Skip to main content
Top

2017 | OriginalPaper | Chapter

Parallel Algorithm for Solving Constrained Global Optimization Problems

Authors : Konstantin Barkalov, Ilya Lebedev

Published in: Parallel Computing Technologies

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This work considers a parallel algorithm for solving multiextremal problems with non-convex constraints. The distinctive feature of this algorithm, which does not use penalty functions, is the separate consideration of each problem constraint. The search process can be conducted by reducing the original multidimensional problem to a number of related one-dimensional problems and solving this set of problems in parallel. An experimental assessment of parallel algorithm efficiency was conducted by finding the numeric solution to several hundred randomly generated multidimensional multiextremal problems with non-convex constraints.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
2.
go back to reference Evtushenko, Y., Malkova, V.U., Stanevichyus, A.A.: Parallel global optimization of functions of several variables. Comput. Math. Math. Phys. 49(2), 246–260 (2009)MathSciNetCrossRefMATH Evtushenko, Y., Malkova, V.U., Stanevichyus, A.A.: Parallel global optimization of functions of several variables. Comput. Math. Math. Phys. 49(2), 246–260 (2009)MathSciNetCrossRefMATH
3.
go back to reference Paulavicius, R., Zilinskas, J., Grothey, A.: Parallel branch and bound for global optimization with combination of Lipschitz bounds. Optim. Methods Softw. 26(3), 487–498 (2011)MathSciNetCrossRef Paulavicius, R., Zilinskas, J., Grothey, A.: Parallel branch and bound for global optimization with combination of Lipschitz bounds. Optim. Methods Softw. 26(3), 487–498 (2011)MathSciNetCrossRef
4.
5.
go back to reference Balandin, D.V., Kogan, M.M.: Optimal linear-quadratic control: from matrix equations to linear matrix inequalities. Autom. Remote Control 72(11), 2276–2284 (2011)MathSciNetCrossRefMATH Balandin, D.V., Kogan, M.M.: Optimal linear-quadratic control: from matrix equations to linear matrix inequalities. Autom. Remote Control 72(11), 2276–2284 (2011)MathSciNetCrossRefMATH
6.
go back to reference Balandin, D.V., Kogan, M.M.: Pareto-optimal generalized H 2-control and vibration isolation problems. Autom. Remote Control 8, 76–90 (2017). [in Russian] Balandin, D.V., Kogan, M.M.: Pareto-optimal generalized H 2-control and vibration isolation problems. Autom. Remote Control 8, 76–90 (2017). [in Russian]
8.
go back to reference Sergeyev, Y.D., Famularo, D., Pugliese, P.: Index branch-and-bound algorithm for Lipschitz univariate global optimization with multiextremal constraints. J. Glob. Optim. 21(3), 317–341 (2001)MathSciNetCrossRefMATH Sergeyev, Y.D., Famularo, D., Pugliese, P.: Index branch-and-bound algorithm for Lipschitz univariate global optimization with multiextremal constraints. J. Glob. Optim. 21(3), 317–341 (2001)MathSciNetCrossRefMATH
9.
go back to reference Barkalov, K.A., Strongin, R.G.: A global optimization technique with an adaptive order of checking for constraints. Comput. Math. Math. Phys. 42(9), 1289–1300 (2002)MathSciNetMATH Barkalov, K.A., Strongin, R.G.: A global optimization technique with an adaptive order of checking for constraints. Comput. Math. Math. Phys. 42(9), 1289–1300 (2002)MathSciNetMATH
10.
go back to reference Gergel, V., Sidorov, S.: A two-level parallel global search algorithm for solution of computationally intensive multiextremal optimization problems. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 505–515. Springer, Cham (2015). doi:10.1007/978-3-319-21909-7_49 CrossRef Gergel, V., Sidorov, S.: A two-level parallel global search algorithm for solution of computationally intensive multiextremal optimization problems. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 505–515. Springer, Cham (2015). doi:10.​1007/​978-3-319-21909-7_​49 CrossRef
12.
go back to reference Gaviano, M., Kvasov, D.E., Lera, D., Sergeyev, Y.: Software for generation of classes of test functions with known local and global minima for global optimization. ACM Trans. Math. Softw. 29(4), 469–480 (2003)MathSciNetCrossRefMATH Gaviano, M., Kvasov, D.E., Lera, D., Sergeyev, Y.: Software for generation of classes of test functions with known local and global minima for global optimization. ACM Trans. Math. Softw. 29(4), 469–480 (2003)MathSciNetCrossRefMATH
13.
go back to reference Sergeyev, Y.D., Kvasov, D.E.: Global search based on efficient diagonal partitions and a set of Lipschitz constants. SIAM J. Optim. 16(3), 910–937 (2006)MathSciNetCrossRefMATH Sergeyev, Y.D., Kvasov, D.E.: Global search based on efficient diagonal partitions and a set of Lipschitz constants. SIAM J. Optim. 16(3), 910–937 (2006)MathSciNetCrossRefMATH
14.
go back to reference Paulavicius, R., Sergeyev, Y., Kvasov, D., Zilinskas, J.: Globally-biased DISIMPL algorithm for expensive global optimization. J. Glob. Optim. 59(2–3), 54–567 (2014)MathSciNetMATH Paulavicius, R., Sergeyev, Y., Kvasov, D., Zilinskas, J.: Globally-biased DISIMPL algorithm for expensive global optimization. J. Glob. Optim. 59(2–3), 54–567 (2014)MathSciNetMATH
15.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
16.
go back to reference Gergel, V.: An approach for generating test problems of constrained global optimization. In: Proceedings of Learning and Intelligent Optimization Conference (to appear) Gergel, V.: An approach for generating test problems of constrained global optimization. In: Proceedings of Learning and Intelligent Optimization Conference (to appear)
17.
Metadata
Title
Parallel Algorithm for Solving Constrained Global Optimization Problems
Authors
Konstantin Barkalov
Ilya Lebedev
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-62932-2_38

Premium Partner