Second order partial derivatives for NK-landscapes

Local search methods based on explicit neighborhood enumeration require at least $O(n)$ time to identify all possible improving moves. For k-bounded pseudo-Boolean optimization problems, recent approaches have achieved $O(k^2*2^{k})$ runtime cost per move, where $n$ is the number of variables and $k$ is the number of variables per subfunction. Even though the bound is independent of $n$, the complexity per move is still exponential in $k$. In this paper, we propose a second order partial derivatives-based approach that executes first-improvement local search where the runtime cost per move is time polynomial in $k$ and independent of $n$. This method is applied to NK-landscapes, where larger values of $k$ may be of particular interest.