Skip to main content
SpringerLink
Log in

The IntSat Method for Integer Linear Programming

  • Conference paper
Principles and Practice of Constraint Programming (CP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8656))

Abstract

Conflict-Driven Clause-Learning (CDCL) SAT solvers can automatically solve very large real-world problems. To go beyond, and in particular in order to solve and optimize problems involving linear arithmetic constraints, here we introduce IntSat, a generalization of CDCL to Integer Linear Programming (ILP). Our simple 1400-line C++ prototype IntSat implementation already shows some competitiveness with commercial solvers such as CPLEX or Gurobi. Here we describe this new IntSat ILP solving method, show how it can be implemented efficiently, and discuss a large list of possible enhancements and extensions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abío, I., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., Stuckey, P.J.: To Encode or to Propagate? The Best Choice for Each Constraint in SAT. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 97–106. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  2. Barrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of Satisfiability, pp. 825–885. IOS Press (2009)

    Google Scholar 

  3. Biere, A. (2010), Lingeling SAT Solver, http://fmv.jku.at/lingeling/

  4. Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T.: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (February 2009)

    Google Scholar 

  5. Bixby, B.: Presentation: 1000X MIP Tricks, Bill Cunninghams 65th (June 12, 2012)

    Google Scholar 

  6. Bofill, M., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: The Barcelogic SMT Solver. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 294–298. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Chvátal, V.: Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Mathematics 4(4), 305–337 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The MathSAT5 SMT Solver. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 93–107. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  9. Cotton, S.: Natural domain SMT: A preliminary assessment. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 77–91. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. de Moura, L., Bjorner, N.: Z3: An Efficient SMT Solver. In: Technical report, Microsoft Research, Redmond (2007), http://research.microsoft.com/projects/z3

  11. Dutertre, B., de Moura, L.: The YICES SMT Solver. In: Technical report, Computer Science Laboratory, SRI International (2006), http://yices.csl.sri.com

  12. Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Gomory, R.E.: Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society 64(5), 275–278 (1973)

    Article  MathSciNet  Google Scholar 

  14. Jovanovic, D., de Moura, L.M.: Cutting to the chase - solving linear integer arithmetic. J. Autom. Reasoning 51(1), 79–108 (2013)

    Article  Google Scholar 

  15. Korovin, K., Voronkov, A.: Solving systems of linear inequalities by bound propagation. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 369–383. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Marques-Silva, J., Sakallah, K.A.: GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)

    Article  MathSciNet  Google Scholar 

  17. McMillan, K.L., Kuehlmann, A., Sagiv, M.: Generalizing DPLL to Richer Logics. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 462–476. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Nieuwenhuis, R.: SAT and SMT Are Still Resolution: Questions and Challenges. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 10–13. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Nieuwenhuis, R.: Intsat source code, makefile, benchmarks and benchmark generators (2014), http://www.lsi.upc.edu/~roberto/IntSatCP2014.tgz

  20. Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT Modulo Theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(T). Journal of the ACM, JACM 53(6), 937–977 (2006)

    Article  MathSciNet  Google Scholar 

  21. Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation = lazy clause generation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 544–558. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Pipatsrisawat, K., Darwiche, A.: On modern clause-learning satisfiability solvers. Journal of Automated Reasoning 44(3), 277–301 (2010)

    Article  MathSciNet  Google Scholar 

  23. Schrijver, A.: Theory of Linear and Integer Programming. John Wiley & Sons, Chichester (1986)

    MATH  Google Scholar 

  24. Tamura, N., Taga, A., Kitagawa, S., Banbara, M.: Compiling finite linear CSP into SAT. Constraints 14(2), 254–272 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Barcelogic.com and Technical University of Catalonia (UPC), Barcelona, Spain

    Robert Nieuwenhuis

Authors
  1. Robert Nieuwenhuis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Insight Centre for Data Analytics, School of Computer Science and IT, University College Cork, Western Road, Cork, Ireland

    Barry O’Sullivan

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Nieuwenhuis, R. (2014). The IntSat Method for Integer Linear Programming. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10428-7_42

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10427-0

  • Online ISBN: 978-3-319-10428-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation