A Fuzzy Programming Based Techniques for Variation Aware Multi-metric Optimization

The uncertainty due to process variations is modeled using interval valued fuzzy numbers and a fuzzy programming based optimization is proposed to improve circuit yield without significant over design. In addition to the statistical optimization methods, we have proposed a novel technique that dynamically detects and creates the slack needed to accommodate the delay due to variations. The variation aware gate sizing technique is formulated as a fuzzy linear program and the uncertainty in delay due to process variations is modeled using fuzzy membership functions. The timing based placement technique; on the other hand, due to its quadratic dependence on wire length is modeled as nonlinear programming problem. The variations in timing based placement are modeled as fuzzy numbers in the fuzzy formulation and as chance constraints in the stochastic formulation. In the context of dynamic variation compensation, a delay detection circuit is used to identify the uncertainty in critical path delay. The delay detection circuit controls the instance of data capture in critical path memory flops to avoid a timing failure in the presence of variations.