Abstract
Purpose
The purpose of this paper is to propose a novel strategy of optimal parameters configuration and placement for sensitive equipment.

Design/methodology/approach
In this study, clamped thin plate is considered as the foundation form, and a novel composite system is proposed based on the two-stage isolation system. By means of the theory of mechanical four-pole connection, the displacement amplitude transmissibility from the thin plate to precision equipment is derived. For the purpose of performing optimal design of the composite system, a novel multi-objective idea is presented. Multi-objective particle swarm optimization (MOPSO) algorithm is adopted as an optimization technique, which can achieve a global optimal solution (gbest), and selecting the desired solution from an equivalent Pareto set can be avoided. Maximum and variance of the four transmitted peak displacements are considered as the fitness functions simultaneously; the purpose is aimed at reducing the amplitude of the multi-peak isolation system, meanwhile pursuing a uniform vibration as far as possible. The optimization is mainly organized as a combination of parameter configuration and placement design, and the traversal search of discrete plate is performed in each iteration for the purpose of achieving the global optimum.

Findings
An important transmissibility based on the mechanical four-pole connection is derived, and a composite vibration isolation system is proposed, and a novel optimization problem is also defined here. This study reports a novel optimization strategy combined with artificial intelligence for parameters and placement design of precision equipment, which can promote the traditional view of two-stage vibration isolation.

Originality/value
Two-stage vibration isolation systems are widely applied to the vibration attenuation of precision equipment, but in these traditional designs, vibration participation of foundation is often ignored. In this paper, participation of foundation of equipment is considered, and a coherent new strategy for equipment isolation and foundation vibration is presented. This study shows a new vision of interdisciplinary including civil engineering, mechanical dynamics and computational science.