IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v252y2016i3p701-727.html
   My bibliography  Save this article

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Author

Listed:
  • Boukouvala, Fani
  • Misener, Ruth
  • Floudas, Christodoulos A.

Abstract

This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:3:p:701-727
    DOI: 10.1016/j.ejor.2015.12.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171501142X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.12.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Brekelmans, Ruud & Driessen, Lonneke & Hamers, Herbert & den Hertog, Dick, 2005. "Constrained optimization involving expensive function evaluations: A sequential approach," European Journal of Operational Research, Elsevier, vol. 160(1), pages 121-138, January.
    3. Marco Locatelli, 2014. "A technique to derive the analytical form of convex envelopes for some bivariate functions," Journal of Global Optimization, Springer, vol. 59(2), pages 477-501, July.
    4. Josef Kallrath & Steffen Rebennack, 2014. "Cutting ellipses from area-minimizing rectangles," Journal of Global Optimization, Springer, vol. 59(2), pages 405-437, July.
    5. Harjunkoski, Iiro & Westerlund, Tapio & Porn, Ray & Skrifvars, Hans, 1998. "Different transformations for solving non-convex trim-loss problems by MINLP," European Journal of Operational Research, Elsevier, vol. 105(3), pages 594-603, March.
    6. Felipe Viana & Raphael Haftka & Layne Watson, 2013. "Efficient global optimization algorithm assisted by multiple surrogate techniques," Journal of Global Optimization, Springer, vol. 56(2), pages 669-689, June.
    7. A. Custódio & J. Madeira, 2015. "GLODS: Global and Local Optimization using Direct Search," Journal of Global Optimization, Springer, vol. 62(1), pages 1-28, May.
    8. Regis, Rommel G. & Shoemaker, Christine A., 2007. "Parallel radial basis function methods for the global optimization of expensive functions," European Journal of Operational Research, Elsevier, vol. 182(2), pages 514-535, October.
    9. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    10. H. Le Thi & A. Vaz & L. Vicente, 2012. "Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 190-214, April.
    11. G. Liuzzi & S. Lucidi & F. Rinaldi, 2012. "Derivative-free methods for bound constrained mixed-integer optimization," Computational Optimization and Applications, Springer, vol. 53(2), pages 505-526, October.
    12. Juliane Müller & Christine Shoemaker, 2014. "Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems," Journal of Global Optimization, Springer, vol. 60(2), pages 123-144, October.
    13. 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.
    14. Miguel F. Anjos & Frauke Liers, 2012. "Global Approaches for Facility Layout and VLSI Floorplanning," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 849-877, Springer.
    15. Rommel Regis & Christine Shoemaker, 2005. "Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions," Journal of Global Optimization, Springer, vol. 31(1), pages 153-171, January.
    16. 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.
    17. P. M. Kleniati & P. Parpas & B. Rustem, 2010. "Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 289-310, May.
    18. Charles Audet & Jack Brimberg & Pierre Hansen & Sébastien Le Digabel & Nenad Mladenovi'{c}, 2004. "Pooling Problem: Alternate Formulations and Solution Methods," Management Science, INFORMS, vol. 50(6), pages 761-776, June.
    19. A. Skjäl & T. Westerlund & R. Misener & C. A. Floudas, 2012. "A Generalization of the Classical αBB Convex Underestimation via Diagonal and Nondiagonal Quadratic Terms," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 462-490, August.
    20. Arthur M. Geoffrion, 1970. "Elements of Large-Scale Mathematical Programming Part I: Concepts," Management Science, INFORMS, vol. 16(11), pages 652-675, July.
    21. Aida Khajavirad & Nikolaos Sahinidis, 2012. "Convex envelopes of products of convex and component-wise concave functions," Journal of Global Optimization, Springer, vol. 52(3), pages 391-409, March.
    22. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Other publications TiSEM e49ba0fc-853c-4a13-b564-d, Tilburg University, School of Economics and Management.
    23. Rommel Regis & Christine Shoemaker, 2013. "A quasi-multistart framework for global optimization of expensive functions using response surface models," Journal of Global Optimization, Springer, vol. 56(4), pages 1719-1753, August.
    24. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    25. Sonia Cafieri & Nicolas Durand, 2014. "Aircraft deconfliction with speed regulation: new models from mixed-integer optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 613-629, April.
    26. Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.
    27. Yichuan Ding & Dongdong Ge & Henry Wolkowicz, 2011. "On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 88-104, February.
    28. Charles Audet & J. Dennis & Sébastien Digabel, 2010. "Globalization strategies for Mesh Adaptive Direct Search," Computational Optimization and Applications, Springer, vol. 46(2), pages 193-215, June.
    29. Achim Wechsung & Spencer Schaber & Paul Barton, 2014. "The cluster problem revisited," Journal of Global Optimization, Springer, vol. 58(3), pages 429-438, March.
