{"type":"ScholarlyArticle","title":"LP Heuristics over Conjunctions: Compilation, Convergence, Nogood Learning","authors":[{"name":"Marcel Steinmetz","slug":"marcel-steinmetz","given":"Marcel","family":"Steinmetz","affiliation":"Saarland University , Saarland Informatics Campus , Saarbrücken , Germany"},{"name":"Joerg Hoffmann","slug":"joerg-hoffmann","given":"Joerg","family":"Hoffmann","affiliation":"Saarland University , Saarland Informatics Campus , Saarbrücken , Germany"}],"abstract":"Two strands of research in classical planning are LP heuristics and conjunctions to improve approximations. Combinations of the two have also been explored. Here, we focus on convergence properties, forcing the LP heuristic to equal the perfect heuristic h* in the limit. We show that, under reasonable assumptions, partial variable merges are strictly dominated by the compilation Pi^C of explicit conjunctions, and that both render the state equation heuristic equal to h* for a suitable set C of conjunctions. We show that consistent potential heuristics can be computed from a variant of Pi^C, and that such heuristics can represent h* for suitable C. As an application of these convergence properties, we consider sound nogood learning in state space search, via refining the set C. We design a suitable refinement method to this end. Experiments on IPC benchmarks show significant performance improvements in several domains.","doi":"10.24963/ijcai.2018/672","url":"https://ijcai.org/proceedings/2018/672","pdf":"https://ijcai.org/proceedings/2018/0672.pdf","markdown":"https://ijcai.org/proceedings/2018/672.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/672","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Planning and Scheduling","track":"Main track","number":672,"pages":{"first":4837,"last":4843},"keywords":["Heuristic Search and Game Playing: Heuristic Search","Planning and Scheduling: Planning Algorithms","Planning and Scheduling: Planning and Scheduling"],"videos":[],"references":[{"position":1,"raw":"[Bäckström and Nebel, 1995] Christer Bäckström and Bern- hard Nebel. Complexity results for SAS + planning. Com- putational Intelligence, 11(4):625-655, 1995.","title":"Christer Bäckström and Bernhard Nebel","authors":"Nebel Bäckström","year":"1995","venue":"Computational Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bonet and van den Briel, 2014] Blai Bonet and Menkes van den Briel. Flow-based heuristics for optimal planning: Landmarks and merges. In Proc. ICAPS'14, pages 47-55, 2014.","title":"Flow-based heuristics for optimal planning: Landmarks and merges","authors":"Van Bonet, Blai Den Briel ;, Menkes Bonet, Van Den, Briel","year":"2014","venue":"Proc. ICAPS'14","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bonet, 2013] Blai Bonet. An admissible heuristic for SAS+ planning obtained from the state equation. In Proc. IJ- CAI'13, pages 2268-2274, 2013.","title":"An admissible heuristic for SAS+ planning obtained from the state equation","authors":"Blai Bonet, Bonet","year":"2013","venue":"Proc. IJ-CAI'13","doi":null,"url":null,"internal_url":"/proceedings/2013/335"},{"position":4,"raw":"[Haslum, 2009] Patrik Haslum. h m (P ) = h 1 (P m ): Alter- native characterisations of the generalisation from h max to h m . In Proc. ICAPS'09, pages 354-357, 2009.","title":"Patrik Haslum. h m (P ) = h 1 (P m ): Alternative characterisations of the generalisation from h max to h m","authors":"Haslum","year":"2009","venue":"Proc. ICAPS'09","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Haslum, 2012] Patrik Haslum. Incremental lower bounds for additive cost planning problems. In Proc. ICAPS'12, pages 74-82, 2012.","title":"Incremental lower bounds for additive cost planning problems","authors":"Patrik Haslum, Haslum","year":"2012","venue":"Proc. ICAPS'12","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Helmert, 2006] Malte Helmert. The Fast Downward plan- ning system. Journal of Artificial Intelligence Research, 26:191-246, 2006.","title":"The Fast Downward planning system","authors":"Malte Helmert","year":"2006","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Helmert, 2009] Malte Helmert. Concise finite-domain rep- resentations for PDDL planning tasks. Artificial Intelli- gence, 173:503-535, 2009.","title":"Concise finite-domain representations for PDDL planning tasks","authors":"Malte Helmert, Helmert","year":"2009","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Keyder et al., 2014] Emil Keyder, Jörg Hoffmann, and Pa- trik Haslum. Improving delete relaxation heuristics through explicitly represented conjunctions. Journal of Ar- tificial Intelligence Research, 50:487-533, 2014.","title":"Improving delete relaxation heuristics through explicitly represented conjunctions","authors":"Keyder","year":"2014","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Nakhost et al., 2012] Hootan Nakhost, Jörg