The question is how to design an effective algorithm to solve this problem:
$$ \underset{k_1,k_2,\cdots ,k_s}{\min}\lVert \sum_{i=1}^s{\mathbf{x}_{k_i}} \rVert _2, $$
where $l (l >> s)$ is the set size, $n$ is the vector size, $ k_i $s are different numbers in $\left\{ 1,2, \cdots, l \right\}$. The set $\left\{ \mathbf{x}_i \right\} _{i=1}^{l}$ is known.
This is an $n$-dimensional version of the (NP-complete) subset sum problem, so you are unlikely to find an efficient algorithm.