    30. Christodoulos A. Floudas & Avanish Aggarwal, 1990. "A Decomposition Strategy for Global Optimum Search in the Pooling Problem," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 225-235, August.
    31. 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.
    32. Evrim Dalkiran & Hanif Sherali, 2013. "Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality," Journal of Global Optimization, Springer, vol. 57(4), pages 1147-1172, December.
    33. Shweta B Shah & Nikolaos V Sahinidis, 2012. "SAS-Pro: Simultaneous Residue Assignment and Structure Superposition for Protein Structure Alignment," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-10, May.
    34. Xiang Li & Asgeir Tomasgard & Paul Barton, 2012. "Decomposition strategy for the stochastic pooling problem," Journal of Global Optimization, Springer, vol. 54(4), pages 765-790, December.
    35. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    36. W. Hare & J. Nutini, 2013. "A derivative-free approximate gradient sampling algorithm for finite minimax problems," Computational Optimization and Applications, Springer, vol. 56(1), pages 1-38, September.
    37. Daniela di Serafino & Susana Gomez & Leopoldo Milano & Filippo Riccio & Gerardo Toraldo, 2010. "A genetic algorithm for a global optimization problem arising in the detection of gravitational waves," Journal of Global Optimization, Springer, vol. 48(1), pages 41-55, September.
    38. 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.
    39. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
    40. Bartholomew-Biggs, M. C. & Parkhurst, S. C. & Wilson, S. P., 2003. "Global optimization approaches to an aircraft routing problem," European Journal of Operational Research, Elsevier, vol. 146(2), pages 417-431, April.
    41. Manuel Ruiz & Olivier Briant & Jean-Maurice Clochard & Bernard Penz, 2013. "Large-scale standard pooling problems with constrained pools and fixed demands," Journal of Global Optimization, Springer, vol. 56(3), pages 939-956, July.
    42. Manuel Laguna & Francisco Gortázar & Micael Gallego & Abraham Duarte & Rafael Martí, 2014. "A black-box scatter search for optimization problems with integer variables," Journal of Global Optimization, Springer, vol. 58(3), pages 497-516, March.
    43. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    44. Luis Rios & Nikolaos Sahinidis, 2010. "Portfolio optimization for wealth-dependent risk preferences," Annals of Operations Research, Springer, vol. 177(1), pages 63-90, June.
    45. Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2015. "Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 933-965, March.
    46. Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
    47. Andreas Lundell & Anders Skjäl & Tapio Westerlund, 2013. "A reformulation framework for global optimization," Journal of Global Optimization, Springer, vol. 57(1), pages 115-141, September.
    48. Polyxeni-Margarita Kleniati & Claire Adjiman, 2014. "Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development," Journal of Global Optimization, Springer, vol. 60(3), pages 425-458, November.
    49. Ruth Misener & Christodoulos Floudas, 2013. "GloMIQO: Global mixed-integer quadratic optimizer," Journal of Global Optimization, Springer, vol. 57(1), pages 3-50, September.
    50. Polyxeni-M. Kleniati & Claire Adjiman, 2014. "Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part II: Convergence analysis and numerical results," Journal of Global Optimization, Springer, vol. 60(3), pages 459-481, November.
    51. Pietro Belotti, 2013. "Bound reduction using pairs of linear inequalities," Journal of Global Optimization, Springer, vol. 56(3), pages 787-819, July.
    52. Rommel G. Regis & Christine A. Shoemaker, 2007. "A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 497-509, November.
    53. 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.
    54. 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.
    55. Martin Ballerstein & Dennis Michaels, 2014. "Extended formulations for convex envelopes," Journal of Global Optimization, Springer, vol. 60(2), pages 217-238, October.
    56. Achim Wechsung & Paul Barton, 2014. "Global optimization of bounded factorable functions with discontinuities," Journal of Global Optimization, Springer, vol. 58(1), pages 1-30, January.
    57. Pia Domschke & Bjorn Geißler & Oliver Kolb & Jens Lang & Alexander Martin & Antonio Morsi, 2011. "Combination of Nonlinear and Linear Optimization of Transient Gas Networks," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 605-617, November.
    58. Keith Zorn & Nikolaos Sahinidis, 2014. "Global optimization of general nonconvex problems with intermediate polynomial substructures," Journal of Global Optimization, Springer, vol. 59(2), pages 673-693, July.
    59. Charles Audet & Anthony Guillou & Pierre Hansen & Frédéric Messine & Sylvain Perron, 2011. "The small hexagon and heptagon with maximum sum of distances between vertices," Journal of Global Optimization, Springer, vol. 49(3), pages 467-480, March.
    60. Mohammed Alfaki & Dag Haugland, 2013. "A multi-commodity flow formulation for the generalized pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 917-937, July.
