Assessing Solution Quality in Stochastic Programs

Abstract

Assessing whether a solution is of high quality
(optimal or near optimal) is a fundamental 
question in optimization. We develop Monte Carlo
sampling-based procedures for assessing solution 
quality in stochastic programs. Quality is defined
via the optimality gap and our procedures' output
is a confidence interval on this gap. We review a
multiple-replications procedure and then present a
result that justifies a computationally simplified
single-replication procedure. Even though the
single replication procedure is computationally
significantly less demanding, the resulting
confidence interval may have low coverage for
small sample sizes on some problems. We provide
variants of this procedure and provide preliminary
guidelines for selecting a candidate solution.
Both are designed to improve the basic procedure's
performance.