# A Brain Storm and Chaotic Accelerated Particle Swarm Optimization Hybridization
## 2 Background
### The BSO Algorithm
\begin{table}
\begin{tabular}{l l l l l l l} \hline  & \multicolumn{2}{c}{\(D\) = 10} & \multicolumn{2}{c}{\(D\) = 20} & \multicolumn{2}{c}{\(D\) = 30} \\ \cline{2-7}  & \(t_{switch}\) & \(\gamma\) & \(t_{switch}\) & \(\gamma\) & \(t_{switch}\) & \(\gamma\) \\ \hline \(f_{1}\) & 50 & 0.9817479430199844 & 50 & 0.9885530946569389 & 50 & 0.9885530946569389 \\ \hline \(f_{2}\) & 250 & 0.9923540961321005 & 250 & 0.9929401613666818 & 250 & 0.9934427784709274 \\ \hline \(f_{3}\) & 200 & 0.9916619195386764 & 200 & 0.9942600739529567 & 200 & 0.9958222329003689 \\ \hline \(f_{4}\) & 400 & 0.9947206857569770 & 400 & 0.9947805211255779 & 400 & 0.994809330498242 \\ \hline \(f_{5}\) & 100 & 0.9885530946569389 & 100 & 0.9892228001155464 & 100 & 0.9902907258434653 \\ \hline \(f_{6}\) & 100 & 0.9885530946569389 & 100 & 0.9954054173515270 & 100 & 0.9967159968972744 \\ \hline \(f_{7}\) & 200 & 0.9942600739529567 & 200 & 0.9958222329003689 & 200 & 0.9967159968972744 \\ \hline \end{tabular}
\end{table} 
Table 2: BSO–CAPSO hybrid parameter values per benchmark function. ## 5 Results

The simulation results are given in Tables 4 and 5 and they are organized per the number of dimensions, \(D\). The results obtained were the mean, best and worst functions' values, as well as average computation times (referred to as time), in seconds. ### Time Calculations

In order to determine the computation time/cost for each experiment, Python 3's library, Time (specifically _time.perf_counter_()), was used to calculate the difference between the moments in time an experiment began and ended. The signaling of an experiment's beginning and ending remained exactly the same for each experiment, so that the results were as accurate as possible. All the experiments were performed on the same personal computer (CPU-AMD Ryzen 5 1600, RAM-8,00 GB @ 1197 MHz, OS-Windows 10 Pro 64-bit). severely improved CAPSO. It specifically seemed to converge (or otherwise \"accelerate\") more efficiently than CAPSO, while also improving the quality of its solutions in the vast majority of cases, especially regarding the complex multimodal functions. The diagrams' data were obtained by the provided detailed results in Tables 4 and 5. Figure 3: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and CAPSO algorithms for the Ackley (\(f_{5}\)) function with \(D=10\). Convergence acceleration occurred after \(t_{switch}=100\). Figure 2: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and stand-alone CAPSO algorithms for the sphere (\(f_{1}\)) function with \(D=10\). Convergence acceleration occurred after \(t_{switch}=50\). Figure 4: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and CAPSO algorithms for the Griewank (\(f_{6}\)) function with \(D=10\). Convergence acceleration occurred after \(t_{switch}=100\). Figure 5: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and stand-alone CAPSO algorithms for the Griewank (\(f_{6}\)) function with \(D=20\). Convergence acceleration occurred after \(t_{switch}=100\). Figure 6: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and stand-alone CAPSO algorithms for the Rosenbrock (\(f_{2}\)) function with \(D=20\). Convergence acceleration occurred after \(t_{switch}=250\). Figure 7: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and stand-alone CAPSO algorithms for the Ackley (\(f_{5}\)) function with \(D=20\). Convergence acceleration occurred after \(t_{switch}=100\). Figure 8: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and stand-alone CAPSO algorithms for the Rosenbrock (\(f_{2}\)) function with \(D=30\). Convergence acceleration occurred after \(t_{switch}=250\). Figure 9: Convergence diagram of the stand-alone BSO, BSO–CAPSO hybrid and stand-alone CAPSO algorithms for the Schwefel 2.21 (\(f_{3}\)) function with \(D=30\). Convergence acceleration occurred after \(t_{switch}=200\).