## 4 Conclusions and Final Remarks  
A simple formulation for the optimal design of reinforced concrete sections under compression and biaxial bending was established in a previous work by the authors. In that work, to verify that the formulation could work well in different types of metaheuristic algorithms, a genetic algorithm and two firefly algorithms were used to obtain the solutions to two problems under the conditions of two different design codes (EC2 and ACI318).  
Figure 11: Cross-section under biaxial bending. Robustness.  
Figure 12: Cross-section under biaxial bending. Accuracy.  
As meta-heuristic algorithms have the common disadvantage of needing to evaluate the objective function many times during the exploration phase, the time required to obtain the solution was extensive.  
For this reason, the authors studied and implemented a simple parallel computing strategy and the corresponding modifications and adjustments in the FA, which is explained in detail in this work, with the aim of: (i) reducing the necessary calculation time and (ii) avoiding any lack of precision regardless of the number of parallel processes adopted.  
In accordance with these two objectives, the two examples show that:  
1. The speed-up increases as more parallel processes are considered. The trend is almost linear up to six parallel processes. From six onwards, there is no significant increase. It can also be seen that the efficiency quickly drops with more than four parallel processes. These results depend on the computer used to run the calculations but not on the proposed design method. To achieve better results, using another computer whose architecture allows more processes in parallel would be sufficient.
2. The method achieves designs close to the global optimum despite the number of parallel processes considered. Small random displacements (LSRD and GSRD) have proven to be essential to avoiding the bias produced by the migration between subpopulations. LSRD shows its effect when there are few subpopulations of many individuals. In contrast, GSRD shows its effect when there are many subpopulations with few individuals. The combined use of LSRD and GSRD slightly improves the results and reduces their sensitivity in relation to the number of parallel processes considered. It should be noted that the proposed method was tested considering only up to 16 parallel processes (or 16 subpopulations). More research should be done considering more parallel processes. To facilitate this task for other potential researchers or for other uses, the authors included the MATLAB(r)code for the complete method in the Appendix A.  
This cross-sectional design method can be integrated into a more general design scheme for three-dimensional reinforced concrete structures by making the necessary changes and adjustments. To facilitate this integration, it was previously designed to be able to solve different load situations, as shown in the two examples included in this work.  
The following are available online at [[https://www.mdpi.com/2076-341/7/11/5/2076/s1](https://www.mdpi.com/2076-341/7/11/5/2076/s1)]([https://www.mdpi.com/2076-341/7/11/5/2076/s1](https://www.mdpi.com/2076-341/7/11/5/2076/s1)).  
Conceptualization, A.T. and G.S.-O.; methodology and algorithm implementation, G.S.-O.; checking the results, A.T.; writing-original draft preparation, G.S.-O.; writing-review and editing, A.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.