We meet with an integer optimization defined as follows:

$\displaystyle v^{*} = argmax \quad
\frac{v^{T}X^{T}\left(\sum_{j=1}^{m}{b_iw_i^{T}}\r ight)Xv}{\sqrt{v^{T}X^{T}Xv}}

Where v denotes $\displaystyle n$ dimensional column parameter vector,
the domain of which is all permutations of $\displaystyle \left\{{1-n,2-n,
\ldots,2i-n-1,\ldots,n-1}\right\}$. The entries matrix $\displaystyle X
\in \mathcal{R}^{n \times s}$ are known. $\displaystyle b_i,w_i$
are $\displaystyle n$ dimensional column vector.

Our Goal

Design a polynomial order algorithm to solve this problem.

Appreciate you very much for your suggestion and advice.