Given an ordered set $X = (x_1, x_2, \dots, x_n), x_i \in \Bbb R^2$ and a permutation $P$ defined on $X$ and that shuffles the order of the elements in $X$,
$$P(X) := (p_1, p_2, \dots, p_n)$$
and we can get the prefix sum set $S$ of $P(X)$
$$S = \left( p_1, p_1+p_2, \dots, \sum_{i=1}^{n} p_i \right)$$
And we can get a convex hull of $CH(S)$, and I'm interested in maximizing the area of $CH(S)$.
Since given $X$, $\text{area}(CH(S)) = f(P)$ is a function of $P$. And there exists $n!$ different $P$, how can one find the optimal permutation as efficient as possible?