Improved Particle Swarm Optimization with wavelet mutation: Application to linear phase FIR filter design

Abstract

In this paper, various swarm based algorithms like conventional Particle Swarm Optimization (PSO), Improved Particle Swarm Optimization (IPSO) and another novel Improved Particle Swarm Optimization with Wavelet Mutation (IPSOWM) have been applied for the optimal design of linear phase FIR filters. Real coded genetic algorithm (RGA) has also been adopted for the sake of comparison. IPSO uses new definition for the velocity vector. Whereas in addition to the above-mentioned new definition added in IPSO, IPSOWM incorporates a new definition of swarm updating with the help of wavelet mutation based on wavelet theory. Wavelet mutation enhances the PSO to explore the solution space more effectively compared to the other optimization methods. IPSOWM is apparently free from getting trapped at local optima and premature convergence. Low pass (LP), high pass (HP), band pass (BP) and band stop (BS) FIR filters are designed with the proposed IPSOWM and other afore-mentioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the IPSOWM over the other optimization techniques for the solution of the multimodal, non-differentiable, highly non-linear, and constrained FIR filter design problems.