# A Hybrid Adaptive Particle Swarm Optimization Algorithm for Enhanced Performance
## 4 Experiments
### Higher-Dimensional Function Analysis
\begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{\(D=\) 500} & \multicolumn{6}{c}{\(D=\) 800} \\ \cline{3-10}
**Fun.** & **Algorithm** & \(V_{avg}\) & \(V_{std}\) & \(V_{max}\) & \(V_{opt}\) & \(V_{avg}\) & \(V_{std}\) & \(V_{max}\) & \(V_{opt}\) \\ \hline \multirow{7}{*}{F\({}_{1}\)} & PSO & 4.52E+05 & 8.36E+04 & 6.37E+05 & 3.32E+05 & 8.70E+05 & 1.12E+05 & 1.17E+06 & 7.06E+05 \\  & AIWPSO & 1.08E+06 & 5.85E+04 & 1.15E+06 & 9.07E+05 & 1.82E+06 & 5.20E+04 & 1.90E+06 & 1.71E+06 \\  & LDWPSO & 5.50E+05 & 4.46E+04 & 6.48E+05 & 4.77E+05 & 9.85E+05 & 8.49E+04 & 1.15E+06 & 8.55E+05 \\  & HPSOTVAC & 1.66E+05 & 3.32E+04 & 2.36E+05 & 1.04E+05 & 2.98E+05 & 2.99E+04 & 3.60E+05 & 2.32E+05 \\  & CPSO & 9.95E+05 & 1.34E+05 & 1.34E+06 & 7.72E+05 & 1.55E+06 & 1.91E+05 & 1.89E+06 & 1.21E+06 \\  & CLPSO & 5.60E+04 & 4.20E+03 & 6.39E+04 & 4.80E+04 & 1.38E+05 & 8.67E+03 & 1.55E+05 & 1.21E+05 \\  & APSO & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** \\ \hline \multirow{7}{*}{F\({}_{5}\)} & PSO & 1.11E+07 & 1.38E+06 & 1.43E+07 & 7.35E+06 & 2.18E+07 & 2.60E+06 & 2.84E+07 & 1.46E+07 \\  & AIWPSO & 3.38E+07 & 2.54E+06 & 3.92E+07 & 2.96E+07 & 5.86E+07 & 3.61E+06 & 6.41E+07 & 4.94E+07 \\  & LDWPSO & 1.53E+07 & 1.60E+06 & 1.86E+07 & 1.26E+07 & 2.67E+07 & 2.44E+06 & 3.25E+07 & 2.18E+07 \\  & HPSOTVAC & 7.99E+05 & 2.27E+05 & 1.40E+06 & 3.36E+05 & 1.77E+06 & 4.61E+05 & 3.35E+06 & 1.15E+06 \\  & CPSO & 1.94E+07 & 3.82E+06 & 2.99E+07 & 1.44E+07 & 3.15E+07 & 7.20E+06 & 4.67E+07 & 1.90E+07 \\  & CLPSO & 7.86E+05 & 1.05E+05 & 1.00E+06 & 5.54E+05 & 2.19E+06 & 1.69E+05 & 2.53E+06 & 1.92E+06 \\  & APSO & **4.99E+02** & **1.05E-01** & **4.99E+02** & **4.98E+02** & **7.99E+02** & **6.32E-02** & **7.99E+02** & **7.99E+02** \\ \hline \multirow{7}{*}{F\({}_{5}\)} & PSO & 4.61E+03 & 2.33E+02 & 5.17E+03 & 4.23E+03 & 8.36E+03 & 3.36E+02 & 9.23E+03 & 7.88E+03 \\  & AIWPSO & 7.53E+03 & 2.12E+02 & 7.90E+03 & 6.87E+03 & 1.24E+04 & 2.43E+02 & 1.28E+04 & 1.18E+04 \\  & LDWPSO & 5.84E+03 & 2.73E+02 & 6.31E+03 & 5.31E+03 & 9.59E+03 & 3.84E+02 & 1.03E+04 & 8.84E+03 \\  & HPSOTVAC & 3.52E+03 & 2.24E+02 & 3.98E+03 & 3.08E+03 & 6.30E+03 & 3.00E+02 & 6.91E+03 & 5.55E+03 \\  & CPSO & 7.45E+03 & 3.85E+02 & 8.23E+03 & 6.73E+03 & 1.23E+04 & 4.73E+02 & 1.31E+04 & 1.09E+04 \\  & CLPSO & 3.71E+03 & 7.99E+01 & 3.88E+03 & 3.49E+03 & 6.49E+03 & 1.01E+02 & 6.66E+03 & 6.22E+03 \\  & APSO & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** & **0.00E+00** \\ \hline \multirow{7}{*}{F\({}_{10}\)} & PSO & 1.92E+01 & 1.87E-01 & 1.98E+01 & 1.89E+01 & 1.94E+01 & 1.53E-01 & 1.96E+01 & 1.90E+01 \\  & AIWPSO & 2.07E+01 & 6.82E-02 & 2.08E+01 & 2.05E+01 & 2.07E+01 & 6.97E-02 & 2.08E+01 & 2.05E+01 \\  & LDWPSO & 1.95E+01 & 1.35E-01 & 1.97E+01 & 1.91E+01 & 1.96E+01 & 1.98E-01 & 2.02E+01 & 1.93E+01 \\ \cline{1-1}  & HPSOTVAC & 1.67E+01 & 5.01E-01 & 1.74E+01 & 1.57E+01 & 1.71E+01 & 3.44E-01 & 1.79E+01 & 1.61E+01 \\ \cline{1-1}  & CFSO & 2.03E+01 & 2.55E-01 & 2.07E+01 & 2.00E+01 & 2.03E+01 & 2.91E-01 & 2.09E+01 & 1.99E+01 \\ \cline{1-1}  & CLPSO & 1.15E+01 & 2.79E-01 & 1.22E+01 & 1.11E+01 & 1.30E+01 & 2.03E-01 & 1.35E+01 & 1.26E+01 \\ \cline{1-1}  & APSO & **4.44E-16** & **0.00E+00** & **4.44E-16** & **4.44E-16** & **4.44E-16** & **0.00E+00** & **4.44E-16** & **4.44E-16** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The experimental results of four representative benchmarking functions on dimensions of 500 and 800, respectively.