Based on the developed dynamic equations of the soil-asymmetric structure-active multiple tuned mass dampers (AMTMD) interaction system considering the ground motion model, the optimum parameter criterion of the AMTMD is defined as minimizing the minimum values of the maximum translational and torsional displacement dynamic magnification factors (DMF) of the asymmetric structure with the AMTMD. The effectiveness criterion of the AMTMD is selected as the ratio of the minimization of the minimum values of the maximum displacement DMF of the asymmetric structure with the AMTMD to the maximum displacement DMF of the asymmetric structure without the AMTMD. Employing the above-defined criteria, the parametric studies for the influences of the normalized eccentricity ratio (NER), torsional to translational frequency ratio (TTFR), stiffness ratio of soil relative to structure (SRSS), and earthquake dominant frequency ratio (EDFR) of the soil-asymmetric structure interaction system are then carried out on the optimum frequency spacing and effectiveness of the AMTMD. Through the extensive numerical analysis, the suggestions obtained herein will be useful for the design and implementation in the earthquake reduction of asymmetric structures built on soft soil foundation.