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

  • Bhagyesh V. PatilEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

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.

Keywords

Test Problem Equality Constraint MINLP Problem Consistency Technique Constraint Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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).

References

  1. 1.
    The Mathworks Inc., MATLAB version 7.1 (R14), Natick, MA (2005)Google Scholar
  2. 2.
    D’Ambrosio, C., Lodi, A.: Mixed integer nonlinear programming tools: an updated practical overview. Annals of Operations Research 204(1), 301–320 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Floudas, C.A.: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, New York (1995)zbMATHGoogle Scholar
  4. 4.
    Garloff, J.: The Bernstein algorithm. Interval Computations 2, 154–168 (1993)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hansen, E.R., Walster, G.W.: Global Optimization Using Interval Analysis, 2nd edn. Marcel Dekker, New York (2005)zbMATHGoogle Scholar
  6. 6.
    Hooker, J.: Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. Wiley, New York (2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    Kuipers, K.: Branch-and-bound solver for mixed-integer nonlinear optimization problems. MATLAB Central for File Exchange. Accessed 18 Dec. 2009Google Scholar
  8. 8.
    GAMS Minlp Model Library: http://www.gamsworld.org/minlp/minlplib/minlpstat.htm. Accessed 20 March 2015
  9. 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)MathSciNetGoogle Scholar
  10. 10.
    NEOS server for optimization.: http://www.neos-server.org/neos/solvers/index.html. Accessed 20 March 2015
  11. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Cambridge Centre for Advanced Research in Energy Efficiency in SingaporeSingaporeSingapore

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