Resistive switching property enables various promising applications such as design of non-volatile in-memory computing devices which has attracted high attention to Resistive Random Access Memories (RRAMs). In this work, we present a multi-objective BDD optimization approach for RRAM based logic circuit design. Dissimilar to classical BDD optimization, evaluating the cost metrics of the circuits in this case does not only depend on the number of BDD nodes but is more advanced. We have utilized a non-dominated sorting genetic algorithm for bi-objective BDD optimization with respect to the number of required RRAMs and computational steps addressing the area and delay of the resulting circuits, respectively. The algorithm also allows preference to one of the objectives if it is of higher significance. Experimental results show that the proposed multi-objective genetic algorithm achieves considerable reduction in both aforementioned criteria in comparison with an existing approach.