design of RCRWs.

**Figure 4.** The flowchart of the design optimization of reinforced concrete retaining walls (RCRWs).
