SagTree: Towards efficient mutation in evolutionary circuit approximation

Abstract

• We thoroughly investigate the performance of various mutation operators for Cartesian Genetic Programming in the context of automated design of complex arithmetic circuits. • We propose a novel mutation operator, so-called SagTree, that is tailored to circuit approximation and combines the classical single active gene mutation with a node deactivation operation. • We perform an extensive experimental comparison with existing mutation operators—our results, grounded on a rigorous statistical evaluation including 39 approximation problems and over 14,000 approximation runs, clearly demonstrate that the SagTree operator significantly outperforms the other operators in CGP-based circuit approximation. • Using the SagTree operator, we obtain complex approximate circuits providing significantly better trade-offs between energy savings and the incurred error compared to existing circuits obtained using both evolutionary and non-evolutionary state-of-the-art techniques. Approximate circuits that trade the chip area for the quality of results play a key role in the development of energy-aware systems. Designing complex approximate circuits is, however, a very difficult and computationally demanding process. Evolutionary approximation—in particular, the method of Cartesian Genetic Programming (CGP)—currently represents one of the most successful approaches for automated circuit approximation. In this paper, we thoroughly investigate mutation operators for CGP with respect to the performance of circuit approximation. We design a novel dedicated operator that combines the classical single active gene mutation with a node deactivation operation (eliminating a part of the circuit forming a tree from an active gate). We show that our new operator significantly outperforms other operators on a wide class of approximation problems (such as 16 bit multipliers and dividers) and thus improves the performance of the state-of-the-art approximation techniques. Our results are grounded on a rigorous statistical evaluation including 39 approximation scenarios and 14,000 runs.