John’s dissertation for the School of Engineering and Applied Science at the University of Virginia was titled “Efficient Optimization through Response Surface Modeling: A GROPE Algorithm”.  GROPE (Global Rd Optimization when Probes are Expensive) is a highly-efficient algorithm for global optimization that employs all known results to minimize the number of probes required.

It is ideal for exploring functions with multiple modes, nonlinear or rough surfaces, a moderate number of dimensions, and an expensive evaluation function -- such as those arising from complex computer simulations. Unlike local search algorithms, it can find the overall global best, even if the surface has extreme changes and multiple local minima.

GROPE also estimates the chance of improving one’s result with further probes, which is useful for planning experiments and knowing when to stop. This library also includes RandomSearch and GridSearch and a Conjugent Gradient Search (Powell’s Algorithm). The routines are in “advisor” rather than driver mode, to facilitate use with large and complex simulations.

White Paper: Global Rd Optimization when Probes are Expensive

Dissertation: Efficient Optimization through Response Surface Modeling