Planning as satisfiability: Heuristics

Reduction to SAT is a very successful approach to solving hard combinatorial problems in Artificial Intelligence and computer science in general. Most commonly, problem instances reduced to SAT are solved with a general-purpose SAT solver. Although there is the obvious possibility of improving the SAT solving process with application-specific heuristics, this has rarely been done successfully. In this work we propose a planning-specific variable selection strategy for SAT solving. The strategy is based on generic principles about properties of plans, and its performance with standard planning benchmarks often substantially improves on generic variable selection heuristics, such as VSIDS, and often lifts it to the same level with other search methods such as explicit state-space search with heuristic search algorithms.

[1]  Adnan Darwiche,et al.  A Lightweight Component Caching Scheme for Satisfiability Solvers , 2007, SAT.

[2]  Daniel S. Weld Recent Advances in AI Planning , 1999, AI Mag..

[3]  Jussi Rintanen,et al.  Asymptotically Optimal Encodings of Conformant Planning in QBF , 2007, AAAI.

[4]  Tad Hogg,et al.  An Economics Approach to Hard Computational Problems , 1997, Science.

[5]  Jussi Rintanen,et al.  Constructing Conditional Plans by a Theorem-Prover , 1999, J. Artif. Intell. Res..

[6]  David G. Mitchell,et al.  A SAT Solver Primer , 2005, Bull. EATCS.

[7]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[8]  Tatsuhiro Tsuchiya,et al.  SAT-Based Verification of Safe Petri Nets , 2004, ATVA.

[9]  F. Post,et al.  An Economics Approach to Hard Computational Problems , 1997 .

[10]  José Júlio Alferes,et al.  Logics in Artificial Intelligence 9th European Conference, Jelia 2004, Lisbon, Portugal, September 27-30, 2004 : Proceedings , 2004 .

[11]  James M. Crawford,et al.  Experimental Results on the Crossover Point in Random 3-SAT , 1996, Artif. Intell..

[12]  Bart Selman,et al.  Pushing the Envelope: Planning, Propositional Logic and Stochastic Search , 1996, AAAI/IAAI, Vol. 2.

[13]  Jussi Rintanen,et al.  TR-CS-1203 Generation of Hard Solvable Planning Problems , 2012 .

[14]  Jussi Rintanen,et al.  Heuristics for Planning with SAT , 2010, CP.

[15]  Bart Selman,et al.  Planning as Satisfiability , 1992, ECAI.

[16]  Jussi Rintanen,et al.  Regression for Classical and Nondeterministic Planning , 2008, ECAI.

[17]  Theo Tryfonas,et al.  Frontiers in Artificial Intelligence and Applications , 2009 .

[18]  Bernhard Nebel,et al.  The FF Planning System: Fast Plan Generation Through Heuristic Search , 2011, J. Artif. Intell. Res..

[19]  Joao Marques-Silva,et al.  GRASP: A Search Algorithm for Propositional Satisfiability , 1999, IEEE Trans. Computers.

[20]  Armin Biere,et al.  Symbolic Model Checking without BDDs , 1999, TACAS.

[21]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[22]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[23]  Stephen F. Smith,et al.  Using Decision Procedures Efficiently for Optimization , 2007, ICAPS.

[24]  Bart Selman,et al.  Algorithm portfolios , 2001, Artif. Intell..

[25]  George J. Pappas,et al.  Bounded Model Checking of Hybrid Dynamical Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[26]  Alban Grastien,et al.  Diagnosis of Discrete Event Systems Using Satisfiability Algorithms: A Theoretical and Empirical Study , 2007, IEEE Transactions on Automatic Control.

[27]  Marco Bozzano,et al.  Verifying Industrial Hybrid Systems with MathSAT , 2005, BMC@CAV.

[28]  Matthew L. Ginsberg,et al.  The Complexity of Optimal Planning and a More Efficient Method for Finding Solutions , 2008, ICAPS.

[29]  Jussi Rintanen Heuristics for Planning with SAT and Expressive Action Definitions , 2011, ICAPS.

[30]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[31]  Hector Geffner,et al.  Branching and pruning: An optimal temporal POCL planner based on constraint programming , 2004, Artif. Intell..

[32]  Jussi Rintanen,et al.  A Planning Algorithm not based on Directional Search , 1998, KR.

