The effect of fin design parameters on the performance of plate-fin heat exchanges was investigated in the paper, in which an improved algorithm combing a Kriging response surface and multi-objective genetic algorithm was used. An ideal gas was adopted as the working fluid and epsilon-NTU method was utilized to determine the heat transfer and pressure drop. The fin height h, fin space s, fin thickness t and interrupted length l of serrated fin and channel inlet Reynolds number are firstly optimized, while the j factor, f factor and JF factor are optimization goals. The results show that when the inlet channel flow is in the laminar flow (Re < 1000), it is beneficial to trade off the j factor and f factor. Furthermore, the total heat flow rate, total annual cost and number of entropy production units of plate-fin heat exchanges are optimized with the specified mass flow rate under given space by multi-objective optimization. Results obtained from the first two objectives and three objectives show that the fin design parameters are very similar except that the latter interrupted length is smaller slightly. A comparison between the results obtained by the previous approaches and the proposed algorithm shows that under the same effectiveness, the annual cost of the proposed algorithm is about 10% lower than the previous ones and it is faster to be converged. Therefore, this study demonstrated that the proposed algorithm is able to optimize the fin design parameter of serrated fin and the obtained results are beneficial to guide the design of plate-fin heat exchanges. (C) 2016 Elsevier Ltd. All rights reserved.