{"type":"ScholarlyArticle","title":"Optimal Planning Modulo Theories","authors":[{"name":"Francesco Leofante","slug":"francesco-leofante","given":"Francesco","family":"Leofante","affiliation":"Imperial College London , United Kingdom"},{"name":"Enrico Giunchiglia","slug":"enrico-giunchiglia","given":"Enrico","family":"Giunchiglia","affiliation":"University of Genoa , Italy"},{"name":"Erika Ábráham","slug":"erika-abraham","given":"Erika","family":"Ábráham","affiliation":"RWTH Aachen University , Germany"},{"name":"Armando Tacchella","slug":"armando-tacchella","given":"Armando","family":"Tacchella","affiliation":"University of Genoa , Italy"}],"abstract":"We consider the problem of planning with arithmetic\r\n theories, and focus on generating optimal \r\n plans for numeric domains with constant and state-dependent action costs. \r\n Solving these problems efficiently requires a seamless integration between\r\n propositional and numeric reasoning. We propose a novel approach that leverages Optimization \r\n Modulo Theories (OMT) solvers to implement a domain-independent optimal \r\n theory-planner. We present a new encoding\r\n for optimal planning in this setting and \r\n we evaluate our approach using well-known, as well as new, numeric benchmarks.","doi":"10.24963/ijcai.2020/571","url":"https://ijcai.org/proceedings/2020/571","pdf":"https://ijcai.org/proceedings/2020/0571.pdf","markdown":"https://ijcai.org/proceedings/2020/571.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/571","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Planning and Scheduling","track":"Main track","number":571,"pages":{"first":4128,"last":4134},"keywords":["Constraints and SAT: Satisfiability Modulo Theories","Planning and Scheduling: Planning Algorithms"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/23996/file_23996.m3u8","length_sec":269,"provider":"hls"}],"references":[{"position":1,"raw":"[Bjørner et al., 2015] Nikolaj Bjørner, Anh-Dung Phan, and Lars Fleckenstein. νz -An optimizing SMT solver. In TACAS, pages 194-199, 2015.","title":"νz -An optimizing SMT solver","authors":"Nikolaj Bjørner, Anh-Dung Phan, Lars Fleckenstein","year":"2015","venue":"TACAS","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Eyerich et al., 2009] Patrick Eyerich, Robert Mattmüller, and Gabriele Röger. Using the context-enhanced additive heuristic for temporal and numeric planning. In ICAPS, pages 130-137, 2009.","title":"Using the context-enhanced additive heuristic for temporal and numeric planning","authors":"Patrick Eyerich, Robert Mattmüller, Gabriele Röger","year":"2009","venue":"ICAPS","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Fox and Long, 2003] Maria Fox and Derek Long. PDDL2.1: An extension to PDDL for expressing temporal planning domains. J. Artif. Intell. Res. (JAIR), 20:61-124, 2003.","title":"PDDL2.1: An extension to PDDL for expressing temporal planning domains","authors":"Maria Fox, Derek Long","year":"2003","venue":"J. Artif. Intell. Res. (JAIR)","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Geißer et al., 2015] Florian Geißer, Thomas Keller, and Robert Mattmüller. Delete relaxations for planning with state-dependent action costs. In IJCAI, pages 1573-1579, 2015.","title":"Delete relaxations for planning with state-dependent action costs","authors":"Geißer","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/225"},{"position":5,"raw":"[Geißer et al., 2016] Florian Geißer, Thomas Keller, and Robert Mattmüller. Abstractions for planning with state- dependent action costs. In ICAPS, pages 140-148, 2016.","title":"Abstractions for planning with statedependent action costs","authors":"Geißer","year":"2016","venue":"ICAPS","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Gelfond and Lifschitz, 1988] Michael Gelfond and Vladimir Lifschitz. The stable model semantics for logic programming. In ICLP, pages 1070-1080, 1988.","title":"The stable model semantics for logic programming","authors":"Michael Gelfond, Vladimir Lifschitz","year":"1988","venue":"ICLP","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Gregory et