Improving Hit-and-Run with single observations for continuous simulation optimization

Many algorithms for continuous simulation optimization have been proposed, but the question of the number of replications at a specific point is always an issue. In this paper, instead of averaging replications of the objective function at a specific point (e.g., sample average), we average observed function evaluations from neighboring points. The Improving Hit-and-Run algorithm is modified to accommodate averaging in a ball of fixed radius, thus only sampling any point once. The computational results suggest an efficiency with single observations per sample point that simultaneously improves the estimation of the function value and samples closer to the optimum as the algorithm progresses.