Advertisement

Introduction

  • Balázs Bánhelyi
  • Tibor Csendes
  • Balázs Lévai
  • László Pál
  • Dániel Zombori
Chapter
Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Abstract

Nowadays, solving global optimization problems is a crucial and inescapable part of the daily operation of almost every branch of natural sciences and the modern industry. The scale and variety of problems are larger than ever. For some time, providing efficient tools for these tasks is not just a challenge for researchers, it is an ever-growing expectation from the stakeholders of the tech industry and indirectly from the information society. In our book, we revisit GLOBAL, a stochastic optimization method aiming to solve nonlinear, bound constrained optimization problems. It is a versatile tool for a broad range of problems, proven to be competitive in multiple comparisons. To extend usability, now we present a Java implementation, GLOBALJ. It is an entire, modularized framework extending the potential of this algorithm.

References

  1. 2.
    Balogh, J., Csendes, T., Stateva, R.P.: Application of a stochastic method to the solution of the phase stability problem: cubic equations of state. Fluid Phase Equilib. 212, 257–267 (2003)CrossRefGoogle Scholar
  2. 3.
    Balogh, J., Csendes, T., Rapcsák, T.: Some Global Optimization Problems on Stiefel Manifolds. J. Glob. Optim. 30, 91–101 (2004)MathSciNetCrossRefGoogle Scholar
  3. 4.
    Banga, J.R., Moles, C.G., Alonso, A.A.: Global optimization of Bioprocesses using Stochastic and hybrid methods. In: C.A. Floudas, P.M. Pardalos (eds.) Frontiers in Global Optimization, pp. 45–70. Springer, Berlin (2003)zbMATHGoogle Scholar
  4. 5.
    Bánhelyi, B., Csendes, T., Garay, B.M.: Optimization and the Miranda approach in detecting horseshoe-type chaos by computer. Int. J. Bifurcation Chaos 17, 735–747 (2007)MathSciNetCrossRefGoogle Scholar
  5. 6.
    Betró, B., Schoen, F.: Optimal and sub-optimal stopping rules for the multistart algorithm in global optimization. Math. Program. 57, 445–458 (1992)MathSciNetCrossRefGoogle Scholar
  6. 7.
    Boender, C.G.E., Rinnooy Kan, A.H.G.: Bayesian stopping rules for multistart global optimization methods. Math. Program. 37, 59–80 (1987)MathSciNetCrossRefGoogle Scholar
  7. 8.
    Boender, C.G.E., Rinnooy Kan, A.H.G.: On when to stop sampling for the maximum. J. Glob. Optim. 1, 331–340 (1991)MathSciNetCrossRefGoogle Scholar
  8. 9.
    Boender, C.G.E., Romeijn, H.E.: Stochastic methods. In: Horst, R., Pardalos, P. (eds.) Handbook of Global Optimization, pp. 829–869. Kluwer, Dordrecht (1995)CrossRefGoogle Scholar
  9. 10.
    Boender, C.G.E., Zielinski, R.: A sequential Bayesian approach to estimating the dimension of a multinominal distribution. In: Sequential Methods in Statistics. Banach Center Publications, vol. 16. PWN-Polish Scientific Publisher, Warsaw (1982)Google Scholar
  10. 11.
    Boender, C.G.E., Rinnooy Kan, A.H.G., Timmer, G., Stougie, L.: A stochastic method for global optimization. Math. Program. 22, 125–140 (1982)MathSciNetCrossRefGoogle Scholar
  11. 12.
    Csendes, T.: Nonlinear parameter estimation by global optimization-efficiency and reliability. Acta Cybernet. 8, 361–370 (1988)MathSciNetzbMATHGoogle Scholar
  12. 13.
    Csendes, T., Garay, B.M., Bánhelyi, B.: A verified optimization technique to locate chaotic regions of Hénon systems. J. Glob. Optim. 35, 145–160 (2006)CrossRefGoogle Scholar
  13. 14.
    Csendes, T., Bánhelyi, B., Hatvani, L.: Towards a computer-assisted proof for chaos in a forced damped pendulum equation. J. Comput. Appl. Math. 199, 378–383 (2007)MathSciNetCrossRefGoogle Scholar
  14. 15.
    Csendes, T., Pál, L., Sendin, J.O.H., Banga, J.R.: The GLOBAL optimization method revisited. Optim. Lett. 2, 445–454 (2008)MathSciNetCrossRefGoogle Scholar
