SDA Pseudocode

Step 0: Preparation

Select the number of search points $m\ge 2$ , parameters $0\le \theta <2\pi ,0<r<1$ of $S_n\left(r,\theta \right)$ , and maximum number of iterations $k_{max}$

Set $k=0$ .

Step 1: Initialization

Set initial points $x_i\left(0\right)\in R^n,i=1,2,\cdots m$ in the feasible region at random and centre $x^{\ast }$ as $x^{\ast }=x_{i_g}\left(0\right)$ , $i_g=\arg {\min }_{i}f\left(x_i\left(0\right)\right),i=1,2,\cdots ,m$ .

Step 2: Updating x_i

$x_i\left(k+1\right)=S_n\left(r,\theta \right)x_i\left(k\right)-\left(S_n\left(r,\theta \right)-I_n\right)x^{\ast }$

$i=1,2,\cdots m$ .

Step 3: Updating $x^{\ast }$

$x^{\ast }=x_{i_g}\left(k+1\right)$ ,

$i_g=\arg {\min }_{i}f\left(x_i\left(k+1\right)\right),i=1,2,\cdots ,m$ .

Step 4: Checking termination criterion

If $k=k_{\max }$ then terminate. Otherwise set $k=k+1$ , and return to step 2