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\end{eqnarray}  where $\bar{A}^t$ stands for the average of the loudness considering all agents at iteration $t$. Finally, the new position of each agent is then computed as follows:  \begin{eqnarray}  \label{e.position_bat}  \textbf{x}^{t+1} & = & \left\{ \begin{array}{ll} \tilde{\textbf{x}}^{t+1} & \mbox{{ with probability $p_r$}} \\  \tilde{\textbf{x}}^{t+1} & \mbox{{ with probability (1-$p_r$)},}  \end{array}\right.  \end{eqnarray}  \subsection{Firefly Algorithm}