This paper presents a surrogate model-based computationally efficient optimization scheme for design problems with multiple, probabilistic objectives estimated through stochastic simulation. It examines the extension of the previously developed MODU-AIM (Multi-Objective Design under Uncertainty with Augmented Input Metamodels) algorithm, which performs well for bi-objective problem but encounters scalability difficulties for applications with more than two objectives. Computational efficiency is achieved by using a single surrogate model, adaptively refined within an iterative optimization setting, to simultaneously support the uncertainty quantification and the design optimization, and the MODU-AIM extension is established by replacing the originally used epsilon-constraint optimizer with a multi-objective evolutionary algorithm (MOEA). This requires various modifications to accommodate MOEA’s unique traits. For uncertainty quantification, a clustering-based importance sampling density selection is introduced to mitigate MOEA’s lack of direct control on Pareto solution density. To address the potentially large solution set of MOEAs, both the termination criterion of the iterative optimization scheme and the design of experiment (DoE) strategy for refinement of the surrogate model are modified, leveraging efficient performance comparison indicators. The importance of each objective in the different parts of the Pareto front is further integrated in the DoE to improve the adaptive selection of experiments.