Expected Solution Quality

This paper presents the Expected Solution Quality (ESQ) method for statistically characterizing scheduling problems and the performance of schedulers. The ESQ method is demonstrated by applying it to a practical telescope scheduling problem. The method addresses the important and difficult issue of how to meaningfully evaluate the performance of a scheduler on a constrained optimization problem for which an optimal solution is not known. At the heart of ESQ is a Monte Carlo algor ithm that estimates a problem's probability density function with respect to solution quality This "quality density function" provides a useful characterization of a scheduling problem, and it also provides a background against which scheduler performance can be meaningfully evaluated. ESQ provides a unitless measure that combines both schedule quality and the amount of time to generate a schedule.