Stochastic Optimization Over Correlated Data Set: A Case Study on VLSI Decoupling Capacitance Budgeting

where pi are the parameters that control the feasible region S of x. For example, in the contingency analysis of power systems, pi is a vector of 0-1 variables, indicating which of the branches are open. Each pi corresponds to one contingency situation. Another example is the decoupling capacitance budgeting for very large scale integrated (VLSI) circuits and systems, where pi can be different load current profile. When the number of possible scenarios are small, we can use enumeration to find out the worst case. But when it is large or even infinite, enumeration becomes computationally expensive, sometimes even infeasible, and accordingly, we need some elegant algorithms that can efficiently solve the problem. In this chapter, we will use the decoupling capacitance budgeting problem in very large scale integrated (VLSI) circuits and systems to illustrate one recently developed algorithm when the Pi’s are correlated. The continuous semiconductor technology scaling leads to growing process variations (Agarwal & Nassif, 2007), and statistical optimization has been actively researched to cope with process variations. Recent examples include stochastic gate sizing for power reduction (Bhardwaj & Vrudhula, 2005; Mani et al., 2005) and for yield optimization (Davoodi & Srivastava, 2006; Sinha et al., 2005), stochastic buffer insertion to minimize clock delay (He et al., 2007), and adaptive body biasing with post-silicon tuning (Mani et al., 2006). However, all these papers ignore operation variation such as crosstalk difference over input vectors, power supply noise fluctuation over time, and processor temperature variation over workload. We Stochastic Optimization Over Correlated Data Set: A Case Study on VLSI Decoupling Capacitance Budgeting 8