基于区间的不确定多目标优化方法及应用

An Uncertainty Multi-objective Optimization Based on Interval Analysis and Its Application

基于非线性区间分析方法,提出了一种区间多目标优化方法。利用非线性区间分析方法求出每一个目标函数和约束在每一设计矢量下的上下界,采用目标函数的中点值来计算多目标优化问题的非劣解,同时,通过数学转换模型区间可能度处理约束问题,将非线性区间多目标优化问题转化为确定性多目标优化问题,利用微型多目标遗传算法(μMOGA)对转换后的确定性多目标问题进行求解。最后,将该方法应用于数值算例以及十杆桁架结构和商用车车架,计算结果证明了该方法的有效性和工程实用性。

An interval multi-objective optimization method was suggested based on non-linear interval analysis methods.The upper and lower bounds of every objective and constraint functions for each vector were calculated,by using the center value of the interval objective function,the non-dominated solution of the multi-objective optimization problems was calculated,with the interval possibility degrees,the nonlinear interval multi-objective problems were changed into the deterministic multi-objective problems.The μMOGA was used to calculate the converted deterministic multi-objective problems.Finally,the method was applied to one numerical example and two engineering problems about ten truss structure and commercial automobile frame optimization.The results of these examples demonstrate the efficiency and engineering practicability of the presented method.