Optimal Filter Design Using Differential Evolution Algorithm and Its Advanced Variants

Since passive elements such as resistors and capacitors used in active filter design change the gain and phase of the filter, their selection is an important issue. The ability of the filter to achieve a targeted quality factor depends on the selection of these components. The filter sections are cascaded to get closer to the ideal filter response; in this case, as the number of components increases, the computational complexity in selecting the optimum values increases. Moreover, in practical applications, the values of the filter components should be fixed to the discrete component values in the industrial component series. Thus, the problem turns into a discrete optimization problem that becomes more difficult and time-consuming. The use of metaheuristic algorithms in solving the problem is an alternative approach. This work propounds a survey on the differential evolution (DE) algorithm and its advanced variants utilized for the selection of optimal component values in filter design. Nine DE algorithms have been used to determine the optimal component values of the tenth-order Multi-Feedback topology Bessel filter. The performance of each algorithm has been evaluated in terms of convergence rate and solution accuracy. Statistical results show that success-history based adaptive DE with linear population size reduction (LSHADE) is superior to other DE variants and can reduce the filter quality factor error value to 4.64E-02 for E12 series, 6.45E-02 for E96 series and 2.23E-02 for E192 series. The obtained results show that LSHADE algorithm are an effective tool for the selection of optimal discrete component values in filter design, increasing computational speed and solution accuracy.