\usepackage{algorithmic}
\begin{algorithm}[htb]
\caption{SDE}
\label{alg2}
\begin{algorithmic}
\STATE Step 1. Compute the covariance matrix $C$ of the current population, then apply Eigen decomposition to $C$ as follows:
$$\label{eve} C=EDE^T$$
where $E$ is the eigenvector matrix of the population, $E^T$ is the corresponding transposed matrix. $D$ is a diagonal matrix composed of eigenvalues.

\STATE Step 2. Compute the the projection of the population with eigenvector matrix $E$.
$$\label{proj} P=X_G\cdot{E}$$

\STATE Step 3. Operate the mutation in Eigen coordinate sysytem.
$$\label{mut} P'=P_{r_1}+F\cdot(P_{r_2}-P_{r_3})$$
where $P_{r_1}$, $P_{r_2}$ and $P_{r_3}$ are sampled randomly from the projection $P$, $P'$ is the projection of mutation vector.

\STATE Step 4. Transform $P'$ to original coordinate system to obtain next generation of population $X_{G+1}$.
$$\label{org} X_{G+1}=P'\cdot{E^T}$$

\end{algorithmic}
\end{algorithm}


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