{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T02:05:07Z","timestamp":1778637907112,"version":"3.51.4"},"reference-count":56,"publisher":"Maximum Academic Press","license":[{"start":{"date-parts":[[2021,6,10]],"date-time":"2021-06-10T00:00:00Z","timestamp":1623283200000},"content-version":"unspecified","delay-in-days":160,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Knowledge Engineering Review"],"published-print":{"date-parts":[[2021]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Automated planning is the field of Artificial Intelligence (AI) that focuses on identifying sequences of actions allowing to reach a goal state from a given initial state. The need of using such techniques in real-world applications has brought popular languages for expressing automated planning problems to provide direct support for continuous and discrete state variables, along with changes that can be either instantaneous or durative. PDDL+ (Planning Domain Definition Language +) models support the encoding of such representations, but the resulting planning problems are notoriously difficult for AI planners to cope with due to non-linear dependencies arising from the variables and infinite search spaces. This difficulty is exacerbated by the potentially huge fully ground representations used by modern planners in order to effectively explore the search space, which can make some problems impossible to tackle.<\/jats:p>\n                  <jats:p>This paper investigates two grounding techniques for PDDL+ problems, both aimed at reducing the size of the full ground representation by reasoning over the lifted, more abstract problem structure. The first method extends the simple mechanism of invariant analysis to limit the groundings of operators upfront. The second method proposes to tackle the grounding process through a PDDL+ to classical planning abstraction; this allows us to leverage the amount of research done in the classical planning area. Our empirical analysis studies the effect of these novel approaches over both real-world hybrid applications and synthetic PDDL+ problems took from standard benchmarks of the planning community; our results reveal that not only the techniques improve the running time of previous grounding mechanisms but also let the planner extend the reach to problems that were not solvable before.<\/jats:p>","DOI":"10.1017\/s0269888921000072","type":"journal-article","created":{"date-parts":[[2021,6,10]],"date-time":"2021-06-10T04:00:35Z","timestamp":1623297635000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["Effective grounding for hybrid planning problems represented in PDDL+"],"prefix":"10.48130","volume":"36","author":[{"given":"Enrico","family":"Scala","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8429-3570","authenticated-orcid":false,"given":"Mauro","family":"Vallati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"27968","published-online":{"date-parts":[[2021,6,10]]},"reference":[{"key":"S0269888921000072_ref6","first-page":"30","volume":"11008","author":"Bit-Monnot","year":"2018"},{"key":"S0269888921000072_ref17","doi-asserted-by":"publisher","DOI":"10.1613\/jair.2044"},{"key":"S0269888921000072_ref28","first-page":"412","author":"Kiam","year":"2020"},{"key":"S0269888921000072_ref34","doi-asserted-by":"crossref","unstructured":"McCluskey, T. L. , Vaquero, T. S. & Vallati, M. 2017. Engineering knowledge for automated planning: towards a notion of quality. In Proceedings of the Knowledge Capture Conference, K-CAP, 14:1\u201314:8.","DOI":"10.1145\/3148011.3148012"},{"key":"S0269888921000072_ref8","doi-asserted-by":"crossref","unstructured":"Bofill, M. , Espasa, J. & Villaret, M. (2016) A semantic notion of interference for planning modulo theories. In Proceedings of the Twenty-Sixth International Conference on Automated Planning and Scheduling, ICAPS, 56\u201364.","DOI":"10.1609\/icaps.v26i1.13734"},{"key":"S0269888921000072_ref27","doi-asserted-by":"publisher","DOI":"10.1609\/aimag.v37i3.2672"},{"key":"S0269888921000072_ref32","doi-asserted-by":"publisher","DOI":"10.1613\/jair.1240"},{"key":"S0269888921000072_ref25","doi-asserted-by":"publisher","DOI":"10.1613\/jair.1144"},{"key":"S0269888921000072_ref9","first-page":"3247","volume-title":"In AAAI","author":"Bryce","year":"2015"},{"key":"S0269888921000072_ref14","unstructured":"Coles, A. J. , Coles, A. , Fox, M. & Long, D. 2010. Forward-chaining partial-order planning. In Proceedings of the 20th International Conference on Automated Planning and Scheduling, ICAPS, 42\u201349."},{"key":"S0269888921000072_ref48","doi-asserted-by":"publisher","DOI":"10.1109\/ICTAI50040.2020.00024"},{"key":"S0269888921000072_ref52","doi-asserted-by":"crossref","unstructured":"Vallati, M. , Chrpa, L. & McCluskey, T. L. 2018. What you always wanted to know about the deterministic part of the international planning competition (IPC) 2014 (but were too afraid to ask). Knowledge Engineering Review. 33, e3.","DOI":"10.1017\/S0269888918000012"},{"key":"S0269888921000072_ref54","first-page":"1704","article-title":"On the effective configuration of planning domain models","author":"Vallati","year":"2015","journal-title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI"},{"key":"S0269888921000072_ref31","doi-asserted-by":"crossref","unstructured":"Lipovetzky, N. , Burt, C. N. , Pearce, A. R. & Stuckey, P. J. 2014. Planning for mining operations with time and resource constraints. In Proceedings of the International Conference on Automated Planning and Scheduling.","DOI":"10.1609\/icaps.v24i1.13666"},{"key":"S0269888921000072_ref10","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1613\/jair.1.11751","volume":"67","author":"Cashmore","year":"2020","journal-title":"Journal of Artificial Intelligence Research"},{"key":"S0269888921000072_ref22","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v33i01.33017602"},{"key":"S0269888921000072_ref44","first-page":"3228","author":"Scala"},{"key":"S0269888921000072_ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2005.04.001"},{"key":"S0269888921000072_ref4","first-page":"305","author":"Barrett","year":"2018"},{"key":"S0269888921000072_ref40","unstructured":"Ram\u00edrez, M. , Papasimeon, M. , Lipovetzky, N. , Benke, L. , Miller, T. , Pearce, A. R. , Scala, E. & Zamani, M. 2018. Integrated hybrid planning and programmed control for real time UAV maneuvering. In Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS, 1318\u20131326."},{"key":"S0269888921000072_ref7","unstructured":"Biundo, S. , Aylett, R. , Beetz, M. , Borrajo, D. , Cesta, A. , Grant, T. , McCluskey, T. , Milani, A. & Verfaillie, G. 2003. PLANET roadmap. http:\/\/planet.hud.ac.uk\/home\/."},{"key":"S0269888921000072_ref41","doi-asserted-by":"crossref","unstructured":"Ridder, B. & Fox, M. 2014. Heuristic evaluation based on lifted relaxed planning graphs. In Proceedings of the Twenty-Fourth International Conference on Automated Planning and Scheduling, ICAPS.","DOI":"10.1609\/icaps.v24i1.13650"},{"key":"S0269888921000072_ref46","doi-asserted-by":"crossref","unstructured":"Scala, E. , Haslum, P. , Thi\u00e9baux, S. & Ram\u00edrez, M. 2020a. Subgoaling techniques for satisficing and optimal numeric planning. Journal of Artificial Intelligence Research 68, 691\u2013752.","DOI":"10.1613\/jair.1.11875"},{"key":"S0269888921000072_ref24","first-page":"278","author":"Henzinger","year":"1996"},{"key":"S0269888921000072_ref26","doi-asserted-by":"crossref","unstructured":"Hoffmann, J. & Nebel, B. 2001. The FF planning system: fast plan generation through heuristic search. Journal of Artificial Intelligence Research 14, 253\u2013302.","DOI":"10.1613\/jair.855"},{"key":"S0269888921000072_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.trc.2018.12.005"},{"key":"S0269888921000072_ref30","first-page":"1594","author":"Lifschitz","year":"2008"},{"key":"S0269888921000072_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068417000187"},{"key":"S0269888921000072_ref16","author":"Della Penna","year":"2009"},{"key":"S0269888921000072_ref18","unstructured":"Fox, M. , Long, D. , Tamboise, G. & Isangulov, R. 2018. Creating and executing a well construction\/operation plan. US Patent App. 15\/541,381."},{"key":"S0269888921000072_ref56","doi-asserted-by":"publisher","DOI":"10.1613\/jair.1136"},{"key":"S0269888921000072_ref53","doi-asserted-by":"publisher","DOI":"10.1007\/s10817-021-09592-1"},{"key":"S0269888921000072_ref45","first-page":"655","volume":"285","author":"Scala"},{"key":"S0269888921000072_ref2","unstructured":"Areces, C. , Bustos, F. , Dominguez, M. & Hoffmann, J. 2014. Optimizing planning domains by automatic action schema splitting. In Proceedings of ICAPS, 11\u201319."},{"key":"S0269888921000072_ref33","doi-asserted-by":"crossref","unstructured":"McCluskey, T. L. & Vallati, M. 2017. Embedding automated planning within urban traffic management operations. In Proceedings of the Twenty-Seventh International Conference on Automated Planning and Scheduling, ICAPS, 391\u2013399.","DOI":"10.24963\/ijcai.2017\/776"},{"key":"S0269888921000072_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2014.02.002"},{"key":"S0269888921000072_ref42","unstructured":"Riddle, P. J. , Barley, M. W. , Franco, S. & Douglas, J. 2015. Automated transformation of PDDL representations. In Proceedings of the International Symposium on Combinatorial Search, SOCS."