# 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!