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Joao Paulo Papa edited Introduction.tex
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Particle Swarm Optimization (PSO) is an algorithm modeled on swarm intelligence dynamics that finds a solution in a search space based on social behavior~\cite{2001}. Each possible solution (agent) is modeled as a particle in the swarm that imitates its neighborhood based on the values of the fitness function found so far.
Each particle has a memory that stores its best solution, as well as the best solution of the entire swarm. Thus, taking this information into account, each particle has the ability to imitate others that obtain the best local and global maxima. This process simulates the social interaction between humans looking for the same objective, or bird flocks looking for food, for instance. This socio-cognitive mechanism can be summarized into three main principles: (i) evaluation, (ii) comparison, and (iii) imitation. Each particle can evaluate others in its neighborhood through some fitness function, can compare it with its own value and, finally, can decide whether it is a good choice to imitate them. PSO makes use of both velocity and position terms to perform optimization at time step $t$, as follows:
\begin{equation}
\label{e.velocity_pso)
\textbf{v}^{t+1}_i=w\textbf{v}^t_i+c_1r_1(\hat{\textbf{x}}_i-\textbf{x}_i)+c_2r_2(\hat{\textbf{g}}-\textbf{x}_i),
\end{equation}
\subsection{Bat Algorithm}
\label{s.ba}