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A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Author

Listed:
  • Ruth Misener

    (Princeton University
    Imperial College London)

  • Christodoulos A. Floudas

    (Princeton University)

Abstract

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi: 10.1007/s10898-012-9874-7 ), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers.

Suggested Citation

  • Ruth Misener & Christodoulos A. Floudas, 2014. "A Framework for Globally Optimizing Mixed-Integer Signomial Programs," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 905-932, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0396-3
    DOI: 10.1007/s10957-013-0396-3
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    References listed on IDEAS

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    1. Sonia Cafieri & Jon Lee & Leo Liberti, 2010. "On convex relaxations of quadrilinear terms," Journal of Global Optimization, Springer, vol. 47(4), pages 661-685, August.
    2. Wang Yanjun & Li Tao & Liang Zhian, 2009. "A general algorithm for solving Generalized Geometric Programming with nonpositive degree of difficulty," Computational Optimization and Applications, Springer, vol. 44(1), pages 139-158, October.
    3. Pietro Belotti & Sonia Cafieri & Jon Lee & Leo Liberti & Andrew J. Miller, 2013. "On the Composition of Convex Envelopes for Quadrilinear Terms," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 1-16, Springer.
    4. Josef Kallrath, 1999. "Mixed-Integer Nonlinear Programming Applications," Palgrave Macmillan Books, in: Tito A. Ciriani & Stefano Gliozzi & Ellis L. Johnson & Roberto Tadei (ed.), Operational Research in Industry, chapter 3, pages 42-76, Palgrave Macmillan.
    5. Niknam, Taher & Khodaei, Amin & Fallahi, Farhad, 2009. "A new decomposition approach for the thermal unit commitment problem," Applied Energy, Elsevier, vol. 86(9), pages 1667-1674, September.
    6. Hanif Sherali & Evrim Dalkiran & Leo Liberti, 2012. "Reduced RLT representations for nonconvex polynomial programming problems," Journal of Global Optimization, Springer, vol. 52(3), pages 447-469, March.
    7. C. E. Gounaris & C. A. Floudas, 2008. "Convexity of Products of Univariate Functions and Convexification Transformations for Geometric Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 407-427, September.
    8. Michael R. Bussieck & Arne Stolbjerg Drud & Alexander Meeraus, 2003. "MINLPLib—A Collection of Test Models for Mixed-Integer Nonlinear Programming," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 114-119, February.
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    Cited by:

    1. Jesco Humpola & Felipe Serrano, 2017. "Sufficient pruning conditions for MINLP in gas network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 239-261, March.
    2. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.

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