Multi-objective optimization of a cross-flow plate fin heat exchanger (PFHE) by means of an entropy generation minimization technique is described. Entropy generation in the PFHE was separated into thermal and pressure entropy generation as two objective functions to be minimized simultaneously. The Pareto optimal frontier was obtained and a final optimal solution was selected. By implementing a decision-making method, here the LINMAP method, the best trade-off was achieved between thermal efficiency and pumping cost. This approach led to a configuration of the PFHE with lower magnitude of entropy generation, reduced pressure drop and pumping power, and lower operating and total cost in comparison to single-objective optimization approaches.