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Plotting: A Planning Problem with Complex Transitions

Authors Joan Espasa , Ian Miguel , Mateu Villaret

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Author Details

Joan Espasa
  • School of Computer Science, University of St Andrews, UK
Ian Miguel
  • School of Computer Science, University of St Andrews, UK
Mateu Villaret
  • Department of Computer Science, Applied Mathematics and Statistics, University of Girona, Spain

Funding

This work uses the Cirrus UK National Tier-2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1).
  • Miguel, Ian: funded by EP/V027182/1.
  • Villaret, Mateu: funded by grant RTI2018-095609-B-I00 (MCIU/AEI/FEDER, UE).

Cite As Get BibTex

Joan Espasa, Ian Miguel, and Mateu Villaret. Plotting: A Planning Problem with Complex Transitions. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CP.2022.22

Abstract

We focus on a planning problem based on Plotting, a tile-matching puzzle video game published by Taito. The objective of the game is to remove at least a certain number of coloured blocks from a grid by sequentially shooting blocks into the same grid. The interest and difficulty of Plotting is due to the complex transitions after every shot: various blocks are affected directly, while others can be indirectly affected by gravity. We highlight the difficulties and inefficiencies of modelling and solving Plotting using PDDL, the de-facto standard language for AI planners. We also provide two constraint models that are able to capture the inherent complexities of the problem. In addition, we provide a set of benchmark instances, an instance generator and an extensive experimental comparison demonstrating solving performance with SAT, CP, MIP and a state-of-the-art AI planner.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Computing methodologies → Planning and scheduling
Keywords
  • AI Planning
  • Modelling
  • Constraint Programming

