In the present work, an improved Entropy Generation Minimisation (EGM) approach aiming at minimising the revised entropy generation number which is the non-dimensionalised entropy by the ratio of heat flow to the input temperature of the cold fluid is developed for a plate-fin heat exchanger design with multiple design variables with the help of genetic algorithm. It is found that the approach can decrease the total fan power dramatically and improve the exchanger effectiveness simultaneously. Finally, this approach is applied to a heat recovery system where the heat exchanger works as a component of the system.