Probabilistic Evaluation of Solutions in Variability-Driven Optimization

Very large-scale integration design optimization requires comparison of different solutions to evaluate 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, the authors propose/evaluate three methods for fast and accurate computation of this probability: 1) regular Monte Carlo (MC) simulation (as a basis of comparison); 2) joint probability density function (jpdf) approximation using moment matching; and 3) bound-based conditional-MC simulation. They integrated these methods in a variability-driven leakage optimization framework using dual threshold voltages. Their results show that jpdf approximation is efficient; however, it results in suboptimal solutions due to lower accuracy approximating jpdf