Second order partial derivatives for NK-landscapes

Authors:
Wenxiang Chen;Darrell Whitley;Doug Hains;Adele Howe
Affiliations:
Colorado State University, Fort Collins, Colorado, USA;Colorado State University, Fort Collins, Colorado, USA;Colorado State University, Fort Collins, Colorado, USA;Colorado State University, Fort Collins, Colorado, USA
Venue:
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Year:
2013

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Abstract

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.