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.
@InProceedings{espasa_et_al:LIPIcs.CP.2022.22, author = {Espasa, Joan and Miguel, Ian and Villaret, Mateu}, title = {{Plotting: A Planning Problem with Complex Transitions}}, booktitle = {28th International Conference on Principles and Practice of Constraint Programming (CP 2022)}, pages = {22:1--22:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-240-2}, ISSN = {1868-8969}, year = {2022}, volume = {235}, editor = {Solnon, Christine}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.22}, URN = {urn:nbn:de:0030-drops-166514}, doi = {10.4230/LIPIcs.CP.2022.22}, annote = {Keywords: AI Planning, Modelling, Constraint Programming} }
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