PARIS: A Polynomial-Time, Risk-Sensitive Scheduling Algorithm for Probabilistic Simple Temporal Networks with Uncertainty

Inspired by risk-sensitive, robust scheduling for planetary rovers under temporal uncertainty, this work introduces the Probabilistic Simple Temporal Network with Uncertainty (PSTNU), a temporal planning formalism that unifies the set-bounded and probabilistic temporal uncertainty models from the STNU and PSTN literature. By allowing any combination of these two types of uncertainty models, PSTNU's can more appropriately reflect the varying levels of knowledge that a mission operator might have regarding the stochastic duration models of different activities. We also introduce PARIS, a novel sound and provably polynomial-time algorithm for risk-sensitive strong scheduling of PSTNU's. Due to its fully linear problem encoding for typical temporal uncertainty models, PARIS is shown to outperform the current fastest algorithm for risk-sensitive strong PSTN scheduling by nearly four orders of magnitude in some instances of a popular probabilistic scheduling dataset, while results on a new PSTNU scheduling dataset indicate that PARIS is, indeed, amenable for deployment on resource-constrained hardware.

[1]  John M. Wilson,et al.  Introduction to Stochastic Programming , 1998, J. Oper. Res. Soc..

[2]  Brian C. Williams,et al.  Chance-Constrained Scheduling via Conflict-Directed Risk Allocation , 2015, AAAI.

[3]  Marco Roveri,et al.  Strong Temporal Planning with Uncontrollable Durations: A State-Space Approach , 2015, AAAI.

[4]  Pascal Van Hentenryck,et al.  A Linear-Programming Approximation of AC Power Flows , 2012, INFORMS J. Comput..

[5]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[6]  Ioannis Tsamardinos,et al.  A Probabilistic Approach to Robust Execution of Temporal Plans with Uncertainty , 2002, SETN.

[7]  Cheng Fang,et al.  Chance-Constrained Probabilistic Simple Temporal Problems , 2014, AAAI.

[8]  Anthony V. Fiacco,et al.  The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method , 1964 .

[9]  Thierry Vidal,et al.  Handling contingency in temporal constraint networks: from consistency to controllabilities , 1999, J. Exp. Theor. Artif. Intell..

[10]  Rina Dechter,et al.  Temporal Constraint Networks , 1989, Artif. Intell..

[11]  François Michaud,et al.  Planning for Concurrent Action Executions Under Action Duration Uncertainty Using Dynamically Generated Bayesian Networks , 2010, ICAPS.

[12]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[13]  Andrew Coles,et al.  COLIN: Planning with Continuous Linear Numeric Change , 2012, J. Artif. Intell. Res..

[14]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[15]  David E. Smith,et al.  Compiling Away Uncertainty in Strong Temporal Planning with Uncontrollable Durations , 2015, IJCAI.