针对高维优化问题的快速追峰采样方法

doi:10.3901/JME.2019.03.138

机械工程学报 ›› 2019, Vol. 55 ›› Issue (3): 138-146.doi: 10.3901/JME.2019.03.138

针对高维优化问题的快速追峰采样方法

武宇飞¹, 龙腾^1,2, 史人赫¹, WANG G Gary³

1. 北京理工大学宇航学院北京 100081;
2. 北京理工大学飞行器动力学与控制教育部重点实验室北京 100081;
3. 西门菲莎大学机电工程学院素里V3T 0A3 加拿大

收稿日期:2018-03-21 修回日期:2018-10-23 出版日期:2019-02-05 发布日期:2019-02-05
通讯作者: 龙腾(通信作者),男,1982年出生,博士,教授,博士研究生导师。主要研究方向为飞行器总体设计、多学科优化理论与应用、飞行器协同控制与决策。Email:tenglong@bit.edu.cn,bitryu@gmail.com
作者简介:武宇飞,男,1996年出生,博士研究生。主要研究方向为飞行器总体设计、多学科优化理论与应用。Email:wuyufei@bit.edu.cn;史人赫,男,1990年出生,博士研究生。主要研究方向为飞行器总体设计、多学科优化理论与应用。Email:shirenhe@bit.edu.cn;WANG G Gary,男,1971年出生,博士,教授,博士研究生导师。主要研究方向为复杂系统设计优化、工程设计优化。E-mail:gary_wang@sfu.ca
基金资助:
国家自然科学基金（51675047，11372036）、航空科学基金（2015ZA72004）、北京理工大学国际科技合作专项计划（GZ2018015101）、北京理工大学研究生科技创新（2018CX10001）资助项目。

A