Simple genetic algorithm (SGA) is a population-based optimization method based on the Darwinian natural selection. The theoretical foundations of SGA are the Schema Theorem and the Building Block Hypothesis. Although SGA does well in many applications as an optimization method, it still does not guarantee the convergence of a global optimum in GA-hard problems and deceptive problems. As an alternative schema, therefore, there is a growing interest in a co-evolutionary system where two populations constantly interact and cooperate each other. In this paper we propose a schema co-evolutionary algorithm (SCEA) and show why the SCEA works better than SGA in terms of an extended schema theorem. The experimental analyses using the Walsh-Schema Transform show that the SCEA works well in GA-hard problems including deceptive problems.

In this paper, we compare the performance of evolutionary digital filters (EDFs) for IIR adaptive digital filters (ADFs) in terms of convergence behavior and stability, and discuss their advantages. The authors have already proposed the EDF which is controlled by adaptive algorithm based on the evolutionary strategies of living things. This adaptive algorithm of the EDF controls and changes the coefficients of inner digital filters using the cloning method or the mating method. Thus, the adaptive algorithm of the EDF is of a non-gradient and multi-point search type. Numerical examples are given to demonstrate the effectiveness and features of the EDF such that (1) they can work as adaptive filters as expected, (2) they can adopt various error functions such as the mean square error, the absolute sum error, and the maximum error functions, and (3) the EDF using IIR filters (IIR-EDF) has a higher convergence rate and smaller adaptation noise than the LMS adaptive digital filter (LMS-ADF) and the adaptive digital filter based on the simple genetic algorithm (SGA-ADF) on a multiple-peak surface.