I need to solve a problem to find out the best permutation matrix $X \in \{0,1\}^{N \times N}$ which would maximize the number of elements in matrix $XAX$ which are above (component-wise) matrix $B$
i.e. \begin{align} &\max_X sum (XAX \geq_c B) \\ &X \in \{0,1\}^{N \times N}\hspace{0.1cm} \text{ is a permutation matrix} \\ &A \in R^{N \times N}\hspace{0.9cm} \text{ is a symmetric Z-matrix} \\ &B \in R^{N \times N}\hspace{0.9cm} \text{ is a symmetric matrix} \end{align}
Can anyone help me in this please?