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A parameter optimal design method for a tank with an inerter system is proposed in this study based on the requirements of tank vibration control to improve the effectiveness and efficiency of vibration control. Moreover, a response indicator and a cost control indicator are selected based on the control targets for liquid storage tanks for simultaneously minimizing the dynamic response and controlling costs. These indicators are reformulated through a random vibration analysis under virtual excitation. The problem is then transformed from a multiobjective optimization problem to a single-objective nonlinear problem using the ε-constraint method, which is consistent with the demand-based method. White noise excitation can be used to design the tank with the inerter system under seismic excitation to simplify the calculation. Subsequently, a MATLAB-based calculation program is compiled, and several optimization cases are examined under different excitation conditions. The effectiveness of the demand-based method is proven through a time history analysis. The results show that specific vibration control requirements can be met at the lowest cost with a simultaneous reduction in base shears and overturning base moments. [ABSTRACT FROM AUTHOR]