## 3 Optimization Algorithms
### Grasshopper Optimization Algorithm (GOA)
## 5 Conclusions

A simple ANN saves time and energy, which are spent on obtaining CS of concrete containing recycled aggregate. However, the ANN should be accurate as well to be useful. Otherwise, it just adds to higher costs. In this study, three different optimization algorithms (GA, SSA, and GOA) are employed to modify ANN for that purpose, and M5P tree served as a good comparison model. Results show that all ANNs have better performances than the M5P tree model. Moreover, the ANN that is hybridized with SSA has the lowest values of error, and the second simplest architecture. ANNGOA, on the other hand, has the simplest structure, with the highest values of error, and finally, ANNGA despite of its architecture, which is the most complex one, is the second most accurate model among the ANNs. Although all the ANNs are so close in both accuracy and complexity, the ANNSA is recommended if accuracy is needed and the ANNGOA should be used if there is a need for simplicity. The compressive strength (CS) of concrete containing different amounts of recycled aggregate (RA) is shown in Figure 9. According to this figure, increasing the amount of RA to 50% causes a decrease in the CS value at all ages. However, the CS value of the samples with 100% RA is higher than that of the samples with 50% RA at the age of 7 and 28 days, while the CS values of these two classes are almost equal at the age of 3 days. **Author Contributions:** Conceptualization, A.K. and M.K. ; methodology, A.K. ; software, A.K. ; validation, A.K. and M.K. ; formal analysis, A.K. ; investigation, A.K. ; data curation, F.S. ; writing\(-\)original draft preparation, A.K. and F.S. ; writing\(-\)review and editing, A.K. and M.K. ; supervision, M.K. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. **Conflicts of Interest:** The authors declare no conflict of interest. Figure 9: The CS of concrete with different amounts of RA. ## Appendix A

### Biases and Weights of the ANNSA Model

Weights of links between input and the first hidden layer

\[= \begin{bmatrix}0.55&1.24&0.55&-2.28&-0.19&0.75&2.44&-0.41&0.72\\ 0.28&1.46&1.31&-0.88&0.02&0.04&-0.38&-0.36&0.27\\ -1.28&-1.06&-1.56&-0.37&-0.20&0.31&1.11&1.30&0.15\\ -0.20&-0.69&-1.74&-0.10&-0.18&0.01&-0.01&0.23&0.53\\ 0.36&0.91&1.68&-0.45&0.12&-0.16&-4.12&2.09&-0.13\\ -0.78&0.08&1.55&1.01&0.03&0.30&3.01&0.30&-0.07\\ \end{bmatrix} \]

Biases of the input layer \(= \begin{bmatrix}[-0.52&-1.32&-0.03&0.26&0.14&0.431\end{bmatrix} \)

Weights of links between hidden and output layer

\[= \begin{bmatrix}0.50&-1.13&-2.18&1.08&1.31&1.54\end{bmatrix} \]

### Biases of the hidden layer \(= \begin{bmatrix}-1.30\end{bmatrix} \)

Weights of links between input and the first hidden layer

\[= \begin{bmatrix}0.88&-2.09&0.52&1.13&0.34&0.28&-1.36&-1.13&0.63\\ -0.29&0.28&2.25&-0.64&2.00&-1.59&0.42&0.03&-0.10\\ 0.14&-0.13&-1.22&-0.21&-0.23&-0.07&-0.27&0.18&0.28\\ -1.79&-1.60&-1.36&-0.27&-0.11&0.91&-2.98&-1.35&0.27\\ 0.68&0.73&-0.60&2.16&-1.08&1.13&-0.19&0.16&-1.07\\ 1.48&0.68&-1.70&-1.82&-0.22&0.06&-1.12&0.57&0.44\\ -1.42&0.73&0.78&3.01&1.20&-0.58&-0.61&-0.07&-1.38\\ \end{bmatrix} \]

Biases of the input layer \(= \begin{bmatrix}0.39\end{bmatrix} \)

\[= \begin{bmatrix}0.64&0.48&-1.89&0.84&-0.96&-0.21&1.38\\ -0.80&-1.09&-0.55&0.76&1.39&0.65&1.57\\ -1.46&-0.29&1.08&-1.76&-1.14&-0.32&0.30\\ -0.04&0.63&-1.38&-1.24&-0.46&-0.85&-1.15\\ 0.15&-1.68&-1.05&-0.74&0.07&1.20&0.28\\ 2.02&1.06&-0.89&-0.03&-1.30&-0.46&-1.14\\ 0.03&1.49&0.20&0.15&1.31&0.92&-0.53\\ 0.69&-0.24&1.26&-1.73&-0.39&-0.76&0.39\\ 1.45&-0.52&-0.17&-0.10&-1.21&-0.85&1.46\end{bmatrix} \]

Biases of the first hidden layer

\[= \begin{bmatrix}-1.59&0.90&0.96&0.31&-0.19&1.10&0.84&-1.04&-0.08\end{bmatrix} \]

Weights of links between the last hidden and output layer

\[=