Focusing on inefficiency and inherent limitations in the traditional optimization methods for complex mechanical structures

an approximation loop optimization approach combining response surface model with multi-objective genetic algorithm is proposed to deal with the optimal design problem for a type of gantry column in machine tools. Investigating the weak links of the column found by static analysis and modal analysis

the double-objective optimization model is established. Then

the Latin hypercube experiment design scheme and the response surface method are combined to construct the initial second-order response surface models of three performance indexes

i.e.

the maximum column deformation

the first-order natural frequency

and its total mass

by fitting with seven design parameters. Furthermore

these response surface models are optimized by using the approximation loop technique of NSGA-Ⅱ

and a distributed Pareto solution set is finally obtained. Remaining the same total column mass

in the optimal solution

the first order natural frequency increases by 15.9% while maximum guide deformation decreases by 7.7%. The optimal solution within the design space can be approximated by limited times of CAE analysis.