The heat exchanger compactness is a key factor in several engineering applications, such as, in automotive applications that use enhanced heat transfer surfaces on the air side to improve the convective heat transfer coefficient. In this study, a combined geometry of louvered fins and vortex generators is numerically simulated to optimize the thermohydraulic behavior of a compact heat exchanger. The influence of eight parameters of the enhanced surface on its thermohydraulic performance is analyzed. The thermohydraulic performance is evaluated through the Performance Evaluation Criterion, which relates the Colburn factor and the friction factor, i.e., the heat transfer enhancement and the increment of the pressure losses of the actual model with respect to a reference one. A metaheuristic tool, based on the NSGA-II genetic algorithms, combined with multi-objective optimization technique, is applied. The objective functions used in the optimization are obtained with numerical methods and computational fluid dynamics techniques. As a novelty, the optimization was carried out individually and under non-stationary flow conditions, for a total of eight magnitudes associated with the vortex generators. The optimized geometry is able to enhance the convective heat transfer between 6.55% and 19.63%, with an increase in pressure losses varying from 10.95% to 20.67% depending on the Reynolds number.