A minimal switching procedure for constrained ranking and selection under independent or common random numbers

<div><p>Constrained Ranking and Selection (R&S) aims to select the best system according to a primary performance measure, while also satisfying constraints on secondary performance measures. Several procedures have been proposed for constrained R&S, but these procedures seek to minimize the number of samples required to choose the best constrained system without taking into account the setup costs incurred when switching between systems. We introduce a new procedure that minimizes the number of such switches, while still making a valid selection of the best constrained system. Analytical and experimental results show that the procedure is valid for independent systems and efficient in terms of total cost (incorporating both switching and sampling costs). We also inspect the use of the Common Random Numbers (CRN) approach to improve the efficiency of our new procedure. When implementing CRN, we see a significant decrease in the samples needed to identify the best constrained system, but this is sometimes achieved at the expense of a valid Probability of Correct Selection (PCS) due to the comparison of systems with an unequal number of samples. We propose four variance estimate modifications and show that their use within our new procedure provides good PCS under CRN at the cost of some additional observations.</p></div>