},{"key":"S0269888921000072_ref15","unstructured":"Corr\u00eaa, A. B. , Pommerening, F. , Helmert, M. & Franc\u00e8s, G. 2020. Lifted successor generation using query optimization techniques. In Proceedings of the Thirtieth International Conference on Automated Planning and Scheduling (ICAPS), 80\u201389."},{"key":"S0269888921000072_ref29","unstructured":"Koehler, J. & Hoffmann, J. 2000. On the instantiation of ADL operators involving arbitrary first-order formulas. In PuK."},{"key":"S0269888921000072_ref20","author":"Garrido"},{"key":"S0269888921000072_ref51","doi-asserted-by":"crossref","unstructured":"Vallati, M. & Chrpa, L. 2019. On the robustness of domain-independent planning engines: the impact of poorly-engineered knowledge. In Proceedings of the 10th International Conference on Knowledge Capture, K-CAP, 197\u2013204.","DOI":"10.1145\/3360901.3364416"},{"key":"S0269888921000072_ref11","unstructured":"Chrpa, L. , Scala, E. & Vallati, M. 2015. Towards a reformulation based approach for efficient numeric planning: numeric outer entanglements. In Proceedings of SOCS."},{"key":"S0269888921000072_ref39","unstructured":"Piotrowski, W. M. , Fox, M. , Long, D. , Magazzeni, D. & Mercorio, F. 2016. Heuristic planning for hybrid systems. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, 4254\u20134255."},{"key":"S0269888921000072_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2008.10.013"},{"key":"S0269888921000072_ref50","unstructured":"Thi\u00e9baux, S. , Coffrin, C. , Hijazi, H. & Slaney, J. 2013. Planning with mip for supply restoration in power distribution systems. In Proceedings of the International Joint Conference on Artificial Intelligence."},{"key":"S0269888921000072_ref55","unstructured":"Vallati, M. , Magazzeni, D. , Schutter, B. D. , Chrpa, L. & McCluskey, T. L. 2016. Efficient macroscopic urban traffic models for reducing congestion: a PDDL+ planning approach. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, 3188\u20133194."},{"key":"S0269888921000072_ref12","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1080\/0952813X.2018.1509377","volume":"30","author":"Chrpa","year":"2018","journal-title":"Journal of Experimental and Theoretical Artificial Intelligence"},{"key":"S0269888921000072_ref38","doi-asserted-by":"crossref","unstructured":"Petrick, R. P. A. & Foster, M. E. 2013. Planning for social interaction in a robot bartender domain. In Proceedings of the Twenty-Third International Conference on Automated Planning and Scheduling, ICAPS.","DOI":"10.1609\/icaps.v23i1.13589"},{"key":"S0269888921000072_ref43","unstructured":"Robinson, N. , Gretton, C. , Pham, D. N. & Sattar, A. 2008. A compact and efficient SAT encoding for planning. In Proceedings of the Eighteenth International Conference on Automated Planning and Scheduling, ICAPS, 296\u2013303."},{"key":"S0269888921000072_ref21","volume-title":"Automated Planning: Theory and Practice","author":"Ghallab","year":"2004"},{"key":"S0269888921000072_ref5","first-page":"135","author":"Bertolucci","year":"2019"},{"key":"S0269888921000072_ref13","doi-asserted-by":"crossref","unstructured":"Coles, A. J. & Coles, A. 2011. LPRPG-P: relaxed plan heuristics for planning with preferences. In Proceedings of the 21st International Conference on Automated Planning and Scheduling, ICAPS.","DOI":"10.1609\/icaps.v21i1.13445"},{"key":"S0269888921000072_ref19","doi-asserted-by":"crossref","unstructured":"Franco, S. , Vallati, M. , Lindsay, A. & McCluskey, T. L. 2019. Improving planning performance in PDDL+ domains via automated predicate reformulation. In Proceedings of the 19th International Conference Computational Science (ICCS), 491\u2013498.","DOI":"10.1007\/978-3-030-22750-0_42"},{"key":"S0269888921000072_ref36","unstructured":"Newton, M. A. H. , Levine, J. , Fox, M. & Long, D. 2007. Learning macro-actions for arbitrary planners and domains. In Proceedings of ICAPS."},{"key":"S0269888921000072_ref35","first-page":"143","author":"McDermott","year":"2003"},{"key":"S0269888921000072_ref47","first-page":"226","author":"Scala"}],"container-title":["The Knowledge Engineering Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0269888921000072","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T14:42:21Z","timestamp":1767624141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0269888921000072\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":56,"alternative-id":["S0269888921000072"],"URL":"https:\/\/doi.org\/10.1017\/s0269888921000072","relation":{},"ISSN":["0269-8889","1469-8005"],"issn-type":[{"value":"0269-8889","type":"print"},{"value":"1469-8005","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}],"article-number":"e9"}}