Where 'Ignoring Delete Lists' Works: Local Search Topology in Planning
  Benchmarks
  Between 1998 and 2004, the planning community has seen vast progress in terms
of the sizes of benchmark examples that domain-independent planners can tackle
successfully. The key technique behind this progress is the use of heuristic
functions based on relaxing the planning task at hand, where the relaxation is
to assume that all delete lists are empty. The unprecedented success of such
methods, in many commonly used benchmark examples, calls for an understanding
of what classes of domains these methods are well suited for. In the
investigation at hand, we derive a formal background to such an understanding.
We perform a case study covering a range of 30 commonly used STRIPS and ADL
benchmark domains, including all examples used in the first four international
planning competitions. We *prove* connections between domain structure and
local search topology -- heuristic cost surface properties -- under an
idealized version of the heuristic functions used in modern planners. The
idealized heuristic function is called h^+, and differs from the practically
used functions in that it returns the length of an *optimal* relaxed plan,
which is NP-hard to compute. We identify several key characteristics of the
topology under h^+, concerning the existence/non-existence of unrecognized dead
ends, as well as the existence/non-existence of constant upper bounds on the
difficulty of escaping local minima and benches. These distinctions divide the
(set of all) planning domains into a taxonomy of classes of varying h^+
topology. As it turns out, many of the 30 investigated domains lie in classes
with a relatively easy topology. Most particularly, 12 of the domains lie in
classes where FFs search algorithm, provided with h^+, is a polynomial solving
mechanism. We also present results relating h^+ to its approximation as
implemented in FF. The behavior regarding dead ends is provably the same. We
summarize the results of an empirical investigation showing that, in many
domains, the topological qualities of h^+ are largely inherited by the
approximation. The overall investigation gives a rare example of a successful
analysis of the connections between typical-case problem structure, and search
performance. The theoretical investigation also gives hints on how the
topological phenomena might be automatically recognizable by domain analysis
techniques. We outline some preliminary steps we made into that direction.
