In this work, multi-objective optimization for design of a benchmark cogeneration system known as CGAM cogeneration system is performed. In optimization approach, the exergetic and economic aspects are considered, simultaneously. The thermoeconomic objective is minimized while the exergetic objective is maximized. A multi-objective particle swarm optimization (MOPSO) algorithm is used to find a set of Pareto optimal solutions with respect to the aforementioned objective functions. An example of fuzzy decision-making is also presented and a final optimal solution is introduced.