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\begin{eqnarray}  \label{e.position_ffa}  \textbf{x}^{t+1}_i & = & \left\{ \begin{array}{ll} \textbf{x}^t_i+\psi e^{-\tau d_{i,j}^2}(\textbf{x}^t_j-\textbf{x}^t_i)+\eta^t\lambda d_{i,j}^2}(\textbf{x}^t_j-\textbf{x}^t_i)+\eta^t\textbf{\lambda}^t_i  & \mbox{{ if $f(\textbf{x}_i^})  \end{array}\right.  \end{eqnarray}  where $\lambda$ $\textbf{\lambda}_i$  is an array  usually sampled from a Gaussian distribution, $\eta^t$ stands for the step size, which can be linearly decreased, $d_{i,j}$ stands for the distance between fireflies $i$ and $j$, and $\psi$ is the so-called ``coefficient of attractiveness". Recall that FFA is reduced to a variant of PSO when $\tau=0$~\cite{Yang_2010}. Additionally, $\textbf{\lambda}$ can be extended to other distributions such as L\'evy flights~\cite{Yang_2010}.  \section{Optimizing $k$-means through Hyper-heuristics}  \label{s.proposed}