Determining Linearity of Optimal Plans by Operator Schema Analysis

Analysing the structures of solution plans generated by
AI Planning engines is helpful in improving the generative
planning process, as well as shedding light in
the study of its theoretical foundations.We investigate a
specific property of solution plans, that we called linearity,
which refers to a situation where each action
achieves an atom (or atoms) for a directly following action,
or achieves goal atom(s). Similarly, linearity can
be defined for parallel plans where each action in a
set of actions executed at some time step, achieves either
goal atom(s) or atom(s) for some action executed
in the directly following time step. In this paper, we
present a general and problem-independent theoretical
framework focusing on the analysis of planning operator
schema, namely relations of achiever, clobberer and
independence, in order to determine whether solvable
planning problems using a given operator schema have
as solutions optimal (parallel) plans which are linear.
The findings presented in this paper deepen current theoretical
knowledge, provide helpful information to engineers
of new planning domain models, and suggest
new ways of improving the performance of state-of-theart
(optimal) planning engines.