Comprehensive comparison based on meta-heuristic algorithms for approximation of the fractional-order Laplacian sα as a weighted sum of first-order high-pass filters

Abstract

To implement an approximation of the fractional order Laplacian operator sα as a weighted sum of high pass filter sections, it is essential to extract the cutoff frequencies and filter gains of each section in order to achieve the lowest error possible. Therefore, in this work, five meta-heuristic optimization algorithms are tested in this problem based on a weighted sum objective function. The employed algorithms include the: ant-lion optimizer, cuckoo search algorithm, flower pollination algorithm, whale optimizer, and multi-verse algorithm. A comparison is carried out between the results of these algorithms based on the relative percentage error in magnitude and phase of the obtained approximation in order to endorse the most recommended algorithm. The main outcome is that the Cuckoo search and ant-lion optimizers are capable of identifying the required filter parameters with the least phase and magnitude relative error and with a higher convergence rate.