Abstract
Some numerical results with an implementation of the DEEPS algorithm, as well as the evolution of the minimizing function values, along the iterations of the optimization process are presented in this chapter. It is shown that the optimization process has two phases. In the first one, the reduction phase, for a small number of iterations, the function values are strongly reduced. In the second one, the stalling phase, the function values are very slowly reduced for a large number of iterations. For some problems, in the first phase of the optimization process, the function values are steadily reduced with some plateaus corresponding to halving the bounds of the domains where the trial points are generated. This is a typical evolution of the function values along the iterations of DEEPS. Intensive numerical results for solving a number of 140 unconstrained optimization problems, out of which 16 are real applications, have proved that DEEPS is able to solve a large variety of problems up to 500 variables. Comparisons with the Nelder-Mead algorithm showed that DEEPS is more efficient and more robust.
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Andrei, N. (2021). Numerical Results. In: A Derivative-free Two Level Random Search Method for Unconstrained Optimization. SpringerBriefs in Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-68517-1_4
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DOI: https://doi.org/10.1007/978-3-030-68517-1_4
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