Product design optimization under model or input variable uncertainty is commonly required, in which robustness and reliability are two important attributes of the design. In structure design, it is critical to maintain the design feasibility (or reliability); while at the same time, to counter manufacturing variations, robust design is employed in order to obtain high product quality. It is necessary, therefore, to establish a multi-objective optimization problem that combines both robustness and reliability considerations, where the product's performance variation and the performance function are simultaneously optimized, subject to probabilistic constraints for design feasibility. Based on the idea of the reliability index and the Most Probable Point (MPP), probabilistic constraints are converted into deterministic constraints. Then an efficient Multi-Objective Memetic Algorithm (MOMA) is presented to minimize robustness and performance value, subject to deterministic constraints. A classical I-beam example with probabilistic constraints illustrating the MOMA concept and applicability is proposed in the paper, the result is a Pareto frontier of robustness and performance value.