Greg Walker

Experimental Optimization Through Visualization

Overview

Optimization can usually be accomplished with one of many gradient techniques that ensure quick and accurate convergence to a desired extremum of a particular objective function. These techniques are most reliable, however, when the function is "well-behaved". Gradient methods tend to fail when the objective function contains many local extrema. In this case, random search methods (such as genetic algorithms) can be used to locate a global extreme at the cost of requiring much longer computation times. An overwhelming advantage of these methods are their simplicity. For even more intricate objective function behaviour, random search methods may not be able to determine the extrema reliably. It is suggested that more insight and reliability can be obtained through visualization of the objective function. Using this method should require a complete parametric evaluation of the function, but retains an encouraging element of simplicity.

Problem Description

Even though a visualization method can be applied to an enormous range of problems, this study will focus on a specific experimental optimization problem.

When new materials are invented the thermophysical properties of the material are usually unknown. For example, our research group is frequently interested in estimating the thermophysical properies of new composites that exhibit anisotropic behavior. To estimate the properties we must design an experiment that will give us the best results. A typical experimental optimization procedure is extremely complicated and usually is performed using a parametric approach, and only one criterion (for determining the "best" experiment) is used.

I suggest that a visual approach can locate the "best" experiment in terms of many criteria.

Project Goals

1. To identify the criteria to be used to determine the "best" experiment.
2. To visualize several optimization criteria as a function of the parameters to be optimized.
3. To locate experimental parameters that produce the "best" experiment.
4. To verify the ability of the experiment to accurately compute the parameters better than previous experiments.
5. To record my findings on this particular problem as well as extrapolations of the method to other situations in a small multi-media presentation.

Tools

The parametric study of the optimization criteria will be performed using a Fortran program (on any platform). The visualization will be accomplished using SpyGlass Dicer and/or AVS. (Even though I would prefer an NCSA viz tool, I would like to learn more about MAC's because I have never used one.) The multi-media presentation will be performed using Director (I think).