Solid oxide fuel cell-proton exchange membrane (SOFC-PEM) hybrid system is being foreseen as a valuable alternative for power generation. As this hybrid system is a conceptual design, many uncertainties involving input values should be considered at the early stage of process optimization. We present in this paper a generalized framework of multi-objective optimization under uncertainty for the synthesis/design optimization of the SOFC-PEM hybrid system. The framework is based on geometric, economic and electrochemical models and focuses on evaluating the effect of uncertainty in operating parameters on three conflicting objectives: electricity efficiency, SOFC current density and capital cost of system. Themulti-objective optimization provides solutions in the form of a Pareto surface, with a range of possible synthesis/design solutions and a logical procedure for searching the global optimum solution for decision maker. Comparing the stochastic and deterministic Pareto surfaces of different objectives, we conclude that the objectives are considerably influenced by uncertainties because the two trade-off surfaces are different. (C) 2014 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.