Complexity Reduction Using Expansive Coding

Abs t rac t . This paper describes a new technique for reducing the complexity of algorithms, such as those used in digital signal processing~ using a genetic algorithm (GA). The method, referred to as expansive coding, is a representation methodology which makes complicated combinatorim optimisation tasks easier to solve for a. GA. Using this technique, the representation, operators and fitness function used by the GA become more complicated, but the search space becomes less epistatic, and therefore easier for the GA to tackle. This reduction in epistasis (interaction between parameters) is essential if the difficult task of complexity reduction is to be successfully achieved. Expansive coding spreads the task's complexity more evenly among the operators, fitness function and search space. We demonstrate how this technique can be applied to two cases of reduction of complexity of algorithms: a multiplier for quaternion numbers, and a Walsh transform computation. We suggest why the technique is more successful on the former task than the latter.