{"type":"ScholarlyArticle","title":"Acquiring Integer Programs from Data","authors":[{"name":"Mohit Kumar","slug":"mohit-kumar","given":"Mohit","family":"Kumar","affiliation":"KU Leuven"},{"name":"Stefano Teso","slug":"stefano-teso","given":"Stefano","family":"Teso","affiliation":"KU Leuven"},{"name":"Luc De Raedt","slug":"luc-de-raedt","given":"Luc","family":"de Raedt","affiliation":"KU Leuven"}],"abstract":"Integer programming (IP) is widely used within operations research to model and solve complex combinatorial problems such as personnel rostering and assignment problems.  Modelling such problems is difficult  for  non-experts  and  expensive  when  hiring domain experts to perform the modelling.  For many  tasks,  however,  examples  of  working  solutions are readily available.  We propose ARNOLD, an approach that partially automates the modelling step  by  learning  an  integer  program  from  example  solutions. Contrary  to  existing  alternatives, ARNOLD natively handles multi-dimensional quantities  and  non-linear  operations,  which  are  at  the core of IP problems, and it only requires examples of feasible solution.  The main challenge is to efficiently  explore  the  space  of  possible  programs. Our  approach  pairs  a  general-to-specific  traversal strategy with a nested lexicographic ordering in order to prune large portions of the space of candidate  constraints  while  avoiding  visiting  the  same candidate multiple times. Our empirical evaluation shows that ARNOLD can acquire models for a number of realistic benchmark problems","doi":"10.24963/ijcai.2019/158","url":"https://ijcai.org/proceedings/2019/158","pdf":"https://ijcai.org/proceedings/2019/0158.pdf","markdown":"https://ijcai.org/proceedings/2019/158.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/158","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Constraints and SAT","track":"Main track","number":158,"pages":{"first":1130,"last":1136},"keywords":["Constraints and SAT: Constraint Satisfaction","Constraints and SAT: Modeling;Formulation","Constraints and SAT: Constraints and Data Mining ; Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Arcangioli et al., 2016] Robin Arcangioli, Christian Bessiere, and Nadjib Lazaar. Multiple constraint aqui- sition. In IJCAI: International Joint Conference on Artificial Intelligence, pages 698-704, 2016.","title":"Robin Arcangioli, Christian Bessiere, and Nadjib Lazaar. Multiple constraint aquisition","authors":"Arcangioli","year":"2016","venue":"IJCAI: International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Beldiceanu and Simonis, 2012] Nicolas Beldiceanu and Helmut Simonis. A Model Seeker: extracting global con- straint models from positive examples. pages 141-157, 2012.","title":"A Model Seeker: extracting global constraint models from positive examples","authors":"Simonis Beldiceanu, Nicolas Beldiceanu, Helmut Simonis","year":"2012","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bessiere et al., 2017] Christian Bessiere, Frédéric Koriche, Nadjib Lazaar, and Barry O'Sullivan. Constraint acquisi- tion. Artificial Intelligence, 244:315-342, 2017.","title":"Christian Bessiere, Frédéric Koriche, Nadjib Lazaar, and Barry O'Sullivan. Constraint acquisition","authors":"Bessiere","year":"2017","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Burke et al., 2004] Edmund K Burke, Patrick De Caus- maecker, Greet Vanden Berghe, and Hendrik Van Lan- deghem. The state of the art of nurse rostering. Journal of scheduling, 7(6):441-499, 2004.","title":"The state of the art of nurse rostering","authors":"Edmund K Burke, Patrick De Causmaecker, Greet Vanden Berghe, Hendrik Van Landeghem","year":"2004","venue":"Journal of scheduling","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[De Raedt and Dehaspe, 1997] Luc De Raedt and Luc De- haspe. Clausal discovery. Machine Learning, 26(2-3):99- 146, 1997.","title":"Luc De Raedt and Luc Dehaspe","authors":"De Raedt, Dehaspe","year":"1997","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[De Raedt et al., 2018] Luc De Raedt, Andrea Passerini, and Stefano Teso. Learning constraints from examples. In Pro- ceedings of AAAI'18, 2018.","title":"Learning constraints from examples","authors":"De Raedt","year":"2018","venue":"Proceedings of AAAI'18","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[De Raedt, 2008] Luc De Raedt. Logical and relational learning. Springer Science & Business