1. A system to manage layer promotion in a routing phase of integrated circuit design, the system comprising: a memory device configured to store instructions; and a processor configured to execute the instructions to identify a set of candidate interconnects for layer promotion, score and sort the set of candidate interconnects according to a respective score to thereby establish a respective rank, assess routing demand and resource availability based on layer promotion of the set of candidate interconnects, and manage the set of candidate interconnects based on the respective rank and the resource availability, the processor assessing the routing demand and resource availability and managing the set of candidate interconnects iteratively, wherein the processor, in at least one iteration, generates a second set of candidate interconnects by reducing the set of candidate interconnects.