    61. Charles Audet & Jordan Ninin, 2013. "Maximal perimeter, diameter and area of equilateral unit-width convex polygons," Journal of Global Optimization, Springer, vol. 56(3), pages 1007-1016, July.
    62. Scott Kolodziej & Pedro Castro & Ignacio Grossmann, 2013. "Global optimization of bilinear programs with a multiparametric disaggregation technique," Journal of Global Optimization, Springer, vol. 57(4), pages 1039-1063, December.
    63. Genetha Anne Gray & Tamara G. Kolda & Ken Sale & Malin M. Young, 2004. "Optimizing an Empirical Scoring Function for Transmembrane Protein Structure Determination," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 406-418, November.
    64. J. Martínez & F. Sobral, 2013. "Constrained derivative-free optimization on thin domains," Journal of Global Optimization, Springer, vol. 56(3), pages 1217-1232, July.
    65. Claudia D’Ambrosio & Andrea Lodi, 2013. "Mixed integer nonlinear programming tools: an updated practical overview," Annals of Operations Research, Springer, vol. 204(1), pages 301-320, April.
    66. A. Tsoukalas & A. Mitsos, 2014. "Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 59(2), pages 633-662, July.
    67. Ning Quan & Jun Yin & Szu Ng & Loo Lee, 2013. "Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints," IISE Transactions, Taylor & Francis Journals, vol. 45(7), pages 763-780.
    68. Qing Zhao & Stefan E. Karisch & Franz Rendl & Henry Wolkowicz, 1998. "Semidefinite Programming Relaxations for the Quadratic Assignment Problem," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 71-109, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fani Boukouvala & M. M. Faruque Hasan & Christodoulos A. Floudas, 2017. "Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption," Journal of Global Optimization, Springer, vol. 67(1), pages 3-42, January.
    2. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    3. Juliane Müller & Joshua D. Woodbury, 2017. "GOSAC: global optimization with surrogate approximation of constraints," Journal of Global Optimization, Springer, vol. 69(1), pages 117-136, September.
    4. Jaromił Najman & Alexander Mitsos, 2019. "On tightness and anchoring of McCormick and other relaxations," Journal of Global Optimization, Springer, vol. 74(4), pages 677-703, August.
    5. 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.
    6. Nikolaos Ploskas & Nikolaos V. Sahinidis, 2022. "Review and comparison of algorithms and software for mixed-integer derivative-free optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 433-462, March.
    7. Akshay Gupte & Shabbir Ahmed & Santanu S. Dey & Myun Seok Cheon, 2017. "Relaxations and discretizations for the pooling problem," Journal of Global Optimization, Springer, vol. 67(3), pages 631-669, March.
    8. Juliane Müller & Christine Shoemaker, 2014. "Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems," Journal of Global Optimization, Springer, vol. 60(2), pages 123-144, October.
    9. Radu Baltean-Lugojan & Ruth Misener, 2018. "Piecewise parametric structure in the pooling problem: from sparse strongly-polynomial solutions to NP-hardness," Journal of Global Optimization, Springer, vol. 71(4), pages 655-690, August.
    10. Zhe Zhou & Fusheng Bai, 2018. "An adaptive framework for costly black-box global optimization based on radial basis function interpolation," Journal of Global Optimization, Springer, vol. 70(4), pages 757-781, April.
    11. Taimoor Akhtar & Christine Shoemaker, 2016. "Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection," Journal of Global Optimization, Springer, vol. 64(1), pages 17-32, January.
    12. Tipaluck Krityakierne & Taimoor Akhtar & Christine A. Shoemaker, 2016. "SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems," Journal of Global Optimization, Springer, vol. 66(3), pages 417-437, November.
    13. Jaromił Najman & Alexander Mitsos, 2016. "Convergence analysis of multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 66(4), pages 597-628, December.
    14. A. Tsoukalas & A. Mitsos, 2014. "Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 59(2), pages 633-662, July.
    15. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
    16. Jaromił Najman & Alexander Mitsos, 2019. "Tighter McCormick relaxations through subgradient propagation," Journal of Global Optimization, Springer, vol. 75(3), pages 565-593, November.
    17. Juliane Müller & Marcus Day, 2019. "Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 689-702, October.
    18. Juliane Müller, 2017. "SOCEMO: Surrogate Optimization of Computationally Expensive Multiobjective Problems," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 581-596, November.
    19. N. Kazazakis & C. S. Adjiman, 2018. "Arbitrarily tight $$\alpha $$ α BB underestimators of general non-linear functions over sub-optimal domains," Journal of Global Optimization, Springer, vol. 71(4), pages 815-844, August.
    20. Artur M. Schweidtmann & Alexander Mitsos, 2019. "Deterministic Global Optimization with Artificial Neural Networks Embedded," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 925-948, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:252:y:2016:i:3:p:701-727. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.