{"type":"ScholarlyArticle","title":"Stochastic Constraint Programming with And-Or Branch-and-Bound","authors":[{"name":"Behrouz Babaki","slug":"behrouz-babaki","given":"Behrouz","family":"Babaki","affiliation":"Department of Computer Science , KU Leuven , Belgium"},{"name":"Tias Guns","slug":"tias-guns","given":"Tias","family":"Guns","affiliation":"Department of Computer Science , KU Leuven , Belgium; Department of Business Technology and Operations , VUB , Belgium"},{"name":"Luc de Raedt","slug":"luc-de-raedt","given":"Luc","family":"de Raedt","affiliation":"Department of Computer Science , KU Leuven , Belgium"}],"abstract":"Complex multi-stage decision making problems often involve uncertainty, for example, regarding demand or processing times. Stochastic constraint programming was proposed as a way to formulate and solve such decision problems, involving arbitrary constraints over both decision and random variables. What stochastic constraint programming still lacks is support for the use of factorized probabilistic models that are popular in the graphical model community. We show how a state-of-the-art probabilistic inference engine can be integrated into standard constraint solvers. The resulting approach searches over the And-Or search tree directly, and we investigate tight bounds on the expected utility objective. This significantly improves search efficiency and outperforms scenario-based methods that ground out the possible worlds.","doi":"10.24963/ijcai.2017/76","url":"https://ijcai.org/proceedings/2017/76","pdf":"https://ijcai.org/proceedings/2017/0076.pdf","markdown":"https://ijcai.org/proceedings/2017/76.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/76","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Constraints and Satisfiability","track":"Main track","number":76,"pages":{"first":539,"last":545},"keywords":["Constraints and Satisfiability: Other approaches","Constraints and Satisfiability: Constraint Optimisation","Constraints and Satisfiability: Solvers and Tools"],"videos":[],"references":[{"position":1,"raw":"[Benedetti et al., 2008] Marco Benedetti, Arnaud Lallouet, and Jérémie Vautard. Quantified Constraint Optimization, pages 463-477. Springer Berlin Heidelberg, Berlin, Hei- delberg, 2008.","title":"Quantified Constraint Optimization","authors":"Marco Benedetti, Arnaud Lallouet, Jérémie Vautard","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Chavira and Darwiche, 2005] Mark Chavira and Adnan Darwiche. Compiling bayesian networks with local struc- ture. In IJCAI, pages 1306-1312. Professional Book Cen- ter, 2005.","title":"Compiling bayesian networks with local structure","authors":"Darwiche Chavira, Mark Chavira, Adnan Darwiche","year":"2005","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2005/111"},{"position":3,"raw":"[Chavira and Darwiche, 2008] Mark Chavira and Adnan Darwiche. On probabilistic inference by weighted model counting. Artif. Intell., 172(6-7):772-799, 2008.","title":"On probabilistic inference by weighted model counting","authors":"Darwiche Chavira, Mark Chavira, Adnan Darwiche","year":"2008","venue":"Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Choi et al., 2006] Chiu Wo Choi, Warwick Harvey, Jimmy Ho-Man Lee, and Peter J Stuckey. Finite domain bounds consistency revisited. In Australasian Joint Conference on Artificial Intelligence, pages 49-58. Springer, 2006.","title":"Finite domain bounds consistency revisited","authors":"Wo Chiu, Warwick Choi, Jimmy Harvey, Ho-Man, Peter J Lee, Stuckey","year":"2006","venue":"Australasian Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chu and Stuckey, 2014] Geoffrey Chu and Peter J. Stuckey. Nested constraint programs. In Principles and Practice of Constraint Programming -20th International Conference, CP 2014, Lyon, France, September 8-12, 2014. Proceed- ings, pages 240-255, 2014.","title":"Nested constraint programs","authors":"Geoffrey Chu, Peter J Stuckey","year":"2014","venue":"Principles and Practice of Constraint Programming -20th International Conference, CP 2014","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Darwiche, 2003] Adnan Darwiche. A differential approach to inference in bayesian networks. J. ACM, 50(3):280- 305, 2003.","title":"A differential approach to inference in bayesian networks","authors":"Adnan Darwiche","year":"2003","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Hnich et al., 2011] Brahim Hnich, Roberto Rossi, S. Arma- gan Tarim, and Steven Prestwich. A survey on CP-AI-OR hybrids for decision making under uncertainty. In Pas- cal van Hentenryck and Michela Milano, editors, Hybrid Optimization: The Ten Years of CPAIOR, pages 227-270. Springer, 2011.","title":"A survey on CP-AI-OR hybrids for decision making under uncertainty","authors":"Brahim Hnich, Roberto Rossi, S Armagan Tarim, Steven Prestwich","year":"2011","venue":"Hybrid Optimization: The Ten Years of CPAIOR","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hnich et al., 2012] Brahim Hnich, Roberto Rossi, S. Arma- gan Tarim, and Steven Prestwich. Filtering algorithms for global chance constraints. Artificial Intelligence, 189:69 - 94, 2012.","title":"Filtering algorithms for global chance constraints","authors":"Brahim Hnich, Roberto Rossi, S Armagan Tarim, Steven Prestwich","year":"2012","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Jensen et al., 1994] Frank Jensen, Finn Verner Jensen, and Søren L. Dittmer. From influence diagrams to junction trees. In UAI, pages 367-373.","title":"From influence diagrams to junction trees","authors":"Frank Jensen, Finn Verner Jensen, Søren L Dittmer","year":null,"venue":"UAI","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"Morgan Kaufmann, 1994.","title":null,"authors":"Morgan Kaufmann","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Koller and Friedman, 2009] Daphne Koller and Nir Fried- man. Probabilistic Graphical Models -Principles and Techniques. MIT Press, 2009.","title":"Probabilistic Graphical Models -Principles and Techniques","authors":"Friedman Koller","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Mateescu and Dechter, 2008] Robert Mateescu and Rina Dechter. Mixed deterministic and probabilistic networks. Ann. Math. Artif. Intell., 54(1-3):3-51, 2008.","title":"Mixed deterministic and probabilistic networks","authors":"Robert Mateescu, Rina Dechter","year":"2008","venue":"Ann. Math. Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Moore, 1966] Ramon E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1966.","title":"Interval Analysis","authors":"Ramon E Moore","year":"1966","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Moore, 1979] Ramon E Moore. Methods and applications of interval analysis. SIAM, 1979.","title":"Methods and applications of interval analysis","authors":"Ramon E, Moore","year":"1979","venue":"SIAM","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Pearl, 1989] Judea Pearl. Probabilistic reasoning in intel- ligent systems -networks of plausible inference. Morgan Kaufmann series in representation and reasoning. Morgan Kaufmann, 1989.","title":"Judea Pearl. Probabilistic reasoning in intelligent systems -networks of plausible inference","authors":"Pearl","year":"1989","venue":"Morgan Kaufmann series in representation and reasoning","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Pralet et al., 2007] Cédric Pralet, Gérard Verfaillie, and Thomas Schiex. An algebraic graphical model for deci- sion with uncertainties, feasibilities, and utilities. J. Artif. Int. Res., 29(1):421-489, August 2007.","title":"An algebraic graphical model for decision with uncertainties, feasibilities, and utilities","authors":"Cédric Pralet, Gérard Verfaillie, Thomas Schiex","year":"2007","venue":"J. Artif. Int. Res","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Qi and Poole, 1995] Runping Qi and David Poole. A new method for influence diagram evaluation. Computational Intelligence, 11(3):498-528, 1995.","title":"Runping Qi and David Poole. A new method for influence diagram evaluation","authors":"Poole Qi","year":"1995","venue":"Computational Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Rossi et al., 2008] Roberto Rossi, S. Armagan Tarim, Brahim Hnich, and Steven Prestwich. Cost-Based Domain Filtering for Stochastic Constraint Programming, pages 235-250. Springer Berlin Heidelberg, Berlin, Heidelberg, 2008.","title":"Cost-Based Domain Filtering for Stochastic Constraint Programming","authors":"Roberto Rossi, S Armagan Tarim, Brahim Hnich, Steven Prestwich","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Tarim et al., 2006] Armagan Tarim, Suresh Manandhar, and Toby Walsh. Stochastic constraint programming: A scenario-based approach. Constraints, 11(1):53-80, 2006.","title":"Stochastic constraint programming: A scenario-based approach","authors":"Armagan Tarim, Suresh Manandhar, Toby Walsh","year":"2006","venue":"Constraints","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Walsh, 2002] Toby Walsh. Stochastic constraint program- ming. In ECAI, pages 111-115. IOS Press, 2002.","title":"Stochastic constraint programming","authors":"Toby Walsh","year":"2002","venue":"ECAI","doi":null,"url":null,"internal_url":"/proceedings/2017/751"},{"position":21,"raw":"[Yuan et al., 2010] Changhe Yuan, XiaoJian Wu, and Eric A. Hansen. Solving multistage influence diagrams using branch-and-bound search. In UAI, pages 691-700. AUAI Press, 2010.","title":"Solving multistage influence diagrams using branch-and-bound search","authors":"Changhe Yuan, Xiaojian Wu, Eric A Hansen","year":"2010","venue":"UAI","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}