The present work aims to investigate the influence of extended surfaces (fins) on the multi-objective optimization of a tubular heat exchanger network (THEN). An increase in the heat transfer area using various extended surfaces (fins) to enhance the performance of the heat exchanger was used while considering the effectiveness and total heat transfer area as two objective functions. In addition to the simulation of simple fins, a new set of fins, called constructal fins, was designed based on the constructal theory. Tubular heat exchanger network design parameters were chosen as optimization variables, and optimization results were achieved in such a way as to enhance the effectiveness and decrease the total heat transfer area. The results show the importance of constructal fins in improving the objective functions of heat exchangers. For instance, the simple fins case enhances the effectiveness by up to 5.3% compared to that without fins (usual heat exchanger) while using constructal fins, in addition to the 7% increment of effectiveness, reduces the total heat transfer area by 9.47%. In order to optimize the heat exchanger, the heat transfer rate and cold fluid temperature must increase, and at the same time, the hot exiting fluid temperature should decrease at the same constant total heat transfer area, which is higher in the constructal fins case. Finally, optimized design variables were studied for different cases, and the effects of various fins were reported.