deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 2800839..4eeec6b 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
...
\end{eqnarray}  where $\xi\sim{\cal U}(0,1)$.  Finally, we can also update the loudness $A_i$  and pulse rate $r_i$  at each iteration as follows: \begin{equation}  \label{e.update_loudness} 
...
\begin{equation}  \label{e.pulse_rate}  r^{t+1}_i=\alpha r^0_i(1-\exp{-\gamma r^{t+1}_i=r^0_i(1-e^{-\gamma  t}), \end{equation}  where $\alpha\sim{\cal U)(0,1)$. U}(0,1)$.  \subsection{Firefly Algorithm}  \label{s.ffa}