Hoffmann, and Martin Müller. Resource-constrained planning: A Monte Carlo random walk approach. In Proc. ICAPS'12, pages 181-189, 2012.","title":"Resource-constrained planning: A Monte Carlo random walk approach","authors":"Hootan Nakhost, Jörg Hoffmann, Martin Müller","year":"2012","venue":"Proc. ICAPS'12","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Pommerening and Helmert, 2015] Florian Pommerening and Malte Helmert. A normal form for classical planning tasks. In Proc. ICAPS'15, pages 188-192, 2015.","title":"Florian Pommerening and Malte Helmert. A normal form for classical planning tasks","authors":"Helmert Pommerening","year":"2015","venue":"Proc. ICAPS'15","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Pommerening et al., 2014] Florian Pommerening, Gabriele Röger, Malte Helmert, and Blai Bonet. LP-based heuris- tics for cost-optimal planning. In Proc. ICAPS'14, pages 226-234, 2014.","title":"LP-based heuristics for cost-optimal planning","authors":"Florian Pommerening, Gabriele Röger, Malte Helmert, Blai Bonet","year":"2014","venue":"Proc. ICAPS'14","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Pommerening et al., 2015] Florian Pommerening, Malte Helmert, Gabriele Röger, and Jendrik Seipp. From non- negative to general operator cost partitioning. In Proc. AAAI'15, pages 3335-3341, 2015.","title":"From nonnegative to general operator cost partitioning","authors":"Florian Pommerening, Malte Helmert, Gabriele Röger, Jendrik Seipp","year":"2015","venue":"Proc. AAAI'15","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Pommerening et al., 2017] Florian Pommerening, Malte Helmert, and Blai Bonet. Higher-dimensional poten- tial heuristics for optimal classical planning. In Proc. AAAI'17, pages 3636-3643, 2017.","title":"Higher-dimensional potential heuristics for optimal classical planning","authors":"Florian Pommerening, Malte Helmert, Blai Bonet","year":"2017","venue":"Proc. AAAI'17","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Seipp et al., 2015] Jendrik Seipp, Florian Pommerening, and Malte Helmert. New optimization functions for poten- tial heuristics. In Proc. ICAPS'15, pages 193-201, 2015.","title":"New optimization functions for potential heuristics","authors":"Seipp","year":"2015","venue":"Proc. ICAPS'15","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Seipp et al., 2016a] Jendrik Seipp, Florian Pommerening, Gabriele Röger, and Malte Helmert. Correlation complex- ity of classical planning domains. In Proc. IJCAI'16, pages 3242-3250, 2016.","title":"Correlation complexity of classical planning domains","authors":"Seipp","year":"2016","venue":"Proc. IJCAI'16","doi":null,"url":null,"internal_url":"/proceedings/2016/459"},{"position":16,"raw":"[Seipp et al., 2016b] Jendrik Seipp, Florian Pommerening, Silvan Sievers, and Martin Wehrle. Fast Downward Ai- dos. In UIPC 2016 planner abstracts, pages 28-38, 2016.","title":"Fast Downward Aidos","authors":"Seipp","year":"2016","venue":"UIPC 2016 planner abstracts","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Steinmetz and Hoffmann, 2017] Marcel Steinmetz and Jörg Hoffmann. State space search nogood learning: Online refinement of critical-path dead-end detectors in planning. Artificial Intelligence, 245:1 -37, 2017.","title":"State space search nogood learning: Online refinement of critical-path dead-end detectors in planning","authors":"Hoffmann Steinmetz, Marcel Steinmetz, Jörg Hoffmann","year":"2017","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Steinmetz and Hoffmann, 2018] Marcel Steinmetz and Jörg Hoffmann. LP heuristics over conjunctions: Compi- lation, convergence, nogood learning (technical report). Technical report, Saarland University, 2018. Available at http://fai.cs.uni-saarland.de/hoffmann/papers/ijcai18b- tr.pdf.","title":"LP heuristics over conjunctions: Compilation, convergence, nogood learning","authors":"Hoffmann Steinmetz, Marcel Steinmetz, Jörg Hoffmann","year":"2018","venue":null,"doi":null,"url":"http://fai.cs.uni-saarland.de/hoffmann/papers/ijcai18b-tr.pdf","internal_url":null},{"position":19,"raw":"[van den Briel et al., 2007a] Menkes van den Briel, J. Ben- ton, Subbarao Kambhampati, and Thomas Vossen. An LP-based heuristic for optimal planning. In Proc. CP'07, pages 651-665, 2007.","title":"An LP-based heuristic for optimal planning","authors":"Van Den Briel","year":"2007","venue":"Proc. CP'07","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[van den Briel et al., 2007b] Menkes van den Briel, Sub- barao Kambhampati, and Thomas Vossen. Fluent merging: A general technique to improve reachability heuristics and factored planning. In Proc. HDIP'07, pages 20-24, 2007.","title":"Fluent merging: A general technique to improve reachability heuristics and factored planning","authors":"Van Den Briel","year":"2007","venue":"Proc. HDIP'07","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}