graphs – Maximal independent set, with non-additive weights

Consider the following variant of the problem of finding the maximal weighted independent set in a vertex-weighted graph $G=G(V,E)$. Weights $w_v$ for $vin V$ need not be positive reals; say they lie in $mathbb{R}_{ge0}^n$. Say we are given a function $f:mathbb{R}_{ge0}^nlongrightarrowmathbb{R}$ (assume it’s efficiently computable, for instance, $f(x_1,dots,x_n)=x_1cdots x_n$). For an independent set $Ssubset V$, call $f(S)=fleft(sumlimits_{sin S}w_sright)$. We seek $max f(S)$ or $mathrm{argmax}f(S)$ (both taken over independent sets $S$). If $n=1$ and $f$ is the identity, then obviously if also $w_vequiv1$ then this is exactly the maximal independent set problem, and removing that last condition, this generalizes to the maximal weighted independent set problem (which I think also has been studied?). What I’m curious about is: is there anything known about more-efficient-than-brute-force methods for solving any other special cases? Another special case of particular interest is $f(x_1,dots,x_n)=begin{cases}x_1+cdots+x_n & forall i:x_ineq0\0&exists i:x_i=0,end{cases}$ and more generally any special case that returns 0 iff some component is 0. Thanks in advance.