Pareto sampling: Choosing the right weights by derivative pursuit

Abstract

The convex weighted-sum method for multi-objective optimization has the desirable property of not worsening the difficulty of the optimization problem, but can lead to very nonuniform sampling. This paper explains the relationship between the weights and the partial derivatives of the tradeoff surface, and shows how to use it to choose the right weights and uniformly sample largely convex tradeoff surfaces. It proposes a novel method, Derivative Pursuit (DP), that iteratively refines a simplicial approximation of the tradeoff surface by using partial derivative information to guide the weights generation. We demonstrate the improvements offered by DP on both synthetic and circuit test cases, including a 22 nm SRAM bitcell design problem with strict read and write yield constraints, and power and performance objectives.