Local Optima Networks of NK Landscapes with Neutrality
  In previous work we have introduced a network-based model that abstracts many
details of the underlying landscape and compresses the landscape information
into a weighted, oriented graph which we call the local optima network. The
vertices of this graph are the local optima of the given fitness landscape,
while the arcs are transition probabilities between local optima basins. Here
we extend this formalism to neutral fitness landscapes, which are common in
difficult combinatorial search spaces. By using two known neutral variants of
the NK family (i.e. NKp and NKq) in which the amount of neutrality can be tuned
by a parameter, we show that our new definitions of the optima networks and the
associated basins are consistent with the previous definitions for the
non-neutral case. Moreover, our empirical study and statistical analysis show
that the features of neutral landscapes interpolate smoothly between landscapes
with maximum neutrality and non-neutral ones. We found some unknown structural
differences between the two studied families of neutral landscapes. But
overall, the network features studied confirmed that neutrality, in landscapes
with percolating neutral networks, may enhance heuristic search. Our current
methodology requires the exhaustive enumeration of the underlying search space.
Therefore, sampling techniques should be developed before this analysis can
have practical implications. We argue, however, that the proposed model offers
a new perspective into the problem difficulty of combinatorial optimization
problems and may inspire the design of more effective search heuristics.
