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

  • Victor Gergel
  • Konstantin BarkalovEmail author
  • Ilya Lebedev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11353)


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.


Global optimization Non-convex constraints Mixed-integer problems 



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


  1. 1.
    Burer, S., Letchford, A.N.: Non-convex mixed-integer nonlinear programming: a survey. Surv. Oper. Res. Manag. Sci. 17, 97–106 (2012)MathSciNetGoogle Scholar
  2. 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)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)CrossRefGoogle Scholar
  4. 4.
    Sergeyev, Ya.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer (2013)Google Scholar
  5. 5.
    Floudas, C.A., Pardalos, P.M.: Handbook of Test Problems in Local and Global Optimization. Springer (1999)Google Scholar
  6. 6.
  7. 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)MathSciNetzbMATHGoogle Scholar
  8. 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)MathSciNetCrossRefGoogle Scholar
  9. 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)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lebedev, I., Gergel, V.: Heterogeneous parallel computations for solving global optimization problems. Procedia Comput. Sci. 66, 53–62 (2015)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Victor Gergel
    • 1
  • Konstantin Barkalov
    • 1
    Email author
  • Ilya Lebedev
    • 1
  1. 1.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

Personalised recommendations