Media, 2008.","title":"Logical and relational learning","authors":"De Raedt, ; Luc, De Raedt","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Jiang et al., 2013] Chuntao Jiang, Frans Coenen, and Michele Zito. A survey of frequent subgraph min- ing algorithms. The Knowledge Engineering Review, 28(1):75-105, 2013.","title":"A survey of frequent subgraph mining algorithms","authors":"Chuntao Jiang, Frans Coenen, Michele Zito","year":"2013","venue":"The Knowledge Engineering Review","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Kumar et al., 2018] Mohit Kumar, Stefano Teso, and Luc De Raedt. Constraint learning using tensors. In EURO, 2018.","title":"Constraint learning using tensors","authors":"Mohit Kumar, Stefano Teso, Luc De, Raedt","year":"2018","venue":"EURO","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Lloyd et al., 2014] James Robert Lloyd, David Duvenaud, Roger Grosse, Joshua Tenenbaum, and Zoubin Ghahra- mani. Automatic construction and natural-language de- scription of nonparametric regression models. In Twenty- eighth AAAI conference on artificial intelligence, 2014.","title":"Automatic construction and natural-language description of nonparametric regression models","authors":"James Robert, Lloyd, David Duvenaud, Roger Grosse, Joshua Tenenbaum, Zoubin Ghahramani","year":"2014","venue":"Twentyeighth AAAI conference on artificial intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Nemhauser and Wolsey, 1989] G. L. Nemhauser and L. A. Wolsey. Optimization. chapter Integer Programming, pages 447-527. Elsevier North-Holland, Inc., New York, NY, USA, 1989.","title":"Optimization. chapter Integer Programming","authors":"G L Nemhauser, L A Wolsey","year":"1989","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Nethercote et al., 2007] Nicholas Nethercote, Peter J Stuckey, Ralph Becket, Sebastian Brand, Gregory J Duck, and Guido Tack. MiniZinc: Towards a standard CP modelling language. In International Conference on Principles and Practice of Constraint Programming, pages 529-543. Springer, 2007.","title":"MiniZinc: Towards a standard CP modelling language","authors":"Nicholas Nethercote, J Peter, Ralph Stuckey, Sebastian Becket, Gregory J Brand, Guido Duck, Tack","year":"2007","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Pawlak, 2019] Tomasz P Pawlak. Synthesis of mathe- matical programming models with one-class evolutionary strategies. Swarm and evolutionary computation, 44:335- 348, 2019.","title":"Synthesis of mathematical programming models with one-class evolutionary strategies","authors":"P Tomasz, Pawlak","year":"2019","venue":"Swarm and evolutionary computation","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Schulte et al., 2006] Christian Schulte, Guido Tack, and Mikael Z Lagerkvist. Modeling and Programming with Gecode. 2006.","title":"Modeling and Programming with Gecode","authors":"Schulte","year":"2006","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Smet et al., 2013] Pieter Smet, Patrick De Causmaecker, Burak Bilgin, and Greet Vanden Berghe. Nurse roster- ing: a complex example of personnel scheduling with per- spectives. In Automated Scheduling and Planning, pages 129-153. Springer, 2013.","title":"Nurse rostering: a complex example of personnel scheduling with perspectives","authors":"Pieter Smet, Patrick De Causmaecker, Burak Bilgin, Greet Vanden, Berghe","year":"2013","venue":"Automated Scheduling and Planning","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Tillé, 2011] Yves Tillé. Sampling algorithms. Springer, 2011.","title":"Sampling algorithms","authors":"Yves Tillé","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Todorovski and Dzeroski, 1997] Ljupco Todorovski and Saso Dzeroski. Declarative bias in equation discovery. In ICML, pages 376-384, 1997.","title":"Declarative bias in equation discovery","authors":"Dzeroski Todorovski, Ljupco Todorovski, Saso Dzeroski","year":"1997","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Tsouros et al., 2018] Dimosthenis C Tsouros, Kostas Ster- giou, and Panagiotis G Sarigiannidis. Efficient methods for constraint acquisition. In International Conference on Principles and Practice of Constraint Programming, pages 373-388. Springer, 2018.","title":"Efficient methods for constraint acquisition","authors":"Kostas Dimosthenis C Tsouros, Panagiotis G Stergiou, Sarigiannidis","year":"2018","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}