Objective functions that are expensive (in time) to evaluate often limit the usefulness of optimzation in time-sensitive applications. Straightforward ways to address this difficulty are parallelization and increased computational power. We are also exploring methods for reducing unrofitable CPU burden through the use of surrogate functions and objective function control via subprocess CPU-time monitoring.

The first work in this area is the master's thesis of Raymond Magallanez Surrogate strategies for computationally expensive optimization problems with CPU-time correlated functions. This work considers objective functions whose return value is strongly correlated with the computational time. Surrogate functions on the objective and the cputime (which double as constraints) are used to guide the search through the most time-profitable region of parameter space. Overall runtimes were shown to be significantly reduced even though more function evaluations may be necessary.

The methods described above can be applied to time reduction in problems whose objective computation is correlated to algorithmic parameters. Common examples of such objectives are finite-element forward-model computations for which the computational time is strongly influenced by the choice of mesh size and time step. By allowing the optimization algorithm to govern the selection of both physical-model and algorithmic parameters, significant overall time savings is likely to be achieved. We have submitted an LDRD-ER proposal for FY08 that will address this interesting area: Improving Parameter Optimization Performance