PTrace: Derivative-free local tracing of bicriterial design tradeoffs

This paper presents a novel method, PTrace, to locally and uniformly trace convex bicriterial Pareto-optimal fronts for bicriterial optimization problems that, unlike existing methods, does not require derivatives of the objectives with respect to the design variables. The method computes a sequence of points along the front in a user-specified direction from a starting point, such that the points are roughly uniformly spaced as per a spacing constraint from the user. At each iteration, a local quadratic model of the front is used to estimate an appropriate weighted sum of objectives that, on optimization, will give the next point on the front. A single objective optimization on this weighted sum then generates the actual point, which is then used to build a new local model. The method uses convexity-based heuristics to improve on mildly sub-optimal results from the optimizer and reuses cached points to improve the optimization speed and quality. We test the method on a synthetic and a 6-T SRAM power-performance tradeoff test case to demonstrate its effectiveness.