Propositional Probabilistic Planning-as-Satisfiability using Stochastic Local Search

Recent times have seen the development of a number of planners that exploit advances in SAT(isfiability) solving technology to achieve good performance. In that spirit we develop the approximate contingent planner PSLSPLAN. Our approach is based on a stochastic local search procedure for solving stochastic SAT (SSAT) representations of probabilistic planning problems. PSLSPLAN first constructs an SSAT representation of the n-timestep probabilistic plangraph for the problem at hand. It then iteratively calls a stochastic local search procedure to find a linear plan (sequence of actions) which achieves the goal (i.e. satisfies the SSAT formula) with non-zero probability. Linear plans thus generated are merged to create a single contingent plan. Successive iterations progress from deciding the outcomes of stochastic actions in order to find a linear plan quickly, to sampling the outcomes of actions. Consequently, PSLSPLAN efficiently finds a linear plan which logically achieves the goal. Over time it refines its contingent plan for likely scenarios. We empirically evaluate PSLSPLAN on benchmarks from the probabilistic track of the 5th International Planning Competi-

[1]  John Langford,et al.  Probabilistic Planning in the Graphplan Framework , 1999, ECP.

[2]  Chu Min Li,et al.  Mv-Satz: A SAT solver for many-valued clausal forms , 2003 .

[3]  John Thornton,et al.  Additive versus Multiplicative Clause Weighting for SAT , 2004, AAAI.

[4]  Yixin Chen,et al.  Long-Distance Mutual Exclusion for Propositional Planning , 2007, IJCAI.

[5]  Stephen M. Majercik.  APPSSAT: Approximate Probabilistic Planning Using Stochastic Satisfiability , 2005, ECSQARU.

[6]  Bart Selman,et al.  Evidence for Invariants in Local Search , 1997, AAAI/IAAI.

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

[8]  Toniann Pitassi,et al.  Stochastic Boolean Satisfiability , 2001, Journal of Automated Reasoning.

[9]  Alan M. Frisch,et al.  Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings , 2001, Journal of Automated Reasoning.

[10]  Thomas Stützle,et al.  Stochastic Local Search: Foundations & Applications , 2004 .

[11]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[12]  Zhe Wu,et al.  An Efficient Global-Search Strategy in Discrete Lagrangian Methods for Solving Hard Satisfiability Problems , 2000, AAAI/IAAI.

[14]  Holger H. Hoos,et al.  Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT , 2002, CP.

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

[16]  Abdul Sattar,et al.  Efficiently Exploiting Dependencies in Local Search for SAT , 2008, AAAI.

[17]  Abdul Sattar,et al.  Building Structure into Local Search for SAT , 2007, IJCAI.

[18]  Byron Boots,et al.  DC-SSAT: A Divide-and-Conquer Approach to Solving Stochastic Satisfiability Problems Efficiently , 2005, AAAI.

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

[20]  Michael L. Littman,et al.  MAXPLAN: A New Approach to Probabilistic Planning , 1998, AIPS.

[21]  Abdul Sattar,et al.  SAT-Based versus CSP-Based Constraint Weighting for Satisfiability , 2005, AAAI.

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

[23]  Michael L. Littman,et al.  Using Caching to Solve Larger Probabilistic Planning Problems , 1998, AAAI/IAAI.

[24]  Michael L. Littman,et al.  The Computational Complexity of Probabilistic Planning , 1998, J. Artif. Intell. Res..