Efficient expected improvement estimation for continuous multiple ranking and selection

This paper considers the problem of identifying the best of a discrete set of alternatives for each of a set of correlated problem instances. We assume that the instances can be described by a set of continuous features and the performance of a particular alternative on a particular problem instance can only be estimated from noisy samples. A possible application is in manufacturing, where we would like to identify the best dispatching rule to be used depending on shop floor conditions, and performance is estimated via stochastic simulation. We propose three myopic sequential sampling methods to collect information, and in particular focus on an efficient estimation of the expected improvement which requires integration over the continuous space of problem instances. Empirical tests show that our method of estimating expected improvement is indeed more efficient than standard Monte Carlo integration, and that our method significantly outperforms a recently published alternative sampling method.