Efficient algorithm for this combinatorial problem [closed]


$ \newcommand{\argmin}{\mathop{\mathrm{argmin}}\limits}$

I am working on a combinatorial optimization problem and I need to figure out a way to solve the following equation. It naturally popped up in a method I chose to use in my assignment I was working on.

Given a fixed set $ \Theta$ with each element $ \in (0,1)$ and total $ N$ elements ($ N$ is about 25), I need to find a permutation of elements in $ \Theta$ such that $ $ \vec K = \argmin_{\vec k = Permutation(\Theta)} \sum_{i=1}^N t_i D(\mu_i||k_i) $ $ where $ \vec t, \vec \mu$ are given vectors of length $ N$ and $ D(p||q)$ is the KL Divergence of the bernoulli distributions with parameters $ p$ and $ q$ respectively. Further, all the $ N$ elements of $ \vec t$ sum to 1 and $ \vec \mu$ has all elements in $ [0,1]$ .

It is just impossible to go through all $ N!$ permutations. A greedy type of algorithm which does not give exact $ \vec K$ would also be acceptable to me if there is no other apparent method. Please let me know how to proceed!