A hybrid moth flame optimization and variable neighbourhood search technique for optimal design of IIR filters

In this manuscript, a hybrid optimization technique, which integrates moth flame optimization (MFO) technique and variable neighbourhood search (VNS) heuristic, has been proposed to search the optimal coefficients of infinite impulse response (IIR) filter. The search process of MFO technique is based on the navigation method of the moths. The moth updates its position around the flame. In order to improve the search ability and convergence precision of MFO technique, the VNS heuristic has been integrated with it. In VNS heuristic, a random solution is generated around the neighbourhood of the best MFO solution. The random solution is updated by local search ‘Powell’s pattern search’ (PPS) method. The PPS method has excellent exploitation capability, which avoids any possible stagnation at local optimal solution. The proposed optimization technique has been applied on the benchmark functions and for the optimal design of five low-pass and six high-pass IIR filters. For low-pass filter (LPF) design problems 1–5, the proposed optimization technique is able to minimize the objective function by at least 50.78%, 205.72%, 122.36%, 20.48% and 28.76% more as compared to the results obtained by other state-of-the-art techniques, respectively. Hence, optimal IIR filter designed by the proposed optimization technique is able to achieve better desirable attributes, i.e. passband error, stopband error, square error, and stopband attenuation as compared to other state-of-the-art techniques.