{"type":"ScholarlyArticle","title":"Compact MDDs for Pseudo-Boolean Constraints with At-Most-One Relations in Resource-Constrained Scheduling Problems","authors":[{"name":"Miquel Bofill","slug":"miquel-bofill","given":"Miquel","family":"Bofill","affiliation":"University of Girona , Spain"},{"name":"Jordi Coll","slug":"jordi-coll","given":"Jordi","family":"Coll","affiliation":"University of Girona , Spain"},{"name":"Josep Suy","slug":"josep-suy","given":"Josep","family":"Suy","affiliation":"University of Girona , Spain"},{"name":"Mateu Villaret","slug":"mateu-villaret","given":"Mateu","family":"Villaret","affiliation":"University of Girona , Spain"}],"abstract":"Pseudo-Boolean (PB) constraints are usually encoded into Boolean clauses using compact Binary Decision Diagram (BDD) representations. Although these constraints appear in many problems, they are particularly useful for representing resource constraints in scheduling problems. Sometimes, the Boolean variables in the PB constraints have implicit at-most-one relations. In this work we introduce a way to take advantage of these implicit relations to obtain a compact Multi-Decision Diagram (MDD) representation for those PB constraints. We provide empirical evidence of the usefulness of this technique for some Resource-Constrained Project Scheduling Problem (RCPSP) variants, namely the Multi-Mode RCPSP (MRCPSP) and the RCPSP with Time-Dependent Resource Capacities and Requests (RCPSP/t). The size reduction of the representation of the PB constraints lets us decrease the number of Boolean variables in the encodings by one order of magnitude. We close/certify the optimum of many instances of these problems.","doi":"10.24963/ijcai.2017/78","url":"https://ijcai.org/proceedings/2017/78","pdf":"https://ijcai.org/proceedings/2017/0078.pdf","markdown":"https://ijcai.org/proceedings/2017/78.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/78","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":78,"pages":{"first":555,"last":562},"keywords":["Constraints and Satisfiability: Modeling/Formulation","Planning and Scheduling: Scheduling"],"videos":[],"references":[{"position":1,"raw":"[Abío and Stuckey, 2014] Ignasi Abío and Peter J Stuckey. Encoding linear constraints into SAT. In International Conference on Principles and Practice of Constraint Pro- gramming, pages 75-91. Springer, 2014.","title":"Encoding linear constraints into SAT","authors":"Ignasi Abío, Peter J Stuckey","year":"2014","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Abío et al., 2012] Ignasi Abío, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, and Valentin Mayer- Eichberger. A new look at BDDs for pseudo-Boolean con- straints. Journal of Artificial Intelligence Research, pages 443-480, 2012.","title":"A new look at BDDs for pseudo-Boolean constraints","authors":"Ignasi Abío, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, Valentin Mayer-Eichberger","year":"2012","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Abío et al., 2015] Ignasi Abío, Valentin Mayer-Eichberger, and Peter J Stuckey. Encoding linear constraints with implication chains to CNF. In International Conference on Principles and Practice of Constraint Programming, pages 3-11. Springer, 2015.","title":"Encoding linear constraints with implication chains to CNF","authors":"Ignasi Abío, Valentin Mayer-Eichberger, Peter J Stuckey","year":"2015","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Abío et al., 2016] Ignasi Abío, Graeme Gange, Valentin Mayer-Eichberger, and Peter J Stuckey. On CNF En- codings of Decision Diagrams. In Integration of AI and OR Techniques in Constraint Programming: 13th Inter- national Conference, CPAIOR 2016, Banff, AB, Canada, May 29-June 1, 2016, Proceedings, volume 9676, page 1. Springer, 2016.","title":"On CNF Encodings of Decision Diagrams","authors":"Ignasi Abío, Graeme Gange, Valentin Mayer-Eichberger, Peter J Stuckey","year":"2016","venue":"Integration of AI and OR Techniques in Constraint Programming: 13th International Conference, CPAIOR 2016","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Ansótegui et al., 2011] Carlos Ansótegui, Miquel Bofill, Miquel Palahí, Josep Suy, and Mateu Villaret. Satis- fiability Modulo Theories: An Efficient Approach for the Resource-Constrained Project Scheduling Problem. In Proceedings of the Ninth Symposium on Abstraction, Reformulation, and Approximation (SARA), pages 2-9. AAAI, 2011.","title":"Satisfiability Modulo Theories: An Efficient Approach for the Resource-Constrained Project Scheduling Problem","authors":"Carlos Ansótegui, Miquel Bofill, Miquel Palahí, Josep Suy, Mateu Villaret","year":"2011","venue":"Proceedings of the Ninth Symposium on Abstraction, Reformulation, and Approximation (SARA)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Artigues et al., 2007] Christian Artigues, Sophie Demassey, and Emmanuel Neron. Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Appli- cations. ISTE Ltd., 2007.","title":"Christian Artigues, Sophie Demassey, and Emmanuel Neron","authors":"Artigues","year":"2007","venue":"Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bofill et al., 2016] Miquel Bofill, Jordi Coll, Josep Suy, and Mateu Villaret. Solving the multi-mode resource- constrained project scheduling problem with SMT. In 28th IEEE International Conference on Tools with Artificial In- telligence, ICTAI 2016, San Jose, CA, USA, November 6-8, 2016, pages 239-246, 2016.","title":"Solving the multi-mode resourceconstrained project scheduling problem with SMT","authors":"Miquel Bofill, Jordi Coll, Josep Suy, Mateu Villaret","year":"2016","venue":"28th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2016","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Brucker et al., 1999] Peter Brucker, Andreas Drexl, Rolf Mhring, Klaus Neumann, and Erwin Pesch. Resource- Constrained Project Scheduling: Notation, Classification, Models, and Methods. European Journal of Operational Research, 112(1):3 -41, 1999.","title":"Resource-Constrained Project Scheduling: Notation, Classification, Models, and Methods","authors":"Brucker","year":"1999","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Cire and van Hoeve, 2012] Andre A Cire and Willem Jan van Hoeve. MDD Propagation for Disjunctive Schedul- ing. In International Conference on Automated Planning and Scheduling (ICAPS), pages 11-19, 2012.","title":"MDD Propagation for Disjunctive Scheduling","authors":"Van Cire, ; Hoeve, A Andre, Willem Cire, Jan Van Hoeve","year":"2012","venue":"International Conference on Automated Planning and Scheduling (ICAPS)","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Dutertre and de Moura, 2006] B. Dutertre and L. de Moura. The Yices SMT Solver. Technical report, Computer Sci- ence Laboratory, SRI International, 2006. Available at http://yices.csl.sri.com. [Eén and Sorensson, 2006] Niklas Eén and Niklas Sorens- son. Translating pseudo-boolean constraints into SAT. Journal on Satisfiability, Boolean Modeling and Compu- tation, 2:1-26, 2006.","title":"Translating pseudo-boolean constraints into SAT","authors":"B Dutertre, L De Moura ; Niklas Eén, Niklas Sorensson","year":"2006","venue":"Journal on Satisfiability, Boolean Modeling and Computation","doi":null,"url":"http://yices.csl.sri","internal_url":null},{"position":11,"raw":"[Fulkerson, 1956] Delbert Ray Fulkerson. Note on Dil- worths decomposition theorem for partially ordered sets. In Proc. Amer. Math. Soc, volume 7, pages 701-702, 1956.","title":"Note on Dilworths decomposition theorem for partially ordered sets","authors":"Delbert Ray Fulkerson, Fulkerson","year":"1956","venue":"Proc. Amer. Math. Soc","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Geiger, 2013] Martin Josef Geiger. Iterated variable neigh- borhood search for the resource constrained multi-mode multi-project scheduling problem. CoRR, abs/1310.0602, 2013.","title":"Iterated variable neighborhood search for the resource constrained multi-mode multi-project scheduling problem","authors":"Josef Martin, Geiger","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hartmann, 2013] Sönke Hartmann. Project scheduling with resource capacities and requests varying with time: a case study. Flexible Services and Manufacturing Journal, 25(1- 2):74-93, 2013.","title":"Project scheduling with resource capacities and requests varying with time: a case study","authors":"Sönke Hartmann, Hartmann","year":"2013","venue":"Flexible Services and Manufacturing Journal","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hartmann, 2015] Sönke