Optimal Computing Budget Allocation for Multi-Objective Ranking and Selection Under Bernoulli Distribution

This paper studies a multi-objective ranking and selection (MORS) issue with observations following Bernoulli distribution. The Pareto-optimal set is aimed to be selected with each design and performance measure pair being evaluated separately. Our contribution is twofold. (i) We provide a frequentist work under Bernoulli assumption in MORS where a robust asymptotic optimal sampling strategy is derived based on large deviation principle (LDP). (ii) From the optimal sampling strategy, we propose a sequential selection procedure, named MOCBA-B. Numerical results based on averaged probability of correct selection (PCS) show that MOCBA-B is significantly superior to equal allocation (EA) and is comparable to the theoretically optimal allocation strategy.