The Metric-FF Planning System: Translating "Ignoring Delete Lists" to
  Numeric State Variables
  Planning with numeric state variables has been a challenge for many years,
and was a part of the 3rd International Planning Competition (IPC-3). Currently
one of the most popular and successful algorithmic techniques in STRIPS
planning is to guide search by a heuristic function, where the heuristic is
based on relaxing the planning task by ignoring the delete lists of the
available actions. We present a natural extension of ``ignoring delete lists''
to numeric state variables, preserving the relevant theoretical properties of
the STRIPS relaxation under the condition that the numeric task at hand is
``monotonic''. We then identify a subset of the numeric IPC-3 competition
language, ``linear tasks'', where monotonicity can be achieved by
pre-processing. Based on that, we extend the algorithms used in the heuristic
planning system FF to linear tasks. The resulting system Metric-FF is,
according to the IPC-3 results which we discuss, one of the two currently most
efficient numeric planners.
