Complex-network analysis of combinatorial spaces: The NK landscape case
This work provides a method for analyzing combinatorial optimization problems, but it is incremental as it applies existing network concepts to a well-known model.
The authors tackled the problem of characterizing combinatorial fitness landscapes by proposing a network-based approach, adapting inherent networks from energy surfaces to NK landscapes, and found that most network properties correlate with search difficulty across varying K values.
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K.