求解昂贵区间多目标优化问题的高斯代理模型
Gaussian surrogate models for expensive interval multi-objective optimization problem

本文将数据挖掘(高斯过程回归建模)和智能进化算法(GA, NSGA–II)进行结合, 用于解决优化函数未知的 昂贵区间多目标优化问题. 首先利用高斯过程对采用中点和不确定度表示的未知目标函数和约束函数进行建模, 由 于相关性和准确性是区间函数模型的两个必备条件, 故提出一种融合多属性决策的双层种群筛选策略, 并将其嵌入 到遗传算法求解高斯模型参数的过程中, 第1层根据相关性属性排除候选解集中部分劣解, 第2层根据准确性属性排 除候选解集中其余超出种群规模的劣解, 两属性的权重系数决定两层排除劣解的比例. 然后将所建模型作为优化 对象的代理模型引导区间NSGA–II算法优化求解, 从而获得所需的Pareto前沿.
In this paper data mining (Gaussian process regression modeling) and intelligent evolutionary algorithm (GA, NSGA–II) are combined to solve the expensive interval multi-objective optimization problem with unknown optimization functions. Firstly, Gaussian process (GP) is used to model the objective functions and constraint functions represented by the midpoint and uncertainty. Because relevance and accuracy are two essential factors of interval function models, A kind of double steps screening strategy based on multiple attribute decision making (MADM) is proposed and it is embedded into the genetic algorithm to identify the parameters of the GP model. In the first step, inferior solutions in candidate solutions are excluded according to relevance. In the second step, the rest of inferior solutions beyond population quantity are excluded according to accuracy. And the proportion of inferior solutions excluded in the two steps is decided by the weight coefficient of two factors. Then, the built GP models for optimization objects are used as surrogate models in the NSGA--II optimization algorithm, so that Pareto front can be found.