Traditional vibration isolation design often aims to suppress vibrations from machinery equipment, while vibrations in the foundation are usually ignored. In this paper, the "machinery equipmentsingle-stage (double-stage) isolators -thin plate foundation" is considered as a composite vibration isolation system, with equipment deployed at four positions on the plate. The forces transmitted from the equipment to the foundation were derived using a mechanical four-pole connection principle, and the displacement admittance of the junctions between the equipment and the plate was used as the key intermediate variable. Multi-objective optimization for the proposed system was subsequently performed, using fitness functions to reduce the maximum power flow transmitted to the plate and ensure a uniform vibration of the machinery equipment. A multi-objective particle swarm optimization (MOPSO) algorithm was used as the optimization tool which offers the advantages of fewer parameter settings, fast convergence, a strong optimization capability, and possession of a unique, global and optimal solution (gbest solution) based on Pareto dominance. The power flow that induced plate vibrations from the machinery isolation system was introduced in this study, which was used to consider the transmitted force and velocity on the plate simultaneously. An advanced theory of clamped plate vibration aptly supported this strategy, and inspiration was also provided by an innovative optimization strategy based on artificial intelligence.