Two-stage ensemble memetic algorithm: Function optimization and digital IIR filter design

The research on optimal design of infinite-impulse response (IIR) filters based on optimization techniques has gained much attention in recent years. However, due to the limited performance of the applied optimization techniques, the orders of the filters, which can be obtained, are very low in the previous research. Memetic algorithms (MAs) are widely recognized to have better convergence capability than their conventional counterparts. However, the universality of the MAs, e.g. the ability of solving diverse kinds of digital IIR filter designs, is still limited. In this paper, we design a Two-Stage ensemble Memetic Algorithm (TSMA) framework to more appropriately synthesize the strengths of the evolutionary global search and local search techniques. In the first optimization stage, a competition is held among the candidate local search techniques. Its major idea is to choose the best local search technique and to obtain good initial state. Inheriting the good information of the first stage, the second optimization stage is to implement effective adaptive MA to pursue high-quality solution. The experimental studies presented in this paper contain three aspects: (1) the benefits of the TSMA framework are experimentally investigated by comparing TSMA with its sub-optimizers and recent effective evolutionary algorithms (EAs) on 26 test functions; then (2) TSMA is compared with 4 MAs on the CEC05 functions to comprehensively show the advantages of TSMA; and (3) the TSMA and 6 state-of-the-art algorithms are applied to design high-order digital infinite-impulse response (IIR) filters. The experimental results definitely demonstrate the excellent effectiveness, efficiency and reliability of TSMA on both function optimization and digital IIR filter design tasks.