# Cost-Partitioned Merge-and-Shrink Heuristics for Optimal Classical Planning

IJCAI, pp. 4152-4160, 2020.

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Keywords:

factored transition systemlinear programpartial state sclassical planningcartesian abstractionMore(11+)

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Abstract:

Cost partitioning is a method for admissibly combining admissible heuristics.
In this work, we extend this concept to merge-and-shrink (M&S) abstractions
that may use labels that do not directly correspond to operators. We
investigate how optimal and saturated cost partitioning (SCP) interact with
M&S transformations and devel...More

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Introduction

- Classical planning [Ghallab et al, 2004] aims to find a sequence of actions that leads from an initial world situation to a specified goal.
- A possible solution to this problem is the combination of different abstractions admissibly with operator cost partitioning [Katz and Domshlak, 2010; Seipp et al, 2017a], which distributes the operator costs among the abstractions guaranteeing that the sum of their heuristic values is admissible
- It has successfully been used with Cartesian abstractions [Seipp and Helmert, 2018] and pattern databases [Edelkamp, 2001], but not yet with M&S.

Highlights

- Classical planning [Ghallab et al, 2004] aims to find a sequence of actions that leads from an initial world situation to a specified goal
- A possible solution to this problem is the combination of different abstractions admissibly with operator cost partitioning [Katz and Domshlak, 2010; Seipp et al, 2017a], which distributes the operator costs among the abstractions guaranteeing that the sum of their heuristic values is admissible
- 4.3 Merging The previous two sections showed transformations that can potentially decrease the value of hOCP. In contrast to these results, we show that the heuristic value of hOCP can only increase after merging
- Thereafter, we show that exact label reduction does not affect the value of hSCP
- We focus on saturated cost partitioning because computing Optimal cost partitioning over large abstractions is often infeasible in practice, but our approach can be used with Optimal cost partitioning in the same way
- Our theoretical analysis investigates the interaction of Optimal cost partitioning and saturated cost partitioning with M&S transformations, and our practical implementation significantly improves regular M&S heuristics

Methods

- The authors implemented the techniques on top of the M&S implementation of Fast Downward [Helmert, 2006], version 19.12.
- The authors use the tasks of all optimal tracks of all International Planning Competitions, a set consisting of 1827 tasks across 65 domains.
- Experiments were run on Intel Xeon Silver 4114 CPUs, using Downward Lab [Seipp et al, 2017b].
- Each planner run is limited to 1800s and 3.5 GiB.
- The code, benchmarks, and experimental data are published online [Sievers et al, 2020a]

Results

- The authors' theoretical analysis investigates the interaction of OCP and SCP with M&S transformations, and the practical implementation significantly improves regular M&S heuristics.

Conclusion

- The authors contribute the first combination of cost partitioning with M&S heuristics.
- The authors' theoretical analysis investigates the interaction of OCP and SCP with M&S transformations, and the practical implementation significantly improves regular M&S heuristics.
- The authors want to investigate better order strategies for SCPs in the context of M&S and to formalize cost partitioning as a transformation of the M&S framework

Summary

## Introduction:

Classical planning [Ghallab et al, 2004] aims to find a sequence of actions that leads from an initial world situation to a specified goal.- A possible solution to this problem is the combination of different abstractions admissibly with operator cost partitioning [Katz and Domshlak, 2010; Seipp et al, 2017a], which distributes the operator costs among the abstractions guaranteeing that the sum of their heuristic values is admissible
- It has successfully been used with Cartesian abstractions [Seipp and Helmert, 2018] and pattern databases [Edelkamp, 2001], but not yet with M&S.
## Methods:

The authors implemented the techniques on top of the M&S implementation of Fast Downward [Helmert, 2006], version 19.12.- The authors use the tasks of all optimal tracks of all International Planning Competitions, a set consisting of 1827 tasks across 65 domains.
- Experiments were run on Intel Xeon Silver 4114 CPUs, using Downward Lab [Seipp et al, 2017b].
- Each planner run is limited to 1800s and 3.5 GiB.
- The code, benchmarks, and experimental data are published online [Sievers et al, 2020a]
## Results:

The authors' theoretical analysis investigates the interaction of OCP and SCP with M&S transformations, and the practical implementation significantly improves regular M&S heuristics.## Conclusion:

The authors contribute the first combination of cost partitioning with M&S heuristics.- The authors' theoretical analysis investigates the interaction of OCP and SCP with M&S transformations, and the practical implementation significantly improves regular M&S heuristics.
- The authors want to investigate better order strategies for SCPs in the context of M&S and to formalize cost partitioning as a transformation of the M&S framework

- Table1: Table 1
- Table2: Coverage with interleaved or offline computation using different order strategies

Funding

- We have received funding for this work from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 817639)

Reference

- [Backstrom and Nebel, 1995] Christer Backstrom and Bernhard Nebel. Complexity results for SAS+ planning. Computational Intelligence, 11(4):625–655, 1995.
- [Drager et al., 2009] Klaus Drager, Bernd Finkbeiner, and Andreas Podelski. Directed model checking with distancepreserving abstractions. International Journal on Software Tools for Technology Transfer, 11(1):27–37, 2009.
- [Edelkamp, 2001] Stefan Edelkamp. Planning with pattern databases. In Amedeo Cesta and Daniel Borrajo, editors, Proceedings of the Sixth European Conference on Planning (ECP 2001), pages 84–90. AAAI Press, 2001.
- [Ghallab et al., 2004] Malik Ghallab, Dana Nau, and Paolo Traverso. Automated Planning: Theory and Practice. Morgan Kaufmann, 2004.
- [Hart et al., 1968] Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4(2):100–107, 1968.
- [Helmert et al., 2014] Malte Helmert, Patrik Haslum, Jorg Hoffmann, and Raz Nissim. Merge-and-shrink abstraction: A method for generating lower bounds in factored state spaces. Journal of the ACM, 61(3):16:1–63, 2014.
- [Helmert, 2006] Malte Helmert. The Fast Downward planning system. Journal of Artificial Intelligence Research, 26:191–246, 2006.
- [Katz and Domshlak, 2010] Michael Katz and Carmel Domshlak. Optimal admissible composition of abstraction heuristics. Artificial Intelligence, 174(12–13):767–798, 2010.
- [Nissim et al., 2011] Raz Nissim, Jorg Hoffmann, and Malte Helmert. Computing perfect heuristics in polynomial time: On bisimulation and merge-and-shrink abstraction in optimal planning. In Toby Walsh, editor, Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pages 1983–1990. AAAI Press, 2011.
- [Pearl, 1984] Judea Pearl. Heuristics: Intelligent Search Strategies for Computer Problem Solving. AddisonWesley, 1984.
- [Pommerening et al., 2015] Florian Pommerening, Malte Helmert, Gabriele Roger, and Jendrik Seipp. From non-negative to general operator cost partitioning. In Blai Bonet and Sven Koenig, editors, Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (AAAI 2015), pages 3335–3341. AAAI Press, 2015.
- [Seipp and Helmert, 2018] Jendrik Seipp and Malte Helmert. Counterexample-guided Cartesian abstraction refinement for classical planning. Journal of Artificial Intelligence Research, 62:535–577, 2018.

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