A study of NK landscapes' basins and local optima networks

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces [5]. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are ‘small-worlds’. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network. Categories and Subject Descriptors I.2.8 [Artificial Intelligence]: Problem Solving, Control Methods, and Search—Heuristic methods; G.2.2 [Discrete Mathematics]: Graph Theory—...

• Type: Conference
• Year: 2008
• Where: GECCO
• Authors: Gabriela Ochoa, Marco Tomassini, Sébastien Vérel, Christian Darabos
• Keywords: GECCO 2008, Inherent Network, Local Maxima, Nk Landscapes, Optimization