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Semiactive model predictive control (sMPC) can be very effective, but its computational cost due to the inherent mixed-integer quadratic programming (MIQP) optimization precludes its use in real-time vibration control. This study proposes training neural networks (NNs) to predict in real-time only the MIQP's integer variables' values, called a strategy, for a given structure state. Because the number of strategies is exponential in the number of sMPC horizon steps, the resulting NN can be massive. This study proposes to reduce the NN dimension by exploiting the homogeneity-of-order-one nature of this control problem and, using state vector statistics, to efficiently choose training samples. The single large NN is proposed to be split into several much smaller NNs, each predicting a strategy grouping, that together uniquely and efficiently predict the strategy. Given the strategy's integer values, the MIQP optimization reduces to a quadratic programming (QP) problem, solved using a fast QP solver with proposed adaptations: exploiting optimization efficiencies and bounding sub-optimality; using several NN predictions; and reverting to a simpler (suboptimal) semiactive control algorithm upon occasional incorrect NN predictions or QP solver nonconvergence. Shear building examples demonstrate significant online computational cost reductions with control performance comparable to the conventional MIQP-based control.