Testowanie nieliniowych algorytmów optymalizacyjnych – zestaw funkcji typu benchmark
Testing nonlinear optimization algorithms ? set of benchmark type functions

Summary/Abstract: The paper presents a specially selected set of classic test functions evaluating the performance of newly created or modified optimization algorithms. Described bench-mark tests can be used to compare the effectiveness of different algorithms minimizing the sums of squares of nonlinear functions. The assessment relates to the effectiveness of meth-ods searching for the local or global extremes of simple tests (in terms of number of variables and sub-functions), but causing great difficulties in the process of finding optimal solu-tions due to their strong nonlinearity, multimodality, very complicated system of contour lines or non-differentiability. Usefulness of this tests set was examined for the modification of the optimization algorithm for least squares methods (proposed by the author), not using any derivatives of functions through a calculation. This is an improved hybrid version of the Levenberg-Marquardt method (ensuring non-singularity of the matrix of numerical esti-mates of derivatives) combined with modified Broyden’s first row updating method for set-ting the direction and length of searching steps. The paper also includes a summary of the numerical results and its evaluation, which proves the usefulness of the dedicated set of tests and pre-validates the effectiveness of the proposed optimization algorithm.

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