As engineering foundations such as standards and abstraction begin to mature within synthetic biology, it is vital that genetic design automation (GDA) tools be developed to enable synthetic biologists to automatically select standardized DNA components from a library to meet the behavioral specification for a genetic circuit. To this end, we have developed a genetic technology mapping algorithm that builds on the directed acyclic graph (DAG) based mapping techniques originally used to select parts for digital electronic circuit designs and implemented it in our GDA tool, iBioSim. It is among the first genetic technology mapping algorithms to adapt techniques from electronic circuit design, in particular the use of a cost function to guide the search for an optimal solution, and perhaps that which makes the greatest use of standards for describing genetic function and structure to represent design specifications and component libraries. This paper demonstrates the use of our algorithm to map the specifications for three different genetic circuits against four randomly generated libraries of increasing size to evaluate its performance against both exhaustive search and greedy variants for finding optimal and near-optimal solutions.