  This chapter overviews a recently introduced network-based model of
combinatorial landscapes: Local Optima Networks (LON). The model compresses the
information given by the whole search space into a smaller mathematical object
that is a graph having as vertices the local optima and as edges the possible
weighted transitions between them. Two definitions of edges have been proposed:
basin-transition and escape-edges, which capture relevant topological features
of the underlying search spaces. This network model brings a new set of metrics
to characterize the structure of combinatorial landscapes, those associated
with the science of complex networks. These metrics are described, and results
are presented of local optima network extraction and analysis for two selected
combinatorial landscapes: NK landscapes and the quadratic assignment problem.
Network features are found to correlate with and even predict the performance
of heuristic search algorithms operating on these problems.
