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GloMIQO: Global mixed-integer quadratic optimizer

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  • Ruth Misener
  • Christodoulos Floudas

Abstract

This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$ -global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2, Couenne 0.4, LindoGLOBAL 6.1.1.588, and SCIP 2.1.0. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Ruth Misener & Christodoulos Floudas, 2013. "GloMIQO: Global mixed-integer quadratic optimizer," Journal of Global Optimization, Springer, vol. 57(1), pages 3-50, September.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:1:p:3-50
    DOI: 10.1007/s10898-012-9874-7
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    References listed on IDEAS

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    1. Maranas, C. D. & Androulakis, I. P. & Floudas, C. A. & Berger, A. J. & Mulvey, J. M., 1997. "Solving long-term financial planning problems via global optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1405-1425, June.
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    Cited by:

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    2. Emily Speakman & Jon Lee, 2018. "On branching-point selection for trilinear monomials in spatial branch-and-bound: the hull relaxation," Journal of Global Optimization, Springer, vol. 72(2), pages 129-153, October.
    3. Wei Xia & Juan C. Vera & Luis F. Zuluaga, 2020. "Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 40-56, January.
    4. Yanchao Liu, 2019. "A Progressive Motion-Planning Algorithm and Traffic Flow Analysis for High-Density 2D Traffic," Transportation Science, INFORMS, vol. 53(6), pages 1501-1525, November.
    5. Frank, Stephen M. & Rebennack, Steffen, 2015. "Optimal design of mixed AC–DC distribution systems for commercial buildings: A Nonconvex Generalized Benders Decomposition approach," European Journal of Operational Research, Elsevier, vol. 242(3), pages 710-729.
    6. Peter Kirst & Oliver Stein & Paul Steuermann, 2015. "Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 591-616, July.
    7. 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.
    8. Timo Berthold, 2018. "A computational study of primal heuristics inside an MI(NL)P solver," Journal of Global Optimization, Springer, vol. 70(1), pages 189-206, January.
    9. Steffen Rebennack & Vitaliy Krasko, 2020. "Piecewise Linear Function Fitting via Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 507-530, April.
    10. Subramanian, Avinash S.R. & Kannan, Rohit & Holtorf, Flemming & Adams, Thomas A. & Gundersen, Truls & Barton, Paul I., 2023. "Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm," Energy, Elsevier, vol. 284(C).

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