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Decomposition Based on Decision Diagrams

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Integration of AI and OR Techniques in Constraint Programming (CPAIOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9676))

Abstract

In recent years, decision diagrams (DDs) have proven useful for solving a variety of optimization problems, often closing long-standing instances from classical benchmarks. This success is primarily driven by a DDs ability to capture structure. This paper exploits this characteristic and proposes a novel solution method which decomposes a problem into highly-structured portions, where the solution set of each portion can be compactly represented using a DD. This technique is applied to a special case of the independent set problem and to unconstrained binary quadratic programming. Preliminary computational results suggest that the proposed decomposition approach can improve upon both standard integer programming models and a single DD approach.

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References

  1. Akers, S.B.: Binary decision diagrams. IEEE Trans. Comput. C–27(6), 509–516 (1978)

    Article  MATH  Google Scholar 

  2. Aldecoa, R., Marín, I.: Surprise maximization reveals the community structure of complex networks. Scientific Reports 3(1060) (2013)

    Google Scholar 

  3. Andersen, H.R., Hadzic, T., Hooker, J.N., Tiedemann, P.: A constraint store based on multivalued decision diagrams. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 118–132. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Balas, E.: Projection, lifting and extended formulation in integer and combinatorial optimization. Ann. Oper. Res. 140(1), 125–161 (2005). http://dx.doi.org/10.1007/s10479-005-3969-1

    Article  MathSciNet  MATH  Google Scholar 

  5. Behle, M.: Binary Decision Diagrams and Integer Programming. Ph.D. thesis, MaxPlanck Institute for Computer Science (2007)

    Google Scholar 

  6. Belik, I.: The analysis of split graphs in social networks based on the k-cardinality assignment problem. NHH Dept. of Business and Management Science Discussion Paper No. 2014/8, (February 2014). http://dx.doi.org/10.2139/ssrn.2405010

  7. Bergman, D.: New Techniques for Discrete Optimization. Ph.D. thesis, Tepper School of Business, Carnegie Mellon University (2013)

    Google Scholar 

  8. Bergman, D., Cire, A.A., van Hoeve, W.-J.: Discrete optimization with decision diagrams. INFORMS J. Comput. (2015, to appear)

    Google Scholar 

  9. Bergman, D., Cire, A.A., van Hoeve, W.-J., Hooker, J.N.: Optimization bounds from binary decision diagrams. INFORMS J. Comput. 26(2), 253–268 (2014)

    Article  MathSciNet  Google Scholar 

  10. Bergman, D., Cire, A., van Hoeve, W.J., Yunes, T.: Bdd-based heuristics for binary optimization. J. Heuristics 20(2), 211–234 (2014)

    Article  Google Scholar 

  11. Bergman, D., van Hoeve, W.-J., Hooker, J.N.: Manipulating MDD relaxations for combinatorial optimization. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 20–35. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Bliek, C., Bonami, P., Lodi, A.: Solving mixed-integer quadratic programming problems with IBM-CPLEX: a progress report. In: Proceedings of the Twenty-Sixth RAMP Symposium (2001)

    Google Scholar 

  13. Bramoull, Y., Kranton, R.: Public goods in networks. J. Econ. Theor. 135(1), 478–494 (2007). http://www.sciencedirect.com/science/article/pii/S0022053106001220

    Article  MathSciNet  MATH  Google Scholar 

  14. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. C–35, 677–691 (1986)

    Article  MATH  Google Scholar 

  15. Cire, A.A., van Hoeve, W.J.: Multivalued decision diagrams for sequencing problems. Oper. Res. 61(6), 1411–1428 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bergman, D., Cire, A.A., van Hoeve, W.-J.: MDD propagation for sequence constraints. J. Artif. Intell. Res. 50, 697–722 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Haus, U.U., Michini, C.: Representations of all solutions of boolean programming problems. In: ISAIM (2014)

    Google Scholar 

  18. Hu, A.J.: Techniques for efficient formal verification using binary decision diagrams. Thesis CS-TR-95-1561, Stanford University, Department of Computer Science, December 1995

    Google Scholar 

  19. Johnson, M., Paulusma, D., van Leeuwen, E.J.: Algorithms to measure diversity and clustering in social networks through dot product graphs. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) Algorithms and Computation. LNCS, vol. 8283, pp. 130–140. Springer, Heidelberg (2013). http://dx.doi.org/10.1007/978-3-642-45030-3_13

    Chapter  Google Scholar 

  20. Judd, S., Kearns, M., Vorobeychik, Y.: Behavioral conflict and fairness in social networks. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) Internet and Network Economics. LNCS, vol. 7090, pp. 242–253. Springer, Heidelberg (2011). http://dx.doi.org/10.1007/978-3-642-25510-6_21

    Chapter  Google Scholar 

  21. Östergård, P.R.: A fast algorithm for the maximum clique problem. Discrete Appl. Math. 120(13), 197–207 (2002). http://www.sciencedirect.com/science/article/pii/S0166218X01002906. Special issue devoted to the 6th Twente Workshop on Graphs and Combinatorial Optimization

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), Discovery Grant.

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Authors and Affiliations

  1. Department of Operations and Information Management, University of Connecticut, Mansfield, USA

    David Bergman

  2. Department of Management, University of Toronto Scarborough, Toronto, Canada

    Andre A. Cire

Authors
  1. David Bergman
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  2. Andre A. Cire
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Corresponding author

Correspondence to David Bergman .

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Editors and Affiliations

  1. Université Laval, Quebec, Québec, Canada

    Claude-Guy Quimper

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Bergman, D., Cire, A.A. (2016). Decomposition Based on Decision Diagrams. In: Quimper, CG. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2016. Lecture Notes in Computer Science(), vol 9676. Springer, Cham. https://doi.org/10.1007/978-3-319-33954-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-33954-2_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33953-5

  • Online ISBN: 978-3-319-33954-2

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