Visualization of trade-offs in optimization of integrated circuits with multiple objectives

In the field of circuit design and optimization, trade-offs often exist between the different circuit performances in the course of circuit optimization. For a particular setting of the designable parameters, the circuit will have its nominal set of responses and characteristic outputs, along with their measures of variability. As we try to improve some performance index, or to reduce the variabilities of some performance, some other objective (mean value of a response, or its variability) might become degraded, giving rise to trade-off situations between two or more circuit performances and/or their variabilities. This paper proposes a methodology for identifying the trade-offs by visualizing them in a qualitative manner, and using this information to direct the optimization process suitably to obtain the desirable performance statistics. This is accomplished by utilizing a novel concept of local Trade-off Matrices able to quickly characterize the existing trade-offs. Trade-offs corresponding to a different direction in the space of optimized parameters can be investigated, and suitable decisions can be made to direct the optimizer