Gaining Insight into Evolutionary Programming Through Landscape Visualization: An Investigation into IIR Filtering

Evolutionary programming (EP) has been used for the adaptation (optimization) of IIR filters. In a previous study [1], the rate of optimization using EP was shown to be dependent on the structure of the filter used during realization. Furthermore, this dependency changes with the filter order. In this paper, the reasons for such a dependence are investigated. Gradient-based algorithms are also affected by the filter realization, which determines the nature of the mean squared error surface. EP is robust to the presence of local minima and while ensuring the stability of the generated solution offers provable global convergence in the limit. The error surfaces, as seen by EP, while modeling these IIR filters in various realizations, namely, direct, cascade, parallel, and lattice form are analyzed. Experimental results show that ‘gradient friendly’ error surfaces, corresponding to favorable realizations when using gradient based techniques, are not necessarily ‘EP friendly’ and vice versa.