SetA*: an efficient BDD-based heuristic search algorithm

In this paper we combine the goal directed search of A* with the ability of BDDs to traverse an exponential number of states in polynomial time. We introduce a new algorithm, SetA*, that generalizes A* to expand sets of states in each iteration. SetA* has substantial advantages over BDDA*, the only previous BDD-based A* implementation we are aware of. Our experimental evaluation proves SetA* to be a powerful search paradigm. For some of the studied problems it outperforms BDDA*, A*, and BDD-based breadth-first search by several orders of magnitude. We believe exploring sets of states to be essential when the heuristic function is weak. For problems with strong heuristics, SetA* efficiently specializes to single-state search and consequently challenges single-state heuristic search in general.

[1]  David L. Dill,et al.  Validation with guided search of the state space , 1998, Proceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175).

[2]  Richard Fikes,et al.  STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving , 1971, IJCAI.

[3]  Frank Reffel,et al.  OBDDs in Heuristic Search , 1998, KI.

[4]  Blai Bonet,et al.  The AIPS-98 Planning Competition , 2000, AI Mag..

[5]  Fausto Giunchiglia,et al.  Planning via Model Checking: A Decision Procedure for AR , 1997, ECP.

[6]  Blai Bonet,et al.  Planning as Heuristic Search: New Results , 1999, ECP.

[7]  Kavita Ravi,et al.  Symbolic guided search for CTL model checking , 2000, Proceedings 37th Design Automation Conference.

[8]  Kenneth L. McMillan,et al.  Symbolic model checking , 1992 .

[9]  Stephan Merz,et al.  Model Checking , 2000 .

[10]  Jesfis Peral,et al.  Heuristics -- intelligent search strategies for computer problem solving , 1984 .

[11]  E BryantRandal.  Graph-Based Algorithms for Boolean Function Manipulation , 1986 .

[12]  Jörg Hoffmann,et al.  Local Search Topology in Planning Benchmarks: An Empirical Analysis , 2001, IJCAI.

[13]  Malte Helmert,et al.  MIPS: The Model-Checking Integrated Planning System , 2001, AI Mag..

[14]  Manuela M. Veloso,et al.  OBDD-based Universal Planning for Synchronized Agents in Non-Deterministic Domains , 2000, J. Artif. Intell. Res..

[15]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[16]  Fahiem Bacchus,et al.  AIPS 2000 Planning Competition: The Fifth International Conference on Artificial Intelligence Planning and Scheduling Systems , 2001 .