al., 2012] Peter Gregory, Derek Long, Maria Fox, and J. Christopher Beck. Planning modulo theories: Extending the planning paradigm. In ICAPS, pages 65-73, 2012.","title":"Planning modulo theories: Extending the planning paradigm","authors":"Peter Gregory, Derek Long, Maria Fox, J Christopher Beck","year":"2012","venue":"ICAPS","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Haslum et al., 2018] Patrik Haslum, Franc Ivankovic, Miquel Ramírez, Dan Gordon, Sylvie Thiébaux, Vikas Shivashankar, and Dana S. Nau. Extending classical planning with state constraints: Heuristics and search for optimal planning. J. Artif. Intell. Res., 62:373-431, 2018.","title":"Extending classical planning with state constraints: Heuristics and search for optimal planning","authors":"Patrik Haslum, Franc Ivankovic, Miquel Ramírez, Dan Gordon, Sylvie Thiébaux, Vikas Shivashankar, Dana S Nau","year":"2018","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Helmert, 2002] Malte Helmert. Decidability and undecid- ability results for planning with numerical state variables. In AIPS, pages 44-53, 2002.","title":"Decidability and undecidability results for planning with numerical state variables","authors":"Malte Helmert, Helmert","year":"2002","venue":"AIPS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Helmert, 2009] Malte Helmert. Concise finite-domain rep- resentations for PDDL planning tasks. Artif. Intell., 173(5- 6):503-535, 2009.","title":"Concise finite-domain representations for PDDL planning tasks","authors":"Malte Helmert, Helmert","year":"2009","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hoffmann, 2003] Jörg Hoffmann. The metric-ff planning system: Translating \"ignoring delete lists\" to numeric state variables. J. Artif. Intell. Res., 20:291-341, 2003.","title":"The metric-ff planning system: Translating \"ignoring delete lists\" to numeric state variables","authors":"Jörg Hoffmann","year":"2003","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Illanes and McIlraith, 2017] Leon Illanes and Sheila A. McIlraith. Numeric planning via abstraction and policy guided search. In IJCAI, pages 4338-4345, 2017.","title":"Numeric planning via abstraction and policy guided search","authors":"Mcilraith Illanes, Leon Illanes, Sheila A Mcilraith","year":"2017","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2017/606"},{"position":13,"raw":"[Ivankovic et al., 2014] Franc Ivankovic, Patrik Haslum, Sylvie Thiébaux, Vikas Shivashankar, and Dana S. Nau. Optimal planning with global numerical state constraints. In ICAPS, pages 145-153, 2014.","title":"Optimal planning with global numerical state constraints","authors":"Ivankovic","year":"2014","venue":"ICAPS","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Ivankovic et al., 2019] Franc Ivankovic, Dan Gordon, and Patrik Haslum. Planning with global state constraints and state-dependent action costs. In ICAPS, pages 232-236, 2019.","title":"Planning with global state constraints and state-dependent action costs","authors":"Ivankovic","year":"2019","venue":"ICAPS","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Kautz and Selman, 1992] Henry A. Kautz and Bart Selman. Planning as satisfiability. In ECAI, pages 359-363, 1992.","title":"Planning as satisfiability","authors":"Henry A Kautz, Bart Selman","year":"1992","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Leofante et al., 2018] Francesco Leofante, Erika Ábrahám, and Armando Tacchella. Task planning with OMT: an ap- plication to production logistics. In IFM, pages 316-325, 2018.","title":"Task planning with OMT: an application to production logistics","authors":"Francesco Leofante, Erika Ábrahám, Armando Tacchella","year":"2018","venue":"IFM","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Leofante et al., 2019] Francesco Leofante, Erika Ábrahám, Tim Niemueller, Gerhard Lakemeyer, and Armando Tac- chella. Integrated synthesis and execution of optimal plans for multi-robot systems in logistics. Information Systems Frontiers, 2019.","title":"Integrated synthesis and execution of optimal plans for multi-robot systems in