Skip to main content
SpringerLink
Log in

The Bernstein Branch-and-Prune Algorithm for Constrained Global Optimization of Multivariate Polynomial MINLPs

  • Conference paper
  • First Online:
Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

  • 718 Accesses

Abstract

This paper address the global optimization problem of polynomial mixed-integer nonlinear programs (MINLPs). A improved branch-and-prune algorithm based on the Bernstein form is proposed to solve such MINLPs. The algorithm use a new pruning feature based on the Bernstein form, called the Bernstein box and Bernstein hull consistency. The proposed algorithm is tested on a set of 16 MINLPs chosen from the literature. The efficacy of the proposed algorithm is brought out via numerical studies with the previously reported Bernstein algorithms and several state-of-the-art MINLP solvers.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Similar content being viewed by others

Notes

  1. 1.

    All the solver were executed in their default options for the 16 test problems considered.

References

  1. The Mathworks Inc., MATLAB version 7.1 (R14), Natick, MA (2005)

    Google Scholar 

  2. D’Ambrosio, C., Lodi, A.: Mixed integer nonlinear programming tools: an updated practical overview. Annals of Operations Research 204(1), 301–320 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Floudas, C.A.: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, New York (1995)

    MATH  Google Scholar 

  4. Garloff, J.: The Bernstein algorithm. Interval Computations 2, 154–168 (1993)

    MathSciNet  MATH  Google Scholar 

  5. Hansen, E.R., Walster, G.W.: Global Optimization Using Interval Analysis, 2nd edn. Marcel Dekker, New York (2005)

    MATH  Google Scholar 

  6. Hooker, J.: Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. Wiley, New York (2000)

    Book  MATH  Google Scholar 

  7. Kuipers, K.: Branch-and-bound solver for mixed-integer nonlinear optimization problems. MATLAB Central for File Exchange. Accessed 18 Dec. 2009

    Google Scholar 

  8. GAMS Minlp Model Library: http://www.gamsworld.org/minlp/minlplib/minlpstat.htm. Accessed 20 March 2015

  9. Nataraj, P.S.V., Arounassalame, M.: An interval Newton method based on the Bernstein form for bounding the zeros of polynomial systems. Reliable Comput. 15(2), 109–119 (2011)

    MathSciNet  Google Scholar 

  10. NEOS server for optimization.: http://www.neos-server.org/neos/solvers/index.html. Accessed 20 March 2015

  11. Patil, B.V., Nataraj, P.S.V.: An improved Bernstein global optimization algorithm for MINLP problems with application in process industry. Math. Comput. Sci. 8(3–4), 357–377 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Patil, B.V., Nataraj, P.S.V., Bhartiya, S.: Global optimization of mixed-integer nonlinear (polynomial) programming problems: the Bernstein polynomial approach. Computing 94(2–4), 325–343 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhu, W.: A provable better branch and bound method for a nonconvex integer quadratic programming problem. J. Comput. Syst. Sci. 70(1), 107–117 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgement

This work was funded by the Singapore National Research Foundation (NRF) under its Campus for Research Excellence And Technological Enterprise (CREATE) programme and the Cambridge Centre for Advanced Research in Energy Efficiency in Singapore (CARES).

Author information

Authors and Affiliations

  1. Cambridge Centre for Advanced Research in Energy Efficiency in Singapore, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Bhagyesh V. Patil

Authors
  1. Bhagyesh V. Patil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bhagyesh V. Patil .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Patil, B.V. (2016). The Bernstein Branch-and-Prune Algorithm for Constrained Global Optimization of Multivariate Polynomial MINLPs. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32859-1_48

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation