Over-Subscription in Planning: a Partial Satisfaction Problem

In many real world planning scenarios, agents often do not have enough resources to achieve all of their goals. Hence, this requires finding plans that satisfy only a subset of the them. Solving such partial satisfaction planning (PSP) problems poses several challenges, including an increased emphasis on modelling and handling plan quality (in terms of action costs and goal utilities). Despite the ubiquity of such PSP problems, very little attention has been paid to them in the planning community. In this paper, we start by describing a spectrum of PSP problems and focus on one of the more general PSP problems, termed PSP NET BENEFIT. We develop two techniques, one based on integer programming, called OptiPlan, and the other based on regression planning with reachability heuristics, called AltAlt . Our empirical studies with these two planners show that the heuristic planner AltAlt generates plans that are quite close to the quality of plans generated by OptiPlan, while incurring only a small fraction of the cost. Finally, we also present interesting connections among our work and over-subscription scheduling.

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

[2]  Henry Kautz,et al.  Blackbox: Unifying sat-based and graph-based planning , 1999, International Joint Conference on Artificial Intelligence.

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

[4]  Subbarao Kambhampati,et al.  Extracting Effective and Admissible State Space Heuristics from the Planning Graph , 2000, AAAI/IAAI.

[5]  Tom Bylander,et al.  The Computational Complexity of Propositional STRIPS Planning , 1994, Artif. Intell..

[6]  David E. Smith.  Choosing Objectives in OverSubscription Planning , 2004 .

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

[8]  M. Johnston,et al.  S PIKE : Intelligent Scheduling of Hubble Space Telescope Observations , 1994 .

[9]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[10]  Al Globus,et al.  Scheduling Earth Observing Satellites with Evolutionary Algorithms , 2003 .

[11]  John Gasch,et al.  A Photo Album of Earth Scheduling Landsat 7 Mission Daily Activities , 1998 .

[12]  Monte Zweben,et al.  Scheduling and rescheduling with iterative repair , 1993, IEEE Trans. Syst. Man Cybern..

[13]  Subbarao Kambhampati,et al.  AltAltp: Online Parallelization of Plans with Heuristic State Search , 2003, J. Artif. Intell. Res..

[14]  Steven Minton,et al.  Minimizing Conflicts: A Heuristic Repair Method for Constraint Satisfaction and Scheduling Problems , 1992, Artif. Intell..

[15]  Drew McDermott,et al.  Using Regression-Match Graphs to Control Search in Planning , 1999, Artif. Intell..

[16]  David E. Smith.  Choosing Objectives in Over-Subscription Planning , 2004, ICAPS.

[17]  Peter Norvig,et al.  Planning and Scheduling for Fleets of Earth Observing Satellites , 2001 .

[18]  Dana S. Nau,et al.  On the Use of Integer Programming Models in AI Planning , 1999, IJCAI.

[19]  Steve Hanks,et al.  Optimal Planning with a Goal-directed Utility Model , 1994, AIPS.

[20]  Subbarao Kambhampati,et al.  Planning Graph-based Heuristics for Cost-sensitive Temporal Planning , 2002, AIPS.

[21]  M. Fox,et al.  Efficient Implementation of the Plan Graph in STAN , 2011, J. Artif. Intell. Res..

[22]  Subbarao Kambhampati,et al.  Planning graph as the basis for deriving heuristics for plan synthesis by state space and CSP search , 2002, Artif. Intell..