deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index c24de0b..aa86f39 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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Based on the behavior of bats, Yang e Gandomi~\cite{Yang_2012} proposed a new meta-heuristic optimization technique called Bat Algorithm (BA), which has been designed to behave as a band of bats tracking prey/foods using their capability of echolocation. BA works under certain assumptions: (i) all bats use echolocation to sense distance, and they also ``know"\ the difference between food/prey and background barriers; and (ii) a bat (agent) $i$ flies randomly with velocity $\textbf{v}_i$ at position $\textbf{x}_i$ and with a fixed frequency $q_i$.  Bat Algorithm  At each time step $t$, the frequency and velocity of each agent $i$ are computed using Equations~\ref{frequency_ba} and~\ref{velocity_ba}, respectively:  \begin{equation} 
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\end{equation}  where $\beta^t\sim{\cal U}(0,1)$, and $\textbf{g}$ stands for the best solution (bat) found so far (similar rationale is also employed by Equation~\ref{velocity_pso}).  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.  %\begin{equation}  %\end{equation}