Journal of Global Optimization

, Volume 67, Issue 1–2, pp 135–149 | Cite as

Interactive model-based search with reactive resource allocation

  • Yue Sun
  • Alfredo GarciaEmail author


We revisit the interactive model-based approach to global optimization proposed in Wang and Garcia (J Glob Optim 61(3):479–495, 2015) in which parallel threads independently execute a model-based search method and periodically interact through a simple acceptance-rejection rule aimed at preventing duplication of search efforts. In that paper it was assumed that each thread successfully identifies a locally optimal solution every time the acceptance-rejection rule is implemented. Under this stylized model of computational time, the rate of convergence to a globally optimal solution was shown to increase exponentially in the number of threads. In practice however, the computational time required to identify a locally optimal solution varies greatly. Therefore, when the acceptance-rejection rule is implemented, several threads may fail to identify a locally optimal solution. This situation calls for reallocation of computational resources in order to speed up the identification of local optima when one or more threads repeatedly fail to do so. In this paper we consider an implementation of the interactive model-based approach that accounts for real time, that is, it takes into account the possibility that several threads may fail to identify a locally optimal solution whenever the acceptance-rejection rule is implemented. We propose a modified acceptance-rejection rule that alternates between enforcing diverse search (in order to prevent duplication) and reallocation of computational effort (in order to speed up the identification of local optima). We show that the rate of convergence in real-time increases with the number of threads. This result formalizes the idea that in parallel computing, exploitation and exploration can be complementary provided relatively simple rules for interaction are implemented. We report the results from extensive numerical experiments which are illustrate the theoretical analysis of performance.


Model-based search Parallel algorithms Reactive resource allocation 


  1. 1.
    Wang, Y., Garcia, A.: Interactive model-based search for global optimization. J. Glob. Optim. 61(3), 479–495 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hu, J., Fu, M., Marcus, S.: A model reference adaptive search algorithm for global optimization. Oper. Res. 55(3), 549–568 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Schoen, F.: Stochastic techniques for global optimization: a survey of recent advances. J. Glob. Optim. 1(3), 207–228 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Martí, R., Moreno-Vega, J., Duarte, A.: Advanced Multi-start Methods. Handbook of Metaheuristics, 2nd edn. Springer, New York (2010)Google Scholar
  5. 5.
    Onbasglu, E., Ozdamar, L.: Parallel simulated annealing algorithms in global optimization. J. Glob. Optim. 19, 27–50 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ferreiro, A., Garcia, J.A., Lopez-Salas, J.G., Vazquez, C.: An efficient implementation of parallel simulated annealing algorithm in GPUs. J. Glob. Optim. 57(3), 863–890 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Schutte, J.F., Reinbolt, J.A., Fregly, B.J., Haftka, R.T., George, A.D.: Parallel global optimization with the particle Swarm algorithm. Comput. Sci. Res. Dev. 61(13), 2296–2315 (2004)zbMATHGoogle Scholar
  8. 8.
    D’Apuzzo, M., Marino, M., Migdalas, A., Pardalos, P.M., Toraldo, G.: Parallel computing in global optimization. In: Kontoghiorghes, E.J. (ed.) Handbook of Parallel Computing and Statistics, pp. 225–258. Chapman and Hall/CRC, London (2005)CrossRefGoogle Scholar
  9. 9.
    Boender, C.G.E., Rinnooy Kan, A.H.G.: Bayesian stopping rules for multistart global optimization methods. Math. Program. 37, 59–80 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gyorgy, A., Kocsis, L.: Efficient multi-start strategies for local search algorithms. J. Artif. Intell. Res. 41, 407–444 (2011)Google Scholar
  11. 11.
    Calvin, J.M., Zilinskas, A.: On a global optimization algorithm for bivariate smooth functions. J. Optim. Theory Appl. 163(2), 528–547 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Zielinski, A.: A statistical estimate of the structure of multi-extremal problems. Math. Program. 21(3), 348–356 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Zhigljavsky, A.: Semiparametric statistical inference in global random search. Acta Appl. Math. 33(1), 69–88 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Ackley, D.H.: A Connectionist Machine for Genetic Hillclimbing. Kluwer, Boston (1987)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringUniversity of Florida GainesvilleFLUSA

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