Evolving parsimonious circuits through Shapley value-based genetic programming

Evolutionary analog circuit design is a challenging task due to the large search space incurred by the circuit topology and device values. Applying genetic operators on randomly selected genes may make it difficult to identify which part of sub-circuit is beneficial to the evolution and even destroy useful sub-circuits, potentially incurring stagnation of the evolutionary process and bloat on the evolved circuits. In this paper, we propose a tree-based approach called Shapley Circuit Tree that incorporates Shapley values for quantifying the contribution of each function node of the circuit tree to the performance of the whole tree, to guide the evolutionary process. Our experiments on three benchmarks show that the proposed approach is able to evolve analog circuits with smaller area while converging faster than existing approaches.