When Gravity Fails: Local Search Topology
  Local search algorithms for combinatorial search problems frequently
encounter a sequence of states in which it is impossible to improve the value
of the objective function; moves through these regions, called plateau moves,
dominate the time spent in local search. We analyze and characterize plateaus
for three different classes of randomly generated Boolean Satisfiability
problems. We identify several interesting features of plateaus that impact the
performance of local search algorithms. We show that local minima tend to be
small but occasionally may be very large. We also show that local minima can be
escaped without unsatisfying a large number of clauses, but that systematically
searching for an escape route may be computationally expensive if the local
minimum is large. We show that plateaus with exits, called benches, tend to be
much larger than minima, and that some benches have very few exit states which
local search can use to escape. We show that the solutions (i.e., global
minima) of randomly generated problem instances form clusters, which behave
similarly to local minima. We revisit several enhancements of local search
algorithms and explain their performance in light of our results. Finally we
discuss strategies for creating the next generation of local search algorithms.
