昂贵黑箱多目标问题的自适应采样代理优化方法  

A Surrogate Optimization Method with Adaptive Sampling for Expensive Black-Box Multi-Objective Problems

作　　者：白富生[1] 魏玉涛 邹东池 BAI Fusheng;WEI Yutao;ZOU Dongchi(National Center for Applied Mathematicsin Chongqing,Chongqing Normal University,Chongqing 401331)

机构地区：[1]重庆师范大学重庆国家应用数学中心,重庆401331

出　　处：《系统科学与数学》2024年第8期2365-2383,共19页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金重大项目(11991024);重庆市教委科学技术研究计划重点项目(KJZD-K202114801);重庆市技术创新与应用发展专项重点项目(cstc2021jscx-jbgsX0001);重庆市自然科学基金创新发展联合基金项目(2022NSCQ-LZX0301)资助课题。

摘　　要：针对昂贵黑箱多目标优化问题,文章提出一种在迭代中使用多种采样策略平衡局部搜索与全局搜索的代理模型方法.在一般的代理模型算法框架下,文章提出的算法使用径向基函数插值模型进行逼近.在算法迭代过程中,执行局部搜索辅助的目标值策略,该策略通过构造多个近似Pareto前沿面,选取多个填补近似前沿面上空隙的值作为候选目标值,并根据已估值决策向量和已有目标值的信息确定新目标值,以及在对应的候选采样点周围进行局部搜索.此外,在代理优化采样策略中通过聚类方法增强采样点的多样性.在58个包括高维和低维问题的标准测试问题及两个实际问题上进行的数值实验说明了所提算法的有效性.This paper presents a surrogate optimization method for the expensive black-box multi-objective optimization problems,which balances local and global searches using multiple sampling strategies in iterations.Under the framework of the surrogate optimization,this method employs a radial basis function interpolation model to approximate.During the iterations of the algorithm,a local search assisted target value strategy is implemented,in which multiple approximate Pareto fronts are constructed,multiple vectors filling the gaps of the approximate Pareto fronts are selected as the candidates of the target value,a new target value is determined based on the evaluated decision vectors and the existing target values,and a local search is undertaken around the corresponding candidate of the sample point.Moreover,a clustering method is used in the surrogate optimization sampling to enhance the diversity of the sample points.Numerical experiments on 58 standard test problems consisting of both low-and high-dimensional ones,as well as two practical problems,demonstrate the effectiveness of the proposed algorithm.

关 键 词：黑箱函数 多目标优化 响应面模型 径向基函数 聚类 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]