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\begin{eqnarray}  \label{e.random_walk_bat}  \tilde{\textbf{x}}^{t+1} & = & \left\{ \begin{array}{ll} \tilde{\textbf{x}}^{t+1}+\epsilon\bar{A} \tilde{\textbf{x}}^{t+1}+\epsilon\bar{A}^t  & \mbox{{ with probability $p_r$}} \\ \tilde{\textbf{x}}^{t+1} & \mbox{{ with probability (1-$p_r$)},}  \end{array}\right.  \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{equation} \begin{eqnarray}  \label{e.position_bat}  \textbf{x}^{t+1} & = & \left\{ \begin{array}{ll} f(\tilde{\textbf{x}}^{t+1}) < f(\textbf{x}^{t}) & \mbox{{ with probability $p_r$}} \\  \tilde{\textbf{x}}^{t+1} & \mbox{{ with probability (1-$p_r$)},}  \end{array}\right.  %\end{equation}  \subsection{Firefly Algorithm}  \label{s.ffa}