Hartmann. Time-varying resource requirements and capacities. In Handbook on Project Management and Scheduling Vol. 1, pages 163-176. Springer, 2015.","title":"Time-varying resource requirements and capacities","authors":"Sönke Hartmann","year":"2015","venue":"Handbook on Project Management and Scheduling","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Kolisch and Sprecher, 1997] Rainer Kolisch and Arno Sprecher. PSPLIB -A Project Scheduling Problem Library. European Journal of Operational Research, 96(1):205-216, 1997.","title":"PSPLIB -A Project Scheduling Problem Library","authors":"Sprecher Kolisch, Rainer Kolisch, Arno Sprecher","year":"1997","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Koné et al., 2011] Oumar Koné, Christian Artigues, Pierre Lopez, and Marcel Mongeau. Event-Based MILP Mod- els for Resource-Constrained Project Scheduling Prob- lems. Computers & Operations Research, 38:3-13, Jan- uary 2011.","title":"Event-Based MILP Models for Resource-Constrained Project Scheduling Problems","authors":"Oumar Koné, Christian Artigues, Pierre Lopez, Marcel Mongeau","year":"2011","venue":"Computers & Operations Research","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Schutt et al., 2013] Andreas Schutt, Thibaut Feydy, and Pe- ter J Stuckey. Explaining time-table-edge-finding propa- gation for the cumulative resource constraint. In Interna- tional Conference on AI and OR Techniques in Constriant Programming for Combinatorial Optimization Problems, pages 234-250. Springer, 2013.","title":"Explaining time-table-edge-finding propagation for the cumulative resource constraint","authors":"Andreas Schutt, Thibaut Feydy, Peter J Stuckey","year":"2013","venue":"International Conference on AI and OR Techniques in Constriant Programming for Combinatorial Optimization Problems","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Srinivasan et al., 1990] Arvind Srinivasan, Timothy Ham, Sharad Malik, and Robert K Brayton. Algorithms for dis- crete function manipulation. In Computer-Aided Design, 1990. ICCAD-90. Digest of Technical Papers., 1990 IEEE International Conference on, pages 92-95. IEEE, 1990.","title":"Algorithms for discrete function manipulation","authors":"Arvind Srinivasan, Timothy Ham, Sharad Malik, Robert K Brayton","year":"1990","venue":"IEEE International Conference on","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Szeredi and Schutt, 2016] Ria Szeredi and Andreas Schutt. Modelling and solving multi-mode resource-constrained project scheduling. In International Conference on Princi- ples and Practice of Constraint Programming, pages 483- 492. Springer, 2016.","title":"Modelling and solving multi-mode resource-constrained project scheduling","authors":"Schutt Szeredi, Ria Szeredi, Andreas Schutt","year":"2016","venue":"International Conference on Principles and Practice of Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Van Peteghem and Vanhoucke, 2014] Vincent Van Pe- teghem and Mario Vanhoucke. An experimental investigation of metaheuristics for the multi-mode resource-constrained project scheduling problem on new dataset instances. European Journal of Operational Research, 235(1):62-72, 2014.","title":"Vincent Van Peteghem and Mario Vanhoucke. An experimental investigation of metaheuristics for the multi-mode resource-constrained project scheduling problem on new dataset instances","authors":"Van Peteghem, Vanhoucke","year":"2014","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Vilím et al., 2015] Petr Vilím, Philippe Laborie, and Paul Shaw. Failure-directed search for constraint-based scheduling. In Integration of AI and OR Techniques in Constraint Programming, pages 437-453. Springer, 2015.","title":"Failure-directed search for constraint-based scheduling","authors":"Vilím","year":"2015","venue":"Integration of AI and OR Techniques in Constraint Programming","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Zhu et al., 2006] Guidong Zhu, Jonathan F. Bard, and Gang Yu. A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem. IN- FORMS J. on Computing, 18(3):377-390, January 2006.","title":"A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem","authors":"Zhu","year":"2006","venue":"IN-FORMS J. on Computing","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}