Selection of the Best System With an Optimized Continuous Variable

In this paper, we consider a generalized ranking and selection problem, where each system's performance depends on a continuous decision variable necessitating optimization. We focus on a fixed confidence formulation, aiming to find a near-optimal system alongside its corresponding decision variable, meeting specified error tolerances with prescribed confidence levels. To achieve this, we introduce a multi-stage optimization-pruning framework. This framework alternates between optimizing systems using stochastic gradient descent and evaluating their performance through feasibility checks. Our proposed approach offers computational savings by identifying sub-optimal systems before investing effort in optimizing them to the desired accuracy. We demonstrate its efficacy through a numerical study.