DIRMIN

DFL - A Derivative-Free Library - DIRMIN: Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization. In this paper we consider bound constrained global optimization problems where first-order derivatives of the objective function can be neither computed nor approximated explicitly. For the solution of such problems the DIRECT algorithm has been proposed which has a good ability to locate promising regions of the feasible domain and convergence properties based on the generation of a dense set of points over the feasible domain. However, the efficiency of DIRECT deteriorates as the dimension and the ill-conditioning of the objective function increase. To overcome these limits, we propose DIRECT-type algorithms enriched by the efficient use of derivative-free local searches combined with nonlinear transformations of the feasible domain and, possibly, of the objective function. We report extensive numerical results both on test problems from the literature and on an application in structural proteomics.


References in zbMATH (referenced in 9 articles )

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  1. Jones, Donald R.; Martins, Joaquim R. R. A.: The DIRECT algorithm: 25 years later (2021)
  2. Lapucci, Matteo; Levato, Tommaso; Sciandrone, Marco: Convergent inexact penalty decomposition methods for cardinality-constrained problems (2021)
  3. Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.: Objective and violation upper bounds on a DIRECT-filter method for global optimization (2020)
  4. Manno, Andrea; Amaldi, Edoardo; Casella, Francesco; Martelli, Emanuele: A local search method for costly black-box problems and its application to CSP plant start-up optimization refinement (2020)
  5. Hassan, Siti Nor Habibah Binti; Niimi, Tomohiro; Yamashita, Nobuo: Augmented Lagrangian method with alternating constraints for nonlinear optimization problems (2019)
  6. Campana, E. F.; Diez, M.; Liuzzi, G.; Lucidi, S.; Pellegrini, R.; Piccialli, V.; Rinaldi, F.; Serani, A.: A multi-objective \textbfDIRECTalgorithm for ship hull optimization (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. Stripinis, Linas; Paulavičius, Remigijus; Žilinskas, Julius: Improved scheme for selection of potentially optimal hyper-rectangles in \textttDIRECT (2018)
  9. Liuzzi, G.; Lucidi, S.; Piccialli, V.: Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization (2016)