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References

  1. Accenture. The Global Gaming Industry Value Now Exceeds $300 Billion, New Accenture Report Finds. https://newsroom.accenture.com/news/global-gaming-industry-value-now-exceeds-300-billion-new-accenture-report-finds.htm, 2021. [Online; accessed 2-Feb-2022].
  2. Özgür Akgün, Ian P. Gent, Christopher Jefferson, Ian Miguel, Peter Nightingale, and András Z. Salamon. Automatic discovery and exploitation of promising subproblems for tabulation. In Principles and Practice of Constraint Programming - 24th International Conference, CP, volume 11008, pages 3-12, 2018. URL: https://doi.org/10.1007/978-3-319-98334-9_1.
  3. Behrouz Babaki, Gilles Pesant, and Claude-Guy Quimper. Solving classical AI planning problems using planning-independent CP modeling and search. In Daniel Harabor and Mauro Vallati, editors, Proceedings of the Thirteenth International Symposium on Combinatorial Search, SOCS, pages 2-10. AAAI Press, 2020. Google Scholar
  4. Christer Bäckström and Bernhard Nebel. Complexity Results for SAS+ Planning. Comput. Intell., 11:625-656, 1995. URL: https://doi.org/10.1111/j.1467-8640.1995.tb00052.x.
  5. Roman Barták, Miguel A Salido, and Francesca Rossi. Constraint satisfaction techniques in planning and scheduling. Journal of Intelligent Manufacturing, 21(1):5-15, 2010. Google Scholar
  6. Roman Barták and Daniel Toropila. Reformulating constraint models for classical planning. In David Wilson and H. Chad Lane, editors, Proceedings of the Twenty-First International Florida Artificial Intelligence Research Society Conference, May 15-17, 2008, pages 525-530. AAAI Press, 2008. Google Scholar
  7. Armin Biere, Katalin Fazekas, Mathias Fleury, and Maximillian Heisinger. CaDiCaL, Kissat, Paracooba, Plingeling and Treengeling entering the SAT Competition 2020. In Tomas Balyo, Nils Froleyks, Marijn Heule, Markus Iser, Matti Järvisalo, and Martin Suda, editors, Proc. of SAT Competition 2020 - Solver and Benchmark Descriptions, volume B-2020-1 of Department of Computer Science Report Series B, pages 51-53. University of Helsinki, 2020. Google Scholar
  8. Geoffrey Chu, Peter J. Stuckey, Andreas Schutt, Thorsten Ehlers, Graeme Gange, and Kathryn Francis. Chuffed 0.10.4. https://github.com/chuffed/chuffed, 2019 (accessed 03-05-2022).
  9. Joan Espasa, Ian Miguel, Jordi Coll, and Mateu Villaret. Towards lifted encodings for numeric planning in essence prime. Proceedings of the 18th International Workshop on Constraint Modelling and Reformulation (ModRef), 2019. Google Scholar
  10. Joan Espasa Arxer, Ian P Gent, Ruth Hoffmann, Christopher Jefferson, Matthew J McIlree, and Alice M Lynch. Towards generic explanations for pen and paper puzzles with MUSes. In Proceedings of the SICSA eXplainable Artifical Intelligence Workshop, 2021. Google Scholar
  11. Maria Fox and Derek Long. PDDL2.1: an extension to PDDL for expressing temporal planning domains. Journal of Artificial Intelligence Research, 20:61-124, 2003. URL: https://doi.org/10.1613/jair.1129.
  12. Ian P Gent, Chris Jefferson, Tom Kelsey, Inês Lynce, Ian Miguel, Peter Nightingale, Barbara M Smith, and S Armagan Tarim. Search in the patience game ‘black hole’. AI Communications, 20(3):211-226, 2007. Google Scholar
  13. Alfonso Gerevini and Derek Long. Plan constraints and Preferences in PDDL3. Technical report, Technical Report 2005-08-07, Department of Electronics for Automation, University of Brescia, Brescia, Italy, 2005, 2005. Google Scholar
  14. Malik Ghallab, Dana Nau, and Paolo Traverso. Automated Planning: theory and practice. Elsevier, 2004. Google Scholar
  15. Nina Ghanbari Ghooshchi, Majid Namazi, M. A. Hakim Newton, and Abdul Sattar. Encoding domain transitions for constraint-based planning. Journal of Artificial Intelligence Research, 58:905-966, 2017. URL: https://doi.org/10.1613/jair.5378.
  16. Gaël Glorian, Adrien Debesson, Sylvain Yvon-Paliot, and Laurent Simon. The dungeon variations problem using constraint programming. In Laurent D. Michel, editor, 27th International Conference on Principles and Practice of Constraint Programming, CP 2021, Montpellier, France, volume 210 of LIPIcs, pages 27:1-27:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.CP.2021.27.
  17. Patrik Haslum, Nir Lipovetzky, Daniele Magazzeni, and Christian Muise. An Introduction to the Planning Domain Definition Language. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers, 2019. URL: https://doi.org/10.2200/S00900ED2V01Y201902AIM042.
  18. Malte Helmert. The Fast Downward Planning System. J. Artif. Intell. Res., 26:191-246, 2006. URL: https://doi.org/10.1613/jair.1705.
  19. Christopher Jefferson, Angela Miguel, Ian Miguel, and Armagan Tarim. Modelling and solving english peg solitaire. Comput. Oper. Res., 33(10):2935-2959, 2006. URL: https://doi.org/10.1016/j.cor.2005.01.018.
  20. Christopher Jefferson, Wendy Moncur, and Karen E Petrie. Combination: Automated generation of puzzles with constraints. In Proceedings of the 2011 ACM Symposium on Applied Computing, pages 907-912, 2011. Google Scholar
  21. Henry A. Kautz and Bart Selman. Planning as Satisfiability. In ECAI, pages 359-363, 1992. Google Scholar
  22. Derek Long. Drilling down: Planning in the field. Invited Talk, Twenty-Ninth International Conference on Automated Planning and Scheduling, (ICAPS), Berkeley, CA, USA, 2019. Google Scholar
  23. Arman Masoumi, Megan Antoniazzi, and Mikhail Soutchanski. Modeling Organic Chemistry and Planning Organic Synthesis. In Global Conference on Artificial Intelligence (GCAI), pages 176-195, 2015. Google Scholar
  24. Ian Miguel, Peter Jarvis, and Qiang Shen. Flexible graphplan. In ECAI, pages 506-510, 2000. Google Scholar
  25. Tim Niemueller, Erez Karpas, Tiago Vaquero, and Eric Timmons. Planning competition for logistics robots in simulation. In Workshop on Planning and Robotics (PlanRob) at International Conference on Automated Planning and Scheduling (ICAPS), 2016. Google Scholar
  26. Peter Nightingale, Özgür Akgün, Ian P. Gent, Christopher Jefferson, Ian Miguel, and Patrick Spracklen. Automatically improving constraint models in Savile Row. Artificial Intelligence, 251:35-61, 2017. Google Scholar
  27. Peter Nightingale and Andrea Rendl. Essence' description. CoRR, abs/1601.02865, 2016. URL: http://arxiv.org/abs/1601.02865.
  28. Andrea Rendl, Ian Miguel, Ian P. Gent, and Peter Gregory. Common subexpressions in constraint models of planning problems. In Eighth Symposium on Abstraction, Reformulation, and Approximation, SARA. AAAI, 2009. Google Scholar
  29. Jussi Rintanen, Keijo Heljanko, and Ilkka Niemelä. Planning as Satisfiability: Parallel Plans and Algorithms for Plan Search. Artificial Intelligence, 170(12-13):1031-1080, 2006. Google Scholar
  30. Peter van Beek and Xinguang Chen. CPlan: A Constraint Programming Approach to Planning. In Sixteenth National Conference on AI and Eleventh Conference on Innovative Applications of AI, pages 585-590, 1999. Google Scholar
  31. Vincent Vidal and Héctor Geffner. Branching and pruning: An optimal temporal POCL planner based on constraint programming. Artificial Intelligence, 170(3):298-335, 2006. Google Scholar
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