MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems. Although DIRECT global optimization algorithm quickly gets close to the basin of the optimum, it often takes much longer to refine the solution to a high degree of accuracy. This behavior of DIRECT is similar to the “smooth mode phenomenon” encountered when solving linear systems discretized from partial differential equation (PDE). In the case of PDE, this smooth mode phenomenon can be eliminated efficiently by the multigrid algorithm in which the PDE solver is applied at different levels of discretization. In this paper, we adapt the multigrid approach to a robust version of DIRECT algorithm, obtaining a “multilevel” robust DIRECT (MrDIRECT) algorithm. Although additional parameters are needed, our numerical results show that MrDIRECT is insensitive to the parameters, and the parameters setting proposed in this paper performs very well on the tested sets of benchmark problems, in terms of the speed with which the global optimum is found to a high degree of accuracy.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Jones, Donald R.; Martins, Joaquim R. R. A.: The DIRECT algorithm: 25 years later (2021)
  2. Stripinis, Linas; Paulavičius, Remigijus: A new \textttDIRECT-GLh algorithm for global optimization with hidden constraints (2021)
  3. Stripinis, Linas; Žilinskas, Julius; Casado, Leocadio G.; Paulavičius, Remigijus: On \textttMATLABexperience in accelerating \textttDIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization (2021)
  4. Guo, Qing; Liu, Yongshou; Liu, Xiaohan; Chen, Bingqian; Yao, Qin: Fatigue dynamic reliability and global sensitivity analysis of double random vibration system based on Kriging model (2020)
  5. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  6. Audet, Charles; Ihaddadene, Amina; Le Digabel, Sébastien; Tribes, Christophe: Robust optimization of noisy blackbox problems using the mesh adaptive direct search algorithm (2018)
  7. Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.: Filter-based DIRECT method for constrained global optimization (2018)
  8. Gimbutas, Albertas; Žilinskas, Antanas: An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section (2018)
  9. Paulavičius, Remigijus; Chiter, Lakhdar; Žilinskas, Julius: Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants (2018)
  10. Stripinis, Linas; Paulavičius, Remigijus; Žilinskas, Julius: Improved scheme for selection of potentially optimal hyper-rectangles in \textttDIRECT (2018)
  11. Liu, Qunfeng; Yang, Guang; Zhang, Zhongzhi; Zeng, Jinping: Improving the convergence rate of the DIRECT global optimization algorithm (2017)
  12. Liu, Qunfeng; Zeng, Jinping; Yang, Gang: MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems (2015)