中文摘要：

采用区间数描述车架材料参数的不确定性,基于车架有限元模型构建了设计变量和不确定变量与目标函数之间的近似模型.采用双层嵌套的遗传算法,内层采用隔代遗传算法（IP-GA）在不确定域求解目标函数区间,外层采用加入精英保持策略和去除重复个体的非支配排序遗传算法（NSGA-Ⅱ）对车架应力和质量最小两个目标进行优化.与确定性多目标优化比较的结果显示了不确定性多目标优化的优越性.

英文摘要：

The uncertain material parameters of frame are described by intervals,and a surrogate model for the relationship between design variables,uncertain variables and objective function is constructed based on the finite element model of frame.A two layer nested genetic algorithm is used to conduct a two objective optimization of minimizing the stress and mass of frame.In inner layer,intergeneration projection genetic algorithm is adopted to find the interval of objective function in uncertain region while in outer layer,non-dominated sorting genetic algorithm （NSGA-Ⅱ） is used with elitist preservation strategy added and duplicate individuals removed.The results of comparison with general multi-objective optimization demonstrate the superiority of uncertainty multi-objective optimization.