Algorithm 3 Simplex method

Input: The highest-quality vertice $X_g$, intermediate-quality vertice $X_b$, lowest-quality vertice $X_s$

Output: new candidate solution $X_{new}$

$X_c={\displaystyle \frac{X_g+X_b}{2}}$   (Centroid calculation)

$X_r=X_c+\alpha \times (X_c-X_s)$   (Reflection operation)

if $f(X_r)<f(X_g)$ then   (Expansion operation)

$X_e=X_c+\gamma (X_r-X_c)$

If $f(X_e)<f(X_g)$ then

$X_s=X_e$

else

$X_s=X_r$

end if

end if

if $f(X_s)<f(X_r)$ then   (Compression operation)

$X_t=X_c+\beta (X_s-X_c)$

if $f(X_t)<f(X_s)$ then

$X_s=X_t$

end if

end if

if $f(X_g)\le f(X_r)\le f(X_s)$ then   (Contraction operation)

$X_w=X_c-\delta (X_s-X_c)$

if $f(X_w)<f(X_s)$ then

$X_s=X_w$

else

$X_s=X_r$

end if

end if

$X_{new}=X_s$