In this research, rotary regenerator (RR) is optimized using constructal theory. For this aim, a heat exchanger with two branches is considered. RR effectiveness and total annual cost (TAC) are deliberated as objective functions and 9 design variables are selected. The multi-objective optimization algorithm is used to obtain the optimal values of objective functions and design variables. The optimum results in the case of constructal are contrasted with optimum results in the conventional RR. The optimum results showed better thermoeconomic results in the case of constructal than conventional RR for the effectiveness higher than 0.6572. As an example, effectiveness improved by 6.98% in the case of constructal in comparison to conventional RR for the constant value of TAC=1821$/year. In addition, the optimum results showed 4.55% improvement in the maximum effectiveness in constructal compared with conventional RR. Finally, distribution of design parameters along with some important parameters such as heat transfer surface area and pressure drop for both studied cases are illustrated, compared and discussed.