[33]  Bart Selman,et al.  Boosting Combinatorial Search Through Randomization , 1998, AAAI/IAAI.

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

[35]  Bart Selman,et al.  Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems , 2000, Journal of Automated Reasoning.

[36]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[37]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[38]  Ivan Serina,et al.  Planning as Propositional CSP: From Walksat to Local Search Techniques for Action Graphs , 2003, Constraints.

[39]  Bart Selman,et al.  Algorithm Portfolio Design: Theory vs. Practice , 1997, UAI.

[40]  Lawrence Ryan Efficient algorithms for clause-learning SAT solvers , 2004 .

[41]  Michael L. Littman,et al.  Contingent planning under uncertainty via stochastic satisfiability , 1999, Artif. Intell..

[42]  Emmanuel Zarpas Simple Yet Efficient Improvements of SAT Based Bounded Model Checking , 2004, FMCAD.

[43]  Blai Bonet,et al.  Automatic Polytime Reductions of NP Problems into a Fragment of STRIPS , 2011, ICAPS.

[44]  Avrim Blum,et al.  Fast Planning Through Planning Graph Analysis , 1995, IJCAI.

[45]  Yannis Dimopoulos,et al.  Constraint Propagation in Propositional Planning , 2010, ICAPS.

[46]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[47]  Jussi Rintanen Engineering Efficient Planners with SAT , 2012, ECAI.

[48]  Lenhart K. Schubert,et al.  Inferring State Constraints for Domain-Independent Planning , 1998, AAAI/IAAI.

[49]  Vincent Vidal,et al.  A Lookahead Strategy for Heuristic Search Planning , 2004, ICAPS.

[50]  Blai Bonet,et al.  Planning as heuristic search , 2001, Artif. Intell..

[51]  Jussi Rintanen Phase Transitions in Classical Planning: An Experimental Study , 2004, ICAPS.

[52]  Silvia Richter,et al.  The LAMA Planner: Guiding Cost-Based Anytime Planning with Landmarks , 2010, J. Artif. Intell. Res..

[53]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[54]  Abdul Sattar,et al.  SAT-Based Parallel Planning Using a Split Representation of Actions , 2009, ICAPS.

[55]  Matti Järvisalo,et al.  Limitations of restricted branching in clause learning , 2008, Constraints.

[56]  Bart Selman,et al.  Unifying SAT-based and Graph-based Planning , 1999, IJCAI.

[57]  Jussi Rintanen,et al.  Planning as Satisfiability with Relaxed $-Step Plans , 2007, Australian Conference on Artificial Intelligence.

[58]  Blai Bonet,et al.  A Robust and Fast Action Selection Mechanism for Planning , 1997, AAAI/IAAI.

[59]  Marco Bozzano,et al.  The MathSAT 3 System , 2005, CADE.

[60]  Yixin Chen,et al.  A Novel Transition Based Encoding Scheme for Planning as Satisfiability , 2010, AAAI.

[61]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[62]  Henry A. Kautz,et al.  Towards Understanding and Harnessing the Potential of Clause Learning , 2004, J. Artif. Intell. Res..

[63]  Bart Selman,et al.  Noise Strategies for Improving Local Search , 1994, AAAI.

[64]  Ilkka Niemelä,et al.  Parallel Encodings of Classical Planning as Satisfiability , 2004, JELIA.

[65]  Jussi Rintanen Planning and SAT , 2009, Handbook of Satisfiability.

[66]  Jussi Rintanen Evaluation Strategies for Planning as Satisfiability , 2004, ECAI.

[67]  Hector Geffner,et al.  Inference and Decomposition in Planning Using Causal Consistent Chains , 2009, ICAPS.

[68]  David A. McAllester,et al.  Systematic Nonlinear Planning , 1991, AAAI.

[69]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

[70]  Ilkka Niemelä,et al.  Planning as satisfiability: parallel plans and algorithms for plan search , 2006, Artif. Intell..

[71]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.

[72]  Tom Bylander,et al.  A Probabilistic Analysis of Propositional STRIPS Planning , 1996, Artif. Intell..

[73]  Gilles Audemard,et al.  Bounded Model Checking for Timed Systems , 2002, FORTE.

[74]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).