Algorithm 2 Pseudo-code of a BVNS

Require:s (Initial Solution), $k_{max}$ (number of neighborhood structures), $Stop\_Condition$. 1:while$Stop\_Condition$ is not met do 2:   $k\leftarrow 1$; 3:   repeat 4:     $s^{\prime }\leftarrow$Shake($s,k$); 5:     $s^{″}\leftarrow$Local_Search($s^{\prime }$); 6:     $s,k\leftarrow$Neighborhood_Change(s, $s^{″}$, k); 7:   until $k=k_{max}$ 8:end while 9:returns;