The objective of this contribution is twofold. First, a multi-objective hydrothermal optimization is performed to determine the optimum nanoparticles (NPs) shape in nanofluid flow through an annular pipe having metal foam fins, in the forced convection regime. Second, the suitability of the performance evaluation criterion (PEC), as a common method to analyze the hydrothermal performance of thermal systems, is examined by comparing the outcomes of the multi-objective optimization method with those obtained by maximizing PEC. It is found that, depending on the value of the Reynolds number, the cylindrical-shaped NPs or the blade-shaped NPs exhibit the highest heat transfer performance. The lowest value of the required pumping power belongs to the spherical-shaped NPs. The results indicate that PEC attains its maximum value in the spherical-shaped NPs, the NPs fraction of 0.01, the nondimensional fin length of 0.4, the Darcy number of 0.01, and the medium porosity of 0.75. However, the multi-objective algorithm provides several optimum circumstances, each for a certain criterion indicating the suitability of this strategy for hydrothermal performance optimization of the system.