| Resumo: | GLODS is a global derivative-free optimization algorithm, relying on local directional direct search, aided by a clever multistart strategy that does not conduct all the lines of search until the end. In 2015, time of the first release of the corresponding solver, GLODS was shown to be competitive when compared to state-of-the-art algorithms, such as MCS or DIRECT. GLODS resorts to sampling techniques to look for minima on a global scale, not taking advantage of the information gathered in previous iterations. As such, the main goal of this work is to replace the pseudo-random sampling approach, used by GLODS to initialize new lines of search, by the minimization of global models of the objective function, defined using radial basis functions, and computed using the points previously evaluated by the algorithm. This should allow a better placement of the starting points for new local lines of search, and, in turn, significantly increase the numerical performance of the algorithm. Naturally, incorporating radial basis functions in GLODS poses new challenges. In this work, we will address questions such as which radial basis functions to use, which points should be selected to compute them, how to minimize these functions, and how to take advantage of their minima in the execution of the algorithm. The new version of GLODS, incorporating radial basis functions, was calibrated to its best numerical performance, and then compared against other state-of-the-art solvers, such as MCS, DIRECT, MATSuMoTo, and ZOOpt. The results obtained are strongly positive. The new algorithm clearly outperforms its previous version, and is competitive with the other solvers tested. Finally, parallel strategies were implemented and tested. Results showed that it is very beneficial to evaluate multiple points simultaneously, for objective functions whose evaluation time is as low as 0.1 seconds. The proposed algorithm, called BoostGLODS, is a cutting-edge, powerful and efficient parallel global derivative-free optimization algo- rithm. |
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