Plan-refinement strategies and search-space size

Abstract

During the planning process, a planner may have many options for refinements to perform on the plan being developed. The planner's efficiency depends on how it chooses which refinement to do next. Recent studies have shown that several versions of the popular “least commitment” plan refinement strategy are often outperformed by a fewest alternatives first (FAF) strategy that chooses to refine the plan element that has the smallest number of alternative refinement options.

In this paper, we examine the FAF strategy in more detail, to try to gain a better understanding of how well it performs and why. We present the following results:

• • A refinement planner's search space is an AND/OR graph, and the planner “serializes” this graph by mapping it into an equivalent state-space graph. Different plan refinement strategies produce different serializations of the AND/OR graph.

• • The sizes of different serializations of the AND/OR graph can differ by an exponential amount. A planner whose refinement strategy produces a small serialization is likely to be more efficient than a planner whose refinement strategy produces a large serialization.

• • The FAF heuristic can be computed in constant time, and in our experimental studies it usually produced an optimal or near-optimal serialization. This suggests that using FAF (or some similar heuristic) is preferable to trying to guarantee an optimal serialization (which we conjecture is a computationally intractible problem).

This research was supported in part by grants from NSF (IRI-9306580 and EEC 94-02384), ONR (N00014-J-91-1451), AFOSR (F49620-93-1-0065), the ARPA/Rome Laboratory Planning Initiative (F30602-93-C-0039), the ARPA 13 Initiative (N00014-94-10907), the ARL (DAAH049610297), and ARPA contract DABT-95-00037. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the view of the funders.