This paper is concerned with the exploitation of genetic algorithms and their application to the development of a new optimization technique for the high-level synthesis of digit-serial digital filter data-paths. In the resulting optimization technique, the cost associated with the final digital filter data-path is minimized subject to user-specified constraints on the number of physical arithmetic functional units employed. The proposed technique is capable of obtaining global area-optimal, time-optimal, or combined area-cum-time-optimal data-paths, where the optimality takes into account not only the cost associated with the required arithmetic functional units but also that associated with the required support cells (multiplexors and registers). This optimization is made computationally effective by encoding the digital filter data flow-graph into chromosomes which preserve the data-dependency relationships in the original digital filter signal flow-graph under the operations of crossover and mutation by the underlying genetic algorithm. The usefulness of the proposed technique is demonstrated by applying to the constrained optimization of a benchmark elliptic wave digital filter for full bit-serial, full bit-parallel, as well as general digit-serial high-level synthesis. The results thus obtained are compared to those of the existing techniques (whenever appropriate) to confirm the validity of the technique.