The optimisation of multiplier-free directed graphs: an approach using genetic algorithms

This paper considers the problem of realising directed graphs using evolutionary optimisation methods. Graphs are constrained to have edge gains equal to powers of two and signal values at internal vertices are required to be weighted by elements of a given coefficient vector. The objective is to synthesise a graph with minimum complexity. The method is developed for the case of a single multiplicative coefficient using vertex cardinality as a measure of solution fitness and extended to the more general case of a multi-element coefficient vector with additional optimisation constraints. The potential of the approach is demonstrated using examples based on FIR digital filters