IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v33y2021i2p421-435.html
   My bibliography  Save this article

Conflict Analysis for MINLP

Author

Listed:
  • Timo Berthold

    (Fair Isaac Germany GmbH, 64625 Bensheim, Germany)

  • Jakob Witzig

    (Zuse Institute Berlin, 14195 Berlin, Germany)

Abstract

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality.

Suggested Citation

  • Timo Berthold & Jakob Witzig, 2021. "Conflict Analysis for MINLP," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 421-435, May.
    • Handle: RePEc:inm:orijoc:v:33:y:2021:i:2:p:421-435
    DOI: 10.1287/ijoc.2020.1050
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2020.1050
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2020.1050?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
    ---><---

    References listed on IDEAS

    as
    1. Bruce Davey & Natashia Boland & Peter J. Stuckey, 2002. "Efficient Intelligent Backtracking Using Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 373-386, November.
    2. John Gleeson & Jennifer Ryan, 1990. "Identifying Minimally Infeasible Subsystems of Inequalities," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 61-63, February.
    3. 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.
    4. Kai Kellner & Marc E. Pfetsch & Thorsten Theobald, 2019. "Irreducible Infeasible Subsystems of Semidefinite Systems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 727-742, June.
    5. Chakravarti, Nilotpal, 1994. "Some results concerning post-infeasibility analysis," European Journal of Operational Research, Elsevier, vol. 73(1), pages 139-143, February.
    6. John W. Chinneck & Erik W. Dravnieks, 1991. "Locating Minimal Infeasible Constraint Sets in Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 157-168, May.
    7. C. E. Lemke, 1954. "The dual method of solving the linear programming problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 36-47, March.
    8. Josef Kallrath, 2005. "Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 339-373, November.
    9. Robert E. Bixby, 2002. "Solving Real-World Linear Programs: A Decade and More of Progress," Operations Research, INFORMS, vol. 50(1), pages 3-15, February.
    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. Jérémy Omer & Michael Poss, 2021. "Identifying relatively irreducible infeasible subsystems of linear inequalities," Annals of Operations Research, Springer, vol. 304(1), pages 361-379, September.
    2. Junhong Guo & William Pozehl & Amy Cohn, 2023. "A two-stage partial fixing approach for solving the residency block scheduling problem," Health Care Management Science, Springer, vol. 26(2), pages 363-393, June.
    3. Yash Puranik & Nikolaos V. Sahinidis, 2017. "Deletion Presolve for Accelerating Infeasibility Diagnosis in Optimization Models," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 754-766, November.
    4. John W. Chinneck, 2001. "Fast Heuristics for the Maximum Feasible Subsystem Problem," INFORMS Journal on Computing, INFORMS, vol. 13(3), pages 210-223, August.
    5. Erick Moreno-Centeno & Richard M. Karp, 2013. "The Implicit Hitting Set Approach to Solve Combinatorial Optimization Problems with an Application to Multigenome Alignment," Operations Research, INFORMS, vol. 61(2), pages 453-468, April.
    6. Kai Kellner & Marc E. Pfetsch & Thorsten Theobald, 2019. "Irreducible Infeasible Subsystems of Semidefinite Systems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 727-742, June.
    7. Richard J. Caron & Tim Traynor & Shafiu Jibrin, 2010. "Feasibility and Constraint Analysis of Sets of Linear Matrix Inequalities," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 144-153, February.
    8. Axel von Kamp & Steffen Klamt, 2014. "Enumeration of Smallest Intervention Strategies in Genome-Scale Metabolic Networks," PLOS Computational Biology, Public Library of Science, vol. 10(1), pages 1-13, January.
    9. Daniel Baena & Jordi Castro & Antonio Frangioni, 2020. "Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy," Management Science, INFORMS, vol. 66(7), pages 3051-3068, July.
    10. Obuchowska, Wieslawa T., 1998. "Infeasibility analysis for systems of quadratic convex inequalities," European Journal of Operational Research, Elsevier, vol. 107(3), pages 633-643, June.
    11. Dursun, Pınar & Taşkın, Z. Caner & Altınel, İ. Kuban, 2019. "The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)," European Journal of Operational Research, Elsevier, vol. 272(1), pages 372-388.
    12. René Brandenberg & Paul Stursberg, 2021. "Refined cut selection for benders decomposition: applied to network capacity expansion problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 383-412, December.
    13. Paula Amaral & Luís Fernandes & Joaquim Júdice & Hanif Sherali, 2009. "On optimal zero-preserving corrections for inconsistent linear systems," Computational Optimization and Applications, Springer, vol. 45(4), pages 645-666, December.
    14. Christian Desrosiers & Philippe Galinier & Alain Hertz & Sandrine Paroz, 2009. "Using heuristics to find minimal unsatisfiable subformulas in satisfiability problems," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 124-150, August.
    15. Wiesława T. Obuchowska, 2015. "Irreducible Infeasible Sets in Convex Mixed-Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 747-766, September.
    16. John W. Chinneck, 1992. "Viability analysis: A formulation aid for all classes of network models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 531-543, June.
    17. Obuchowska, Wiesława T., 2014. "Feasible partition problem in reverse convex and convex mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 235(1), pages 129-137.
    18. Gianpiero Canessa & Julian A. Gallego & Lewis Ntaimo & Bernardo K. Pagnoncelli, 2019. "An algorithm for binary linear chance-constrained problems using IIS," Computational Optimization and Applications, Springer, vol. 72(3), pages 589-608, April.
    19. Wen Sun & Jin-Kao Hao & Alexandre Caminada, 2019. "Iterated backtrack removal search for finding k-vertex-critical subgraphs," Journal of Heuristics, Springer, vol. 25(4), pages 565-590, October.
    20. Aigerim Saken & Emil Karlsson & Stephen J. Maher & Elina Rönnberg, 2023. "Computational Evaluation of Cut-Strengthening Techniques in Logic-Based Benders’ Decomposition," SN Operations Research Forum, Springer, vol. 4(3), pages 1-53, September.

    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:inm:orijoc:v:33:y:2021:i:2:p:421-435. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.