Two-phase ejectors are highly useful devices because they can recover and use the energy lost in the expansion process of the refrigeration cycle. However, in a small-sized household refrigeration cycle, a modified ejector cycle is required due to the low operating pressure and mass flow rate. In this study, a dual evaporator ejector cycle (DEEC), which is advantageous for household refrigeration, was applied. In the DEEC, unlike the conventional ejector cycle, the motive nozzle exit position (NXP) considerably affects the cycle performance. The objective of this study was to optimize the NXP of a DEEC for a household refrigeration cycle with low-pressure refrigerants via an artificial neural network (ANN) model. Using the developed model, the DEEC pressure lifting ratio and coefficient of performance (COP) were analyzed under various operating and ejector geometry conditions. Moreover, the optimal NXP of a small-sized household DEEC was proposed using the developed correlation to achieve maximum performance under different operating conditions. The COP of the DEEC with the optimized NXP is 2.3% and 8.4% higher than those of the DEEC with the conventional NXP and the baseline cycle, respectively. These results validate the ANN model used for optimization and serve as design guidelines for obtaining optimized NXPs and cycle performance with increased energy efficiency.