The most prevalent problem in washing machines is the vibration incurred during the spin cycles. The balance of the washing machine plays an important role in reducing the vibrations from an unbalanced mass by injecting salt water into an automatic balancer. In this study, we determined the optimal dimension of layers and the amount of salt water for an automatic liquid balancer in order to minimize the maximum displacement of a low-speed spin cycle while satisfying the design constraint on the maximum displacement of a high-speed spin cycle. The maximum displacements for a specified design point were obtained by performing laboratory experiments. For design optimization, approximate models of the maximum displacements were created by employing radial basis function regression (RBFr) models based on the experimental data at full factorial design points. Then, an optimization algorithm was applied to the RBFr models to obtain the optimum solution. Using the proposed design approach, the optimal value of the maximum displacement of a low-speed spin cycle was reduced by 13.1%, compared to the initial value, while satisfying the design constraint on the maximum displacement of a high-speed spin cycle.