In this paper a plate fin heat exchanger (PFHE) with constructal configuration is modeled and optimized and the results are compared with a conventional configuration. Effectiveness as well as the total annual cost (TAC) are considered as two objective functions and 12 design parameters related to the fin and size of PFHE are selected in constructal case (it is 6 in conventional case). Multi objective optimization is performed in each case using Particle Swarm Optimization algorithm. Constructal PFHE is a thermo-economically optimum for the effectiveness higher than 0.747 while conventional PFHE is thermo-economically optimum for the effectiveness lower than 0.747. In addition, the higher values of fin parameters and lower values of PFHE size are required in the constructal compared with conventional PFHE for a specific effectiveness. Moreover, the higher values of the fin sizing parameters are selected in the second part compared with first part of constructal PFHE. Furthermore, the higher values of PFHE sizing parameters are selected in the second part compared with first part of constructal PFHE. Finally, optimum results show that the higher heat exchanger volume is required in the second part than the first part of the constructal PFHE.