Indifference-zone-free procedures for constrained selection of the best

Selection of the best involves identifying the best system design with the largest (or smallest) mean performance from a finite set of alternatives, which has many important applications in operations research and machine learning. This study focuses on the constrained selection of the best, considering the selection of the alternative with the best primary mean performance while satisfying a finite number of secondary mean constraints. Unlike prevalent procedures that rely on the indifference-zone (IZ) formulation, this paper proposes two novel procedures: a two-stage procedure and a simultaneously running procedure, and both are based on the IZ-free formulation. The former incorporates a tolerance level (TL) parameter, first providing a feasible set of alternatives and then selecting the best feasible one. In contrast, the latter is designed to focus solely on selecting the best feasible alternative rather than determining the feasibility of all alternatives. Theoretical analysis demonstrates that both procedures ensure the probability of correct selection (PCS) for the best feasible alternative. Numerical experiments further showcase the efficacy of our proposed procedures compared to representative ones.