logistics","authors":"Francesco Leofante, Erika Ábrahám, Tim Niemueller, Gerhard Lakemeyer, Armando Tacchella","year":"2019","venue":"Information Systems Frontiers","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Li et al., 2018] Dongxu Li, Enrico Scala, Patrik Haslum, and Sergiy Bogomolov. Effect-abstraction based relax- ation for linear numeric planning. In IJCAI, pages 4787- 4793, 2018.","title":"Effect-abstraction based relaxation for linear numeric planning","authors":"Li","year":"2018","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2018/665"},{"position":19,"raw":"[Lin and Zhao, 2002] Fangzhen Lin and Yuting Zhao. AS- SAT: computing answer sets of a logic program by SAT solvers. In AAAI, pages 112-118, 2002.","title":"AS-SAT: computing answer sets of a logic program by SAT solvers","authors":"Lin, Zhao, Fangzhen Lin, Yuting Zhao","year":"2002","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Piacentini et al., 2018a] Chiara Piacentini, Margarita P. Castro, André Augusto Ciré, and J. Christopher Beck. Compiling optimal numeric planning to mixed integer lin- ear programming. In ICAPS, pages 383-387, 2018.","title":"Compiling optimal numeric planning to mixed integer linear programming","authors":"Piacentini","year":"2018","venue":"ICAPS","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Piacentini et al., 2018b] Chiara Piacentini, Margarita P. Castro, André Augusto Ciré, and J. Christopher Beck. Linear and integer programming-based heuristics for cost- optimal numeric planning. In AAAI, pages 6254-6261, 2018.","title":"Linear and integer programming-based heuristics for costoptimal numeric planning","authors":"Piacentini","year":"2018","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Rintanen et al., 2006] Jussi Rintanen, Keijo Heljanko, and Ilkka Niemelä. Planning as satisfiability: parallel plans and algorithms for plan search. Artif. Intell., 170(12- 13):1031-1080, 2006.","title":"Planning as satisfiability: parallel plans and algorithms for plan search","authors":"Rintanen","year":"2006","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Rintanen, 2009] Jussi Rintanen. Planning and SAT. In Handbook of Satisfiability, pages 483-504. 2009.","title":"Planning and SAT","authors":"Jussi Rintanen","year":"2009","venue":"Handbook of Satisfiability","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Scala et al., 2016a] Enrico Scala, Patrik Haslum, and Sylvie Thiébaux. Heuristics for numeric planning via subgoaling. In IJCAI, pages 3228-3234, 2016.","title":"Heuristics for numeric planning via subgoaling","authors":"Scala","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/457"},{"position":25,"raw":"[Scala et al., 2016b] Enrico Scala, Patrik Haslum, Sylvie Thiébaux, and Miquel Ramírez. Interval-based relaxation for general numeric planning. In ECAI, pages 655-663, 2016.","title":"Interval-based relaxation for general numeric planning","authors":"Scala","year":"2016","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Scala et al., 2017] Enrico Scala, Patrik Haslum, Daniele Magazzeni, and Sylvie Thiébaux. Landmarks for numeric planning problems. In IJCAI, pages 4384-4390, 2017.","title":"Landmarks for numeric planning problems","authors":"Enrico Scala, Patrik Haslum, Daniele Magazzeni, Sylvie Thiébaux","year":"2017","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2017/612"},{"position":27,"raw":"[Sebastiani and Tomasi, 2015] Roberto Sebastiani and Silvia Tomasi. Optimization modulo theories with linear rational costs. ACM Trans. Comput. Log., 16(2):12:1-12:43, 2015.","title":"Optimization modulo theories with linear rational costs","authors":"Tomasi Sebastiani, Roberto Sebastiani, Silvia Tomasi","year":"2015","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Shin and Davis, 2005] Ji-Ae Shin and Ernest Davis. Pro- cesses and continuous change in a sat-based planner. Artif. Intell., 166(1-2):194-253, 2005.","title":"Ji-Ae Shin and Ernest Davis. Processes and continuous change in a sat-based planner","authors":"Davis Shin","year":"2005","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}