Multi-objectives optimization problems are often solved constructing the Pareto front and applying a decision-making strategy to select the preferred solution among the Pareto-optimal solutions. With the aim to reduce the computational effort in multi-objective optimization problems, this paper presents a procedure for the direct evaluation of the preferred updated model, without the need to evaluate the whole Pareto front. For this purpose, the objective function to minimize is defined as the distance between a candidate point and the equilibrium point in the objective function space. The choice of the criterion of the minimum distance from the equilibrium point comes from a preliminary study carried out to assess the performances of different selection criteria. The robustness and the efficiency of the proposed procedure are assessed through the comparison with the results obtained from the estimation of the Pareto-optimal solutions and the subsequent selection of the preferred one for two numerical case studies. The proposed procedure is finally applied to the calibration of a complex FE model with respect to experimental modal data. Results show that the proposed procedure is effective and considerably reduces the computational effort. Moreover, the procedure is able to directly estimate the optimal weighting factor that allows to know the relative importance between the selected objectives and can be used to solve the multi-objective optimization with the weighed sum method.

多目标优化问题通常是通过构造帕累托前沿并应用决策策略从帕累托最优解中选择首选方案来解决的。为了减少多目标优化问题中的计算量，本文提出了一种直接评估首选更新模型的过程，而无需评估整个帕累托前沿。为此，将最小化的目标函数定义为目标函数空间中候选点和平衡点之间的距离。距平衡点最小距离的标准的选择来自进行初步评估以评估不同选择标准的性能。通过与从帕累托最优解的估计以及随后的两个数值案例研究中选择的最优解的估计结果进行比较，来评估所提出程序的鲁棒性和效率。最后，将所提出的程序应用于相对于实验模态数据的复杂有限元模型的校准。结果表明，所提出的程序是有效的，并且大大减少了计算量。此外，该程序能够直接估计最佳加权因子，从而可以了解所选目标之间的相对重要性，并可用于通过加权和方法求解多目标优化。