VLSI design optimization requires evaluation of different solutions, to compare superiority of one over the other. Typically, a solution is superior if it has a better associated timing and cost. In the presence of fabrication variability, the timing and cost of a solution become random variables with spatial and functional correlations. Therefore the evaluation of solutions shall be performed probabilistically to determine the probability that a solution has better cost and timing. In this paper we propose and evaluate three methods for fast and accurate probabilistic comparison of solutions: 1) regular Monte Carlo simulation (as a basis of comparison), 2) joint-pdf approximation using moment matching, and 3) bound-based Conditional Monte Carlo simulation.We integrated these methods in a variability-driven leakage optimization framework using dual threshold voltages. Experimental results show that joint-pdf based approximation is very fast, however it results in sub-optimal solutions due to lower accuracy. Conditional Monte Carlo method is on average 25 times faster than regular Monte Carlo, but slower than approximating joint-pdf. It also results in additional improvement in expected leakage, when compared to joint-pdf method. Monte Carlo simulation is extremely slow and inapplicable to an optimization framework. Deterministic approaches that are based on worst-case estimates had the highest expected leakage.
['Azadeh Davoodi', 'Ankur Srivastava']
Probabilistic evaluation of solutions in variability-driven optimization