Autonomous Application of Netlist Transformations Inside Lagrangian Relaxation-Based Optimization

Timing closure is a complex process that involves many iterative optimization steps applied in various phases of the physical design flow. Lagrangian Relaxation (LR)-based optimization has been established as a viable approach for this. We extend LR-based optimization by interleaving in each iteration various techniques, such as: gate and flip-flop sizing; buffering to fix late and early timing violations; pin swapping; gate merge/split transformations; and useful clock skew. In all cases, locally optimal decisions are made using LR-based cost functions. In each iteration of LR-based optimization, we leverage the Multi-Armed Bandit (MAB) model to automatically pick which optimization heuristic should be applied to the design. The goal is to improve the performance metrics based on the rewards learned from the previous applications of each heuristic and the runtime cost paid for the received reward. The fine-grained combination of an LR-based optimization flow with a statistical recommendation system allows for the autonomous execution of the optimization flow and results in significant quality-of-results improvement relative to the state-of-the-art. More specifically, our flow achieves 17% lower clock period, while also saving 15% power and 6% area, on average, on the TAU2019 benchmarks, as compared to the TAU2019 contest winner, and 25% better leakage power on the ISPD13 benchmarks, as compared to the best reported results.