<p>Constrained multi-objective optimization problems frequently arise in domains, such as industrial production, supply chain management, and finance. However, despite their widespread relevance, these problems have received limited attention in the simulation optimization literature. This paper considers a multi-objective ranking and selection problem with stochastic constraints, where each alternative has multiple performance measures and is subject to different constraints. Given a fixed simulation budget, the objective is to develop an efficient simulation budget allocation strategy to accurately identify the set of Pareto-optimal and feasible alternatives from a finite set of candidates. To this end, an optimal computing budget allocation (OCBA) problem is formulated to maximize the probability of correctly selecting the Pareto feasible set. Then, a lower bound on the probability of correct selection for the Pareto feasible set is derived, and used to construct an OCBA rule along with a sequential allocation procedure. Numerical experiments and a portfolio selection case study demonstrate the effectiveness of the proposed OCBA rule in significantly improving simulation sampling efficiency.</p>