# Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review
## 5 Experiment, Result, and Discussion
### Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Function**} & \multirow{3}{*}{**Value**} & \multicolumn{8}{c}{**Bat Algorithm**} \\ \cline{3-10}  & & **Pop = 10** & **Pop = 20** & **Pop = 30** & **Pop = 50** & **Pop = 100** & **Pop = 300** & **Pop = 500** & **Pop = 1000** \\ \cline{3-10}  & & **Iter = 1000** & **Iter = 900** & **Iter = 800** & **Iter = 600** & **Iter = 500** & **Iter = 300** & **Iter = 100** & **Iter = 10** \\ \hline \multirow{3}{*}{Sphere} & Mean & 1.94E+04 & 1.68E+04 & 1.59E+04 & 1.55E+04 & 1.43E+04 & 1.1882E+04 & 1.1242E+04 & 1.0300E+04 \\ \cline{2-10}  & Stand.Div & 1.98E+04 & 1.72E+04 & 1.64E+04 & 1.61E+04 & 1.46E+04 & 1.2227E+04 & 1.1441E+04 & 1.0369E+04 \\ \cline{2-10}  & Best & 1.15E+04 & 7.26E+03 & 1.05E+04 & 9.01E+03 & 8.02E+03 & 5.5988E+03 & 7.3909E+03 & 7.0207E+03 \\ \cline{2-10}  & Worst & 2.78E+04 & 2.38E+04 & 2.46E+04 & 2.42E+04 & 1.98E+04 & 1.6507E+04 & 1.6244E+04 & 1.1869E+04 \\ \cline{2-10}  & MeanRunTimes & 1.53E+00 & 2.86E+00 & 7.23E+00 & 8.54E+00 & 1.64E+01 & 1.1428E+01 & 12.8373 & 6.8391 \\ \hline \multirow{3}{*}{Rastrigin} & Mean & 3.16E+02 & 3.04E+02 & 2.90E+02 & 2.83E+02 & 2.77E+02 & 2.7082E+02 & 264.1494 & 252.9087 \\ \cline{2-10}  & Stand.Div & 3.18E+02 & 3.05E+02 & 2.91E+02 & 2.84E+02 & 2.78E+02 & 2.7126E+02 & 264.4724 & 253.7484 \\ \cline{2-10}  & Best & 2.15E+02 & 2.73E+02 & 2.43E+02 & 2.43E+02 & 2.16E+02 & 2.3388E+02 & 238.5740 & 206.2512 \\ \cline{2-10}  & Worst & 3.73E+02 & 3.59E+02 & 3.36E+02 & 3.14E+02 & 3.29E+02 & 2.9137E+02 & 285.5669 & 289.4242 \\ \cline{2-10}  & MeanRunTimes & 1.85E+00 & 3.22E+00 & 4.54E+00 & 6.18E+00 & 9.79E+00 & 1.1708E+01 & 13.1386 & 6.9371 \\ \hline \multirow{3}{*}{Rosenbrock} & Mean & 2.96E+07 & 2.26E+07 & 1.76E+07 & 1.40E+07 & 1.52E+07 & 9.0472E+06 & 7.6228E+06 & 6.7477E+06 \\ \cline{2-10}  & Stand.Div & 3.40E+07 & 2.42E+07 & 2.00E+07 & 1.51E+07 & 1.59E+07 & 9.8445E+06 & 8.0408E+06 & 6.9390E+06 \\ \cline{2-10}  & Best & 1.09E+07 & 6.00E+06 & 6.26E+06 & 2.39E+06 & 5.92E+06 & 2.5159E+06 & 3.8750E+06 & 3.8616E+06 \\ \cline{2-10}  & Worst & 7.99E+07 & 4.30E+07 & 4.11E+07 & 2.49E+07 & 2.55E+07 & 1.6890E+07 & 1.3239E+07 & 9.3581E+06 \\ \cline{2-10}  & MeanRunTimes & 1.45E+00 & 3.09E+00 & 6.45E+00 & 4.81E+00 & 1.14E+01 & 1.1363E+01 & 12.6469 & 6.7982 \\ \hline \multirow{3}{*}{Griewank} & Mean & 1.94E+02 & 1.67E+02 & 1.54E+02 & 1.43E+02 & 1.18E+02 & 1.1163E+02 & 93.7006 & 94.5310 \\ \cline{2-10}  & Stand.Div & 2.01E+02 & 1.71E+02 & 1.57E+02 & 1.46E+02 & 1.21E+02 & 1.1527E+02 & 95.0456 & 97.1846 \\ \cline{2-10}  & Best & 1.09E+02 & 1.09E+02 & 7.05E+01 & 9.88E+01 & 7.94E+01 & 4.0860E+01 & 65.6311 & 49.3315 \\ \cline{2-10}  & Worst & 3.16E+02 & 2.51E+02 & 2.09E+02 & 2.01E+02 & 1.76E+02 & 1.6464E+02 & 134.4593 & 139.8530 \\ \cline{2-10}  & MeanRunTimes & 1.94E+00 & 3.54E+00 & 7.19E+00 & 8.81E+00 & 1.66E+01 & 1.6149E+01 & 13.4474 & 7.1280 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Result for Bat Algorithm. The results of experiments that were conducted to show the effect of 10 different initialisation schemes on the algorithms are presented, and the findings in the experiments are discussed. The best, worst, mean, standard deviation, and the mean runtime results obtained from the experiments are shown in Tables 17-19. It can be seen from the results, that the ten different initialisation schemes have a different effect on the performance of the algorithms. For some functions, the results are better than others. For some functions, the results appeared to be inconsistent because, while the best value is accurate, the mean value seemed to be inaccurate. The inconsistency could mean that the initial population is close to the global optimum when the best value was returned. It could also mean that the diversity is best suited to the function, hence, its ability to yield a good result. In other cases, more iterations might be needed, or a different diverse population might be used to achieve the desired result.