Skip to main content
SpringerLink
Log in

A Resource Constraint Approach for One Global Constraint MINLP

  • Conference paper
  • First Online:
Computational Science and Its Applications – ICCSA 2020 (ICCSA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12251))

Included in the following conference series:

Abstract

Many industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, where low-dimensional sub-problems are linked by a (linear) knapsack-like coupling constraint. This paper investigates exploiting this structure using decomposition and a resource constraint formulation of the problem. The idea is that one outer approximation master problem handles sub-problems that can be solved in parallel. The steps of the algorithm are illustrated with numerical examples which shows that convergence to the optimal solution requires a few steps of solving sub-problems in lower dimension.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Belotti, P., Lee, J., Liberti, L., Margot, F., Wächter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Softw. 24(4–5), 597–634 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Bodur, M., Ahmed, S., Boland, N., Nemhauser, G.L.: Decomposition of loosely coupled integer programs: a multiobjective perspective (2016). http://www.optimization-online.org/DB_FILE/2016/08/5599.pdf

  3. Burer, S., Letchford, A.: Non-convex mixed-integer nonlinear programming: a survey. Surv. Oper. Res. Manage. Sci. 17(2), 97–106 (2012)

    MathSciNet  Google Scholar 

  4. Bussieck, M.R., Vigerske, S.: MINLP Solver Software (2014). www.math.hu-berlin.de/~stefan/minlpsoft.pdf

  5. Duran, M., Grossmann, I.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Program. 36, 307–339 (1986)

    MathSciNet  MATH  Google Scholar 

  6. Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66(3(A)), 327–349 (1994)

    MathSciNet  MATH  Google Scholar 

  7. Lin, Y., Schrage, L.: The global solver in the LINDO API. Optim. Methods Softw. 24(4–5), 657–668 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Misener, R., Floudas, C.: ANTIGONE: Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations. J. Glob. Optim. 59(2–3), 503–526 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Muts, P., Nowak, I., Hendrix, E.M.T.: The decomposition-based outer approximation algorithm for convex mixed-integer nonlinear programming. J. Glob. Optim. 77(1), 75–96 (2020). https://doi.org/10.1007/s10898-020-00888-x

    Article  MathSciNet  MATH  Google Scholar 

  10. Nowak, I., Breitfeld, N., Hendrix, E.M.T., Njacheun-Njanzoua, G.: Decomposition-based Inner- and Outer-Refinement Algorithms for Global Optimization. J. Glob. Optim. 72(2), 305–321 (2018). https://doi.org/10.1007/s10898-018-0633-2

    Article  MathSciNet  MATH  Google Scholar 

  11. Tawarmalani, M., Sahinidis, N.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103(2), 225–249 (2005)

    MathSciNet  MATH  Google Scholar 

  12. Vigerske, S.: Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming. Ph.D. thesis, Humboldt-Universität zu Berlin (2012)

    Google Scholar 

  13. Vigerske, S.: MINLPLib (2018). http://minlplib.org/index.html

  14. Westerlund, T., Petterson, F.: An extended cutting plane method for solving convex MINLP problems. Comput. Chem. Eng. 21, 131–136 (1995)

    Google Scholar 

  15. Yuan, X., Zhang, S., Piboleau, L., Domenech, S.: Une methode d’optimisation nonlineare en variables mixtes pour la conception de procedes. RAIRO 22(4), 331–346 (1988)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This paper has been supported by The Spanish Ministry (RTI2018-095993-B-100) in part financed by the European Regional Development Fund (ERDF) and by Grant 03ET4053B of the German Federal Ministry for Economic Affairs and Energy.

Author information

Authors and Affiliations

  1. Hamburg University of Applied Sciences, Hamburg, Germany

    Pavlo Muts & Ivo Nowak

  2. Computer Architecture, Universidad de Málaga, 29080, Málaga, Spain

    Eligius M. T. Hendrix

Authors
  1. Pavlo Muts
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivo Nowak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eligius M. T. Hendrix
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eligius M. T. Hendrix .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Chair- Center of ICT/ICE, Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Clayton School of Information Technology, Monash University, Clayton, VIC, Australia

    David Taniar

  7. Department of Information Science, Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

  11. Department of Neurology, University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Muts, P., Nowak, I., Hendrix, E.M.T. (2020). A Resource Constraint Approach for One Global Constraint MINLP. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12251. Springer, Cham. https://doi.org/10.1007/978-3-030-58808-3_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-58808-3_43

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58807-6

  • Online ISBN: 978-3-030-58808-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation