Algorithm 1. Particle Swarm Initialization.

1.  Define particle swarm $\mathrm{X}=\left\{X_1,\cdots ,X_i,\hspace{0.17em}\cdots ,\hspace{0.17em}{X}_I\right\}$, in which $X_i\cdot p={\left(x_i^1,\cdots ,x_i^n,\cdots ,x_i^N\right)}^T$, $X_i.v={\left(v_i^1,\cdots v_i^n,\cdots ,v_i^N\right)}^T$ and $X_i.d={\left(d_i^1,d_i^2,\cdots d_i^N\right)}^T$, respectively.

2.  Construct $N$ spatial neighborhoods, each denoted as $N_{r1\times r1}\left(P_n\right)$, $n\in \left[1,\hspace{0.17em}N\right]$. 3.  Set the range of equidistant values of particle position points as $\left[d_1,d_2\right]$. 4.  for each $X_i\in X$ do 5.   Randomly sample a point $P_n^s$ in each $N_{r1\times r1}\left(P_n\right)$, and all sampled points form a point set $P^s=\left\{P_1^s,\hspace{0.17em}\cdots ,P_n^s,\hspace{0.17em}\cdots ,P_N^s\right\}$. 6.   Randomly sample $N$ values in interval $\left[d_1,d_2\right]$ to form a equidistant set $D^S=\left\{d_1^s,\hspace{0.17em}\cdots ,d_n^s,\hspace{0.17em}\cdots ,d_N^s\right\}$. 7.   for each $n\in \left[1,N\right]$ do 8.    $x_i^n={\left(P_n^s\cdot x,\hspace{0.17em}\hspace{0.17em}{P}_n^s\cdot y\right)}^T$, $v_i^n={\left(0,0\right)}^T$ and $d_i^n=d_n^s$. 9.   end for 10. end for