Heat exchangers are key components of thermal energy conversion systems, however, their optimal design is still based on reduced order models relying on semi-empirical heat transfer correlations. CFD-based design optimization emerged as a viable method to provide a significant improvement in performance at an affordable cost. This study presents a framework to optimize multiple heat transfer surfaces concurrently using the adjoint method. The heat transfer surfaces are parametrized using a CAD-based parametrization method, and their performance is evaluated using a RANS solver complemented by its discrete adjoint counterpart for gradient computation. The optimization framework is applied to minimize the pressure drop across a bare-tube heat exchanger while constraining the heat transfer rate. Two variants of the same optimization problem are formulated: in the first one, the sensitivities are averaged and the tubes are constrained to maintain the same shape, while in the second variant, the shape of the tubes can vary, resulting in an optimum solution with non-identical tube shapes. The results show that the optimized geometry reduces the pressure drop by 19% if the tube shapes are identical, and by 25% in the case of non-identical shapes, compared to the baseline. To identify the physical mechanisms contributing to the fluid-dynamic losses, entropy generation along the flow path was investigated. The results reveal that the major loss reduction observed for the case of non-identical tube shapes is due to the better thermo-hydraulic performance of the first and last tubes.@en