In many circumstances, chemical process design can be formulated as a multi-objective optimization (MOO) problem. Examples include bi-objective optimization problems, where the economic objective is maximized and environmental impact is minimized simultaneously. Moreover, the random behavior in the process, property, market fluctuation, errors in model prediction and so on would affect the performance of a process. Therefore, it is essential to develop a MOO methodology under uncertainty. In this article, the authors propose a generic and systematic optimization methodology for chemical process design under uncertainty. It aims at identifying the optimal design from a number of candidates. The utility of this methodology is demonstrated by a case study based on the design of a condensate treatment unit in an ammonia plant.