  15. 25.
    Hendrix, E.M.T., G.-Tóth, B.: Introduction to Nonlinear and Global Optimization. Optimization and its Application. Springer, Berlin (2010)Google Scholar
  16. 27.
    Horst, R., Pardalos, P.M. (eds.): Handbook of Global Optimization. Kluwer, Dordrecht (1995)zbMATHGoogle Scholar
  17. 34.
    Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)CrossRefGoogle Scholar
  18. 37.
    Locatelli, M., Schoen, F.: Random linkage: a family of acceptance/rejection algorithms for global optimization. Math. Program. 2, 379–396 (1999)CrossRefGoogle Scholar
  19. 38.
    Locatelli, M., Schoen, F.: Global Optimization: Theory, Algorithms, and Applications. MOS-SIAM Series on Optimization. SIAM, Philadelphia (2013)Google Scholar
  20. 39.
    Markót, M.Cs., Csendes, T.: A new verified optimization technique for the “packing circles in a unit square” problems. SIAM J. Optim. 16, 193–219 (2005)Google Scholar
  21. 40.
    Mockus, J.: Bayesian Approach to Global Optimization. Kluwer, Dordrecht (1989)Google Scholar
  22. 41.
    Moles, C.G., Gutierrez, G., Alonso, A.A., Banga, J.R.: Integrated process design and control via global optimization – A wastewater treatment plant case study. Chem. Eng. Res. Des. 81, 507–517 (2003)CrossRefGoogle Scholar
  23. 42.
    Moles, C.G., Banga, J.R., Keller, K.: Solving nonconvex climate control problems: pitfalls and algorithm performances. Appl. Soft Comput. 5, 35–44 (2004)CrossRefGoogle Scholar
  24. 51.
    Pintér, J.D.: Global Optimization in Action. Kluwer, Dordrecht (1996)CrossRefGoogle Scholar
  25. 53.
    Pošík, P., Huyer, W., Pál, L.: A comparison of global search algorithms for continuous black box optimization. Evol. Comput. 20(4), 509–541 (2012)CrossRefGoogle Scholar
  26. 59.
    Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic global optimization methods Part I: Clustering methods. Math. Program. 39, 27–56 (1987)Google Scholar
  27. 60.
    Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic global optimization methods part II: Multi level methods. Math. Program. 39, 57–78 (1987)CrossRefGoogle Scholar
  28. 63.
    Rosenbrock, H.H.: An Automatic Method for Finding the Greatest or Least Value of a Function. Comput. J. 3, 175–184 (1960)MathSciNetCrossRefGoogle Scholar
  29. 65.
    Sendín, J.O.H., Banga, J.R., Csendes, T.: Extensions of a Multistart Clustering Algorithm for Constrained Global Optimization Problems. Ind. Eng. Chem. Res. 48, 3014–3023 (2009)CrossRefGoogle Scholar
  30. 66.
    Sergeyev, Y.D., Kvasov, D.E.: Deterministic Global Optimization: An Introduction to the Diagonal Approach. Springer, New York (2017)CrossRefGoogle Scholar
  31. 67.
    Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer Briefs in Optimization. Springer, New York (2013)Google Scholar
  32. 68.
    Szabó, P.G., Markót, M.Cs., Csendes, T., Specht, E., Casado, L.G., Garcia, I.: New Approaches to Circle Packing in a Square – With Program Codes. Springer, New York (2007)Google Scholar
  33. 71.
    Törn, A.A.: A search clustering approach to global optimization. In: Dixon, L., Szegő, G. (eds.) Towards Global Optimization, vol. 2, pp. 49–62. North-Holland, Amsterdam (1978)Google Scholar
  34. 72.
    Törn, A., Zilinskas, A.: Global Optimization. Lecture Notes in Computer Science, vol. 350. Springer, Berlin (1989)Google Scholar
  35. 74.
    Zhigljavsky, A.A., Zilinskas, A.: Stochastic Global Optimization. Springer, New York (2008)zbMATHGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Balázs Bánhelyi
    • 1
  • Tibor Csendes
    • 1
  • Balázs Lévai
    • 2
  • László Pál
    • 3
  • Dániel Zombori
    • 1
  1. 1.Department of Computational OptimizationUniversity of SzegedSzegedHungary
  2. 2.NNG IncSzegedHungary
  3. 3.Sapientia Hungarian University of TransylvaniaMiercurea CiucRomania

Personalised recommendations