  We consider bi-objective ranking and selection problems, where the goal is to
correctly identify the Pareto optimal solutions among a finite set of
candidates for which the two objective outcomes have been observed with
uncertainty (e.g., after running a multiobjective stochastic simulation
optimization procedure). When identifying these solutions, the noise perturbing
the observed performance may lead to two types of errors: solutions that are
truly Pareto-optimal can be wrongly considered dominated, and solutions that
are truly dominated can be wrongly considered Pareto-optimal. We propose a
novel Bayesian bi-objective ranking and selection method that sequentially
allocates extra samples to competitive solutions, in view of reducing the
misclassification errors when identifying the solutions with the best expected
performance. The approach uses stochastic kriging to build reliable predictive
distributions of the objective outcomes, and exploits this information to
decide how to resample. Experimental results show that the proposed method
outperforms the standard allocation method, as well as a well-known the
state-of-the-art algorithm. Moreover, we show that the other competing
algorithms also benefit from the use of stochastic kriging information; yet,
the proposed method remains superior.
