Dynamic Defense against Stealth Malware Propagation in Cyber-Physical Systems: A Game-Theoretical Framework

. 2020 Aug 15;22(8):894. doi: 10.3390/e22080894

Algorithm 1 S-BD: Benders Decompostion for SSPTI

1:
Initialize $\hat{Y} \leftarrow \emptyset$ , $\underline{z} \leftarrow - \infty$ , $\bar{z} \leftarrow + \infty$ , $\hat{x} \leftarrow 0$ , $ϵ$
2:
while $\bar{z} - \underline{z} \leq ϵ$ do
3:
Solve [Sub( $\hat{x}$ )] for $\hat{y}$ and objective value $z_{\hat{x}}$
4:
$\hat{Y} \leftarrow \hat{Y} \cup \hat{y}$
5:
if $\underline{z} < z_{\hat{x}}$ then $\underline{z} \leftarrow z_{\hat{x}}$
6:
Solve [Master( $\hat{Y}$ )] for $\hat{x}$ and objective value $z_{\hat{Y}}$
7:
$\bar{z} \leftarrow z_{\hat{Y}}$
8:
Return $x^{ϵ} \leftarrow \hat{x}$