Designing of optimal digital IIR filter in the multi-objective framework using an evolutionary algorithm

Abstract

In this work, an optimization technique i.e. diversity-driven multi-parent evolutionary algorithm with adaptive non-uniform mutation (DDMPEA-ANUM) has been used to design a digital IIR filter considering the magnitude response error of pass-band and stop-band and linear phase response error as fitness functions. The proposed algorithm utilizes population space aggregation and fitness variance concepts to guide the solution so that it will not stuck in local optima. The efficacy of the developed method is tested on twenty-three benchmark functions and compared with other state of art algorithms in terms of best, worst, average and standard deviation. The statistical analysis of the developed algorithm has also been carried out through Wilcoxon’s rank-sum to confirm its effectiveness. The developed algorithm while designing the IIR filter design problem obtained the least values for magnitude response error of pass-band and stop-band and linear phase response when compared to other state of art algorithms. For instance, the developed algorithm obtained magnitude response error for pass band and stop band and linear phase response error of 0.0101, 0.727 and 3.3903 ×10−06 for LP, 0.0073, 0.003 and 2.3933 ×10−06 for HP, 0.0018, 0.0260 and 4.4429 ×10−06 for bandpass filter and 0.0445, 0.0209 and 1.3081 ×10−06 for band stop filter.