**6. Conclusions**

In the present study, three well-known methods of Meyerhof, Hansen, and Vesic were considered for the computation of the bearing capacity of RCRWs and, in particular, their influence on the optimum design of the wall. Three heights of walls were examined in the three test cases—4.0 m, 5.5 m, and 7.0 m. A code was developed in MATLAB where the PSO method was implemented for solving the constrained optimization problem. The design criteria were considered in accordance with ACI318-14 design code [20], where two sets of constraints were taken into account, the first on geotechnical requirements (wall stability) and the second on structural requirements (required strength of wall components and reinforcement arrangements). The PSO algorithm was successful in finding the optimum solutions fast and in a consistent way in all design cases, while the constraint handling mechanism was successful, managing to yield optimum solutions that satisfied the constraints in all cases.

The three methods resulted in slightly di fferent designs for all the optimum RCRWs with di fferent heights. In all three test examples, the MM (Meyerhof) method resulted in the design with the minimum total cost in comparison to the other two methods. It was also shown that the di fferences among the methods decreased with increasing the height of the RCRWs. When the height of the wall increases, the ratio of the cost of concrete to the total cost decreases, and the opposite happens with steel; the ratio of the cost of steel to the total cost increases. This observation was general and was made in all the three design methods examined. As regards the amounts of needed reinforcement, it can be concluded that the three methods give di fferent results for the individual elements of the wall. On the other hand, as a general conclusion, it can be noted that the total cost of the wall corresponding to the three methods had only a small variation. In comparison to Meyerhof as the benchmark method, the maximum di fference in the total cost was observed for the *H* = 4.0 m case and the VM method, and that accounted for only 3.26%. In all other cases the di fference was even smaller.

In addition, the e ffect of the backfill slope β and the surcharge load *q* were examined. It was found that by increasing either the backfill slope or the surcharge load we obtained a higher total cost, but again in all cases the di fferences between the three methods were rather small, accounting for up to 4.5%. Finally, the results of the study were compared to results from an example of the work of Gandomi et al. [6] and were found only slightly di fferent, which can be attributed to the di fferent analysis method and the di fferent load combinations used.

**Author Contributions:** Conceptualization, N.M. and S.G.; methodology, N.M. and S.G.; software, N.M. and S.G.; validation, V.P.; formal analysis, N.M., S.G. and V.P.; investigation, N.M., S.G. and V.P.; data curation, N.M. and S.G.; writing—original draft preparation, N.M. and S.G.; writing—review and editing, S.G. and V.P.; visualization, S.G., V.P.; supervision, S.G. and V.P.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
