## Appendix A  
The pseudo-code of the standard ABC algorithm is given below:  
```
Input \(D\): Dimension of \(\mathbf{x}\) \(f(\mathbf{x})\): Objective function, \(x=(x_{1},x_{2},\cdots x_{D})\) \(\mathbf{x}^{\max}\): Upper bound of \(\mathbf{x}\) \(\mathbf{x}^{\min}\): Lower bound of \(\mathbf{x}\)  Output \(x_{opt}\): Optimal solution \(\left.\right.\) /Parameters initialization*/ \(MCN\): Max cycle number \(SN\): Half of population size \(limit\): Number of cycles for abandonment \(iter\): Iterations of the algorithm /*Population initialization*/ for\(i=1\) to \(SN\)do for\(j=1\) to \(D\)do \(x_{i,j}=x_{j}^{min}+\text{rand}(0,1)(x_{j}^{max}-x_{j}^{min})\) endfor \(\text{trial}(i)=0\) endfor while(\(iter<MCN\))do /*The employed bee phase*/ for\(i=1\) to \(SN\)do  Randomly choose \(j\) from \(\{1,2,\ldots,D\}\) and \(k\) from \(\{1,2,\ldots,SN\}\) that \(k\
eq i\)  Randomly choose \(\varphi_{i,j}\) from [-1,1] \(v_{i,j}=x_{i,j}+\varphi_{i,j}\left(x_{i,j}-x_{k,j}\right)\) if\(f(v_{i})<f(x_{i})\) trial(\(i\)) = 0 elsetial(\(i\)) = trial(\(i\))+1 endif endfor \(x_{opt}\) = best() /*The onlookers phase*/ for\(i=1\) to \(SN\)do \(f_{i}\)= \(fitness_{i}/\sum\limits_{i=1}^{SN}fitness_{i}\) endfor for\(i=1\) to \(SN\)do
```  
**Algorithm A1** Standard ABC algorithm```
\(q=\text{routineWheel}(f_{i})\) Randomly choose \(\varphi_{q,j}\) from [\(-1\),\(1\)] Randomly choose \(j\) from [\(1\), \(2\), \(\dots\), \(D\)] and \(k\) from {1, \(2\), \(\dots\), \(SN\)} that \(k\
eq i\)\(v_{q,j}=x_{q,j}+\varphi_{q,j}\Big{(}x_{q,j}-x_{k,j}\Big{)}\) if\(f\big{(}v_{q}\big{)}<f\big{(}x_{q}\big{)}\) trial(\(i\)) = 0 else trial(\(q\)) = trial(\(q\))+1 endif endfor \(x_{opt}=\text{best}()\) /*The scouts phase*/ for\(i=1\) to \(SN\)do if trial(\(i\)) > limit for\(j=1\) to \(D\)do \(x_{i,j}=x_{j}^{min}+\text{rand}(0,1)(x_{j}^{max}-x_{j}^{min})\) endfor endif endfor \(iter=iter+1\) endwhile (\(m=MCN\))
```

**Algorithm 2** Modified ABC algorithm with [PERSON]'s method (MABC-Powell)

## Appendix B

The pseudo-code of the Modified ABC algorithm with [PERSON]'s method is given below:

```
Input \(D\): Dimension of \(\mathbf{x}\)\(f(\mathbf{x})\): Objective function, \(\mathbf{x}=(x_{1},x_{2},\dots x_{D})\)\(\mathbf{x}^{\text{max}}\): Upper bound of \(\mathbf{x}\)\(\mathbf{x}^{\text{min}}\): Lower bound of \(\mathbf{x}\) Output \(x_{opt}\): Optimal solution /*Parameters initialization*/ MCN: Max cycle number \(SN\): Half of population size \(limit\): Number of cycles for abandonment \(iter\): Iterations of the algorithm /*Population initialization*/ for\(i=1\) to \(SN\)do for\(j=1\) to \(D\)do \(x_{i,j}=x_{j}^{min}+\text{rand}(0,1)(x_{j}^{max}-x_{j}^{min})\) endfor \(\text{trial}(i)=0\) endfor while(\(iter<MCN\))do /*The employed bee phase*/ for\(i=1\) to \(SN\)do  Randomly choose \(j\) from {1, \(2\), \(\dots\), \(D\)}  Randomly choose \(\varphi_{i,j}\) from [\(-1\),\(1\)]  Randomly choose N neighbors and calculate the best neighbor \(X_{best}\)\(v_{i,j}=x_{best,j}+x_{iter}\varphi_{i,j}\big{(}x_{nbest,j}-x_{i,j}\big{)}\) if\(f\big{(}v_{i}\big{)}<f\big{(}x_{i}\big{)}\) trial(\(i\)) = 0 else trial(\(i\)) = trial(\(i\))+1 endif endfor
```

**Algorithm 3** Modified ABC algorithm with Powell's method (MABC-Powell)

## References

* [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON], K.C.S. Machine learning-based prediction of crosswind vibrations of rectangular cylinders. _J. Wind Eng. Ind. Aerodyn._**2021**, _211_, 104549. [CrossRef]
* [PERSON] and [PERSON] (2020) [PERSON]; [PERSON]. Predicting wind pressures around circular cylinders using machine learning techniques. _J. Wind Eng. Ind. Aerodyn._**2020**, _198_, 104099. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]. Deep learning-based investigation of wind pressures on tall building under interference effects. _J. Wind Eng. Ind. Aerodyn._**2020**, _201_, 104138. [CrossRef]
* [PERSON] and [PERSON] (2015) [PERSON]; [PERSON]; [PERSON] Wind tunnel: A fundamental tool for long-span bridge design. _Struct. Infrastruct.