deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index aa86f39..08c5ae7 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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The Bat Algorithm works with the definition of ``temporary position", i.e., at each iteration we maintain two structures to store the current position of each bat: its usual position $\textbf{x}$ and the temporary position $\tilde{\textbf{x}}$, which is used to check whether the new generated solution is better than the previous one.  After computing the frequency and velocity using Equations~\ref{e.frequency_ba} and~\ref{e.velocity_ba}, we can start working with the movement of each agent, as follows:  \begin{equation}  \label{e.position_tmp_bat}  \tilde{\textbf{x}}^{t+1}=\textbf{x}^t_i+\textbf{v}^{t+1}_i,  \end{equation}  %\begin{equation}  %\end{equation}