Convective heat transfer can be enhanced by streamwise vortices and coherent flow structures produced downstream Vortex Generators (VGs). The thermal performance depends on the VG shape which controls the intensity and topology of the vortices. Thus, VG shape optimization is a major challenge in designing sustainable and efficient heat exchangers. In the present study, a multi-objective optimization is performed through large space exploration design to find optimal VG shapes that adapt to different flow regimes. Simulations are carried out in parallel plate turbulent flow for three different Reynolds numbers; and . The present numerical results are first validated against numerical and experimental data from the open literature. Then, and for the first time, seven design parameters are investigated, based on VG shape dimensions. The new optimized VG show a thermal enhancement factor between 11 and 35%, relative to a smooth channel case, and between 3 and 14%, relative to different VG shapes from the recent open literature. The present results are analyzed in details by focusing on the physics of the flow structure and its correlation to the convective heat transfer enhancement using local criteria for flow visualization and vortex intensity quantification.