Skip to main content

Experiments with a Feasibility Pump Approach for Nonconvex MINLPs

  • Conference paper
Experimental Algorithms (SEA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6049))

Included in the following conference series:

Abstract

We present a new Feasibility Pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programming problems. Differences with the previously proposed Feasibility Pump algorithms and difficulties arising from nonconvexities in the models are extensively discussed. The main methodological innovations of this variant are: (a) the first subproblem is a nonconvex continuous Nonlinear Program, which is solved using global optimization techniques; (b) the solution method for the second subproblem is complemented by a tabu list. We exhibit computational results showing the good performance of the algorithm on instances taken from the MINLPLib.

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

Access this chapter

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. Glover, F., Kochenberger, G. (eds.): Handbook of Metaheuristics. Kluwer Academic Publishers, Dordrecht (2003)

    MATH  Google Scholar 

  2. Fischetti, M., Glover, F., Lodi, A.: The feasibility pump. Mathematical Programming 104, 91–104 (2004)

    Article  MathSciNet  Google Scholar 

  3. Bertacco, L., Fischetti, M., Lodi, A.: A feasibility pump heuristic for general mixed-integer problems. Discrete Optimization 4, 63–76 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Achterberg, T., Berthold, T.: Improving the feasibility pump. Discrete Optimization 4, 77–86 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fischetti, M., Lodi, A.: Local branching. Mathematical Programming 98, 23–47 (2002)

    Article  MathSciNet  Google Scholar 

  6. Danna, E., Rothberg, E., Pape, C.L.: Exploiting relaxation induced neighborhoods to improve MIP solutions. Mathematical Programming 102, 71–90 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Duran, M., Grossmann, I.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming 36, 307–339 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bonami, P., Cornuéjols, G., Lodi, A., Margot, F.: A feasibility pump for mixed integer nonlinear programs. Mathematical Programming 119, 331–352 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Abhishek, K.: Topics in Mixed Integer Nonlinear Programming. PhD thesis, Lehigh University (2008)

    Google Scholar 

  10. Bonami, P., Gonçalves, J.: Primal heuristics for mixed integer nonlinear programs. Technical report, IBM Research Report RC24639 (2008)

    Google Scholar 

  11. Vavasis, S.: Nonlinear Optimization: Complexity Issues. Oxford University Press, Oxford (1991)

    MATH  Google Scholar 

  12. Liberti, L., Nannicini, G., Mladenovic, N.: A good recipe for solving MINLPs. In: Maniezzo, V., Stützle, T., Voß, S. (eds.) Matheuristics. Annals of Information Systems, vol. 10, pp. 231–244. Springer, US (2008)

    Chapter  Google Scholar 

  13. Nannicini, G., Belotti, P., Liberti, L.: A local branching heuristic for MINLPs. ArXiv, paper 0812.2188 (2009)

    Google Scholar 

  14. Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Mathematical Programming 66, 327–349 (1994)

    Article  MathSciNet  Google Scholar 

  15. Fletcher, R., Leyffer, S.: Numerical experience with lower bounds for MIQP branch-and-bound. SIAM Journal of Optimization 8, 604–616 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Westerlund, T., Pörn, R.: Solving pseudo-convex mixed integer optimization problems by cutting plane techniques. Optimization and Engineering 3, 235–280 (2002)

    Article  Google Scholar 

  17. Westerlund, T.: Some transformation techniques in global optimization. In: Liberti, L., Maculan, N. (eds.) Global Optimization: from Theory to Implementation, pp. 45–74. Springer, Berlin (2006)

    Google Scholar 

  18. ARKI Consulting and Development. SBB Release Notes (2002)

    Google Scholar 

  19. Abhishek, K., Leyffer, S., Linderoth, J.: FilMINT: An outer-approximation based solver for nonlinear mixed-integer programs. Technical report, Argonne National Laboratory (2007)

    Google Scholar 

  20. Fischetti, M., Salvagnin, D.: Feasibility pump 2.0. Technical report, DEI, University of Padova (September 2008)

    Google Scholar 

  21. Schoen, F.: Two-phase methods for global optimization. In: Pardalos, P., Romeijn, H. (eds.) Handbook of Global Optimization, vol. 2, pp. 151–177. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  22. Fourer, R., Gay, D., Kernighan, B.: AMPL: A Modeling Language for Mathematical Programming, 2nd edn. Duxbury Press/Brooks/Cole Publishing Co. (2003)

    Google Scholar 

  23. Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming 106, 25–57 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  24. Ilog-Cplex (v. 11.0), http://www.ilog.com/products/cplex

  25. D’Ambrosio, C., Frangioni, A., Liberti, L., Lodi, A.: On Interval-subgradient and No-good Cuts. Technical report, Dipartimento di Elettronica, Informatica e Sistemistica, Università di Bologna (2009)

    Google Scholar 

  26. Liberti, L., Cafieri, S., Tarissan, F.: Reformulations in mathematical programming: a computational approach. In: Abraham, A., Hassanien, A.E., Siarry, P., Engelbrecht, A. (eds.) Foundations of Computational Intelligence. SCI, vol. 3, pp. 153–234. Springer, Berlin (2009)

    Chapter  Google Scholar 

  27. Liberti, L.: Writing global optimization software. In: Liberti, L., Maculan, N. (eds.) Global Optimization: from Theory to Implementation, pp. 211–262. Springer, Berlin (2006)

    Google Scholar 

  28. Bussieck, M., Drud, A., Meeraus, A.: MINLPLib - a collection of test models for mixed-integer nonlinear programming. INFORMS Journal on Computing 15, 114–119 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

D’Ambrosio, C., Frangioni, A., Liberti, L., Lodi, A. (2010). Experiments with a Feasibility Pump Approach for Nonconvex MINLPs. In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13193-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13192-9

  • Online ISBN: 978-3-642-13193-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics