A multi-objective optimization of main heat exchanger in a regenerative Brayton cycle system is carried out based on entransy dissipation. The best trade-off between the entransy dissipation numbers caused by heat transfer and fluid friction is achieved in the Pareto optimal solutions, the decrease of entransy dissipation related to heat transfer inevitably leads to the increase of entransy dissipation due to fluid friction, and vice versa. The entransy dissipation due to heat transfer rather than that due to fluid friction plays a decisive role in the net work output. The Pareto optimal schemes are widely superior to the random design schemes at both component and system levels. The diversity of Pareto design schemes is very convenient for users to choose the most appropriate design scheme according to the practical needs. (C) 2013 Elsevier Ltd. All rights reserved.