Digital filter design using multiple pareto fronts

Abstract

Evolutionary approaches have been used in a large variety of design domains, from aircraft engineering to the designs of analog filters. Many of these approaches use measures to improve the variety of solutions in the population. One such measure is clustering. In this paper, clustering and Pareto optimisation are combined into a single evolutionary design algorithm. The population is split into a number of clusters, and parent and offspring selection, as well as fitness calculation, are performed on a per-cluster basis. The objective of this is to prevent the system from converging prematurely to a local minimum and to encourage a number of different designs that fulfil the design criteria. Our approach is demonstrated in the domain of digital filter design. Using a polar coordinate based pole-zero representation, two different lowpass filter design problems are explored. The results are compared to designs created by a human expert. They demonstrate that the evolutionary process is able to create designs that are competitive with those created using a conventional design process by a human expert. They also demonstrate that each evolutionary run can produce a number of different designs with similar fitness values, but very different characteristics.