Algorithm 4 MC-CLFV Algorithm

Check out all flexible vertices $V{F}_1^{s_i},V{F}_2^{s_i}, \mathrm{\dots },V{F}_{n1}^{s_i}$ and all fixed vertices $V{D}_1^{s_i},\mathrm{\dots }V{D}_{n2}^{s_i}$ in $s_i,i=1, \mathrm{\dots }, k$ , sorted them counter-clockwise

Setting base search radius, $r_0$, and its decrease rate in every iteration,${\mathsf{\sigma }}^1$= 0.96

Calculate the value of the evaluation function, $F^0$ ;Calculate initial the standard deviation ${\Gamma }_0$

While${\Gamma }_0>\tau$ ($\tau$ is maximum acceptable standard deviation)

$r=r_0 \times {\mathsf{\sigma }}^1$

For i = 1:length(VF)

$\mathsf{\theta }$ = 2π× rand()

x($V{F}_i^{s_i}$) = x($V{F}_i^{s_i}$) + $r$ × rand() × cos $\mathsf{\theta }$;

y($V{F}_i^{s_i}$) =y($V{F}_i^{s_i}$) + $r$ × rand() × sin $\mathsf{\theta }$;

end

VD and renewed $VF$, constitute a new shape of sector.

If concave shape checking or minimum distance checking is not true

Continue;

end

G = g($VF,VD$,B,L)

Calculate F = F($G$,$f$)

$\Delta \mathrm{F}$ = $F^0-F_{opt}$

$\Gamma =\sqrt{\frac{1}{k}{\displaystyle {\displaystyle \sum }_{j=1}^k}{\left(F_j-\overline{F}\right)}^2}$

If $\Delta \mathrm{F}\le 0$ and $\Gamma \le {\Gamma }_0$ and ${\beta }_1$ × mean($F_j,j=1\dots k)\le$. min($F_j,j=1\dots k$. ) and max($F_j,j=$. $1\dots k$) $\le$ ${\beta }_2$ × $w{l}_{max}$

$F_{opt}$ = $F^0$

${\Gamma }_0= \Gamma$

$G_{opt}$ = G

end

end