# Revised Gravitational Search Algorithms Based on Evolutionary-Fuzzy Systems
## 2 The Gravitational Search Algorithm
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\mathbf{F_{8}}\) & \(\mathbf{F_{9}}\) & \(\mathbf{F_{10}}\) & \(\mathbf{F_{11}}\) & \(\mathbf{F_{12}}\) & \(\mathbf{F_{13}}\) \\ \hline FGSA-GA & \(2.63\times 10^{3}\) & \(1.56\times 10^{1}\) & \(8.44\times 10^{-15}\) & \(1.70\times 10^{-9}\) & \(2.04\times 10^{-21}\) & \(1.47\times 10^{-2}\) \\  & \(4.45\times 10^{2}\) & \(3.52\times 10^{0}\) & \(1.21\times 10^{-15}\) & \(4.48\times 10^{-10}\) & \(4.15\times 10^{-22}\) & \(2.90\times 10^{-3}\) \\  & \(2.49\times 10^{3}\) & \(1.59\times 10^{1}\) & \(7.99\times 10^{-15}\) & \(3.53\times 10^{-8}\) & \(6.73\times 10^{-21}\) & \(3.39\times 10^{-2}\) \\ \hline FGSA-PSO & \(2.79\times 10^{3}\) & \(1.82\times 10^{1}\) & \(6.44\times 10^{-11}\) & \(1.50\times 10^{1}\) & \(1.07\times 10^{-2}\) & \(1.80\times 10^{1}\) \\  & \(5.15\times 10^{2}\) & \(4.62\times 10^{0}\) & \(2.78\times 10^{-11}\) & \(3.94\times 10^{0}\) & \(3.26\times 10^{-3}\) & \(1.03\times 10^{1}\) \\  & \(2.63\times 10^{3}\) & \(1.89\times 10^{1}\) & \(7.38\times 10^{-11}\) & \(1.36\times 10^{1}\) & \(9.66\times 10^{-3}\) & \(1.71\times 10^{1}\) \\ \hline FGSA-DE & \(2.65\times 10^{3}\) & \(1.55\times 10^{1}\) & \(7.99\times 10^{-15}\) & \(6.18\times 10^{-2}\) & \(2.68\times 10^{-1}\) & \(2.23\times 10^{-2}\) \\  & \(3.57\times 10^{2}\) & \(4.30\times 10^{0}\) & \(1.30\times 10^{-15}\) & \(6.37\times 10^{-2}\) & \(3.69\times 10^{-1}\) & \(3.21\times 10^{-3}\) \\  & \(2.66\times 10^{3}\) & \(1.49\times 10^{1}\) & \(7.99\times 10^{-15}\) & \(5.37\times 10^{-2}\) & \(1.13\times 10^{-1}\) & \(1.38\times 10^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Comparisons between FGSA-GA, FGSA-PSO and FGSA-DE over 16 runs for multimodal functions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{3}}\) & \(\mathbf{F_{4}}\) & \(\mathbf{F_{5}}\) & \(\mathbf{F_{6}}\) & \(\mathbf{F_{7}}\) \\ \hline FGSA-GA & \(1.73\times 10^{-26}\) & \(2.01\times 10^{-12}\) & \(3.22\times 10^{-4}\) & \(8.29\times 10^{-11}\) & \(2.10\times 10^{1}\) & \(2.50\times 10^{-11}\) & \(2.15\times 10^{-2}\) \\  & \(3.31\times 10^{-27}\) & \(6.75\times 10^{-13}\) & \(2.99\times 10^{-5}\) & \(2.77\times 10^{-12}\) & \(3.55\times 10^{-1}\) & \(4.47\times 10^{-12}\) & \(1.40\times 10^{-3}\) \\  & \(1.66\times 10^{-26}\) & \(2.08\times 10^{-12}\) & \(1.90\times 10^{-4}\) & \(1.29\times 10^{-10}\) & \(2.12\times 10^{1}\) & \(2.78\times 10^{-11}\) & \(1.84\times 10^{-2}\) \\ \hline FGSA-PSO & \(8.91\times 10^{-25}\) & \(7.26\times 10^{-7}\) & \(5.77\times 10^{2}\) & \(2.26\times 10^{0}\) & \(5.07\times 10^{1}\) & \(8.36\times 10^{-11}\) & \(3.38\times 10^{-2}\) \\  & \(3.27\times 10^{-26}\) & \(2.19\times 10^{-7}\) & \(1.44\times 10^{2}\) & \(1.49\times 10^{0}\) & \(5.01\times 10^{0}\) & \(1.45\times 10^{-12}\) & \(1.54\times 10^{-2}\) \\  & \(8.28\times 10^{-25}\) & \(7.29\times 10^{-7}\) & \(5.37\times 10^{2}\) & \(2.16\times 10^{0}\) & \(2.76\times 10^{1}\) & \(7.56\times 10^{-11}\) & \(3.18\times 10^{-2}\) \\ \hline FGSA-DE & \(2.58\times 10^{-35}\) & \(5.17\times 10^{-17}\) & \(2.58\times 10^{-4}\) & \(3.11\times 10^{-11}\) & \(2.12\times 10^{1}\) & \(8.36\times 10^{-11}\) & \(2.41\times 10^{-2}\) \\  & \(2.23\times 10^{-35}\) & \(1.28\times 10^{-18}\) & \(2.48\times 10^{-4}\) & \(5.78\times 10^{-12}\) & \(1.75\times 10^{-1}\) & \(4.21\times 10^{-12}\) & \(8.14\times 10^{-3}\) \\  & \(2.00\times 10^{-35}\) &

## 5 Conclusions

The challenge of improving the performances of the search algorithms is an open problem. However, there is no specific algorithm to achieve the best solution of the optimization problems. GSA is a recent search method to find the global optimum. Many researches proposed revised versions of GSA to reduce the time for finding the global optimum. Following this, intelligent techniques have been applied to increase the search performances of GSA. In this paper, some revised FGSA based on the optimization through GA, PSO and DE are proposed.