Skip to main content

A Global Optimization Algorithm for Non-Convex Mixed-Integer Problems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11353))

Abstract

In the present paper, the mixed-integer global optimization problems are considered. A novel deterministic algorithm for solving the problems of this class based on the information-statistical approach to solving the continuous global optimization problems has been proposed. The comparison of this algorithm with known analogs demonstrating the efficiency of the developed approach has been conducted. The stable operation of the algorithm was confirmed also by solving a series of several hundred mixed-integer global optimization problems.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

References

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

    MathSciNet  Google Scholar 

  2. Boukouvala, F., Misener, R., Floudas, C.A.: Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization CDFO. Eur. J. Oper. Res. 252, 701–727 (2016)

    Article  MathSciNet  Google Scholar 

  3. Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  Google Scholar 

  4. Sergeyev, Ya.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer (2013)

    Google Scholar 

  5. Floudas, C.A., Pardalos, P.M.: Handbook of Test Problems in Local and Global Optimization. Springer (1999)

    Google Scholar 

  6. https://www.mathworks.com/help/gads/mixed-integer-optimization.html

  7. Deep, K., Singh, K.P., Kansal, M.L., Mohan, C.: A real coded genetic algorithm for solving integer and mixed integer optimization problems. Appl. Math. Comput. 212(2), 505–518 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Paulavičius, R., Sergeyev, Y., Kvasov, D., Žilinskas, J.: Globally-biased DISIMPL algorithm for expensive global optimization. J. Glob. Optim. 59(2–3), 545–567 (2014)

    Article  MathSciNet  Google Scholar 

  9. Sergeyev, Y.D., Kvasov, D.E.: A deterministic global optimization using smooth diagonal auxiliary functions. Commun. Nonlinear. Sci. Numer. Simul. 21(1–3), 99–111 (2015)

    Article  MathSciNet  Google Scholar 

  10. Lebedev, I., Gergel, V.: Heterogeneous parallel computations for solving global optimization problems. Procedia Comput. Sci. 66, 53–62 (2015)

    Article  Google Scholar 

  11. Gergel, V., Sidorov, S.: A two-level parallel global search algorithm for solution of computationally intensive multiextremal optimization problems. Lect. Notes Comput. Sci. 9251, 505–515 (2015)

    Article  Google Scholar 

Download references

Acknowledgments

This study was supported by the Russian Science Foundation, project No 16-11-10150.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Konstantin Barkalov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gergel, V., Barkalov, K., Lebedev, I. (2019). A Global Optimization Algorithm for Non-Convex Mixed-Integer Problems. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 12 2018. Lecture Notes in Computer Science(), vol 11353. Springer, Cham. https://doi.org/10.1007/978-3-030-05348-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-05348-2_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05347-5

  • Online ISBN: 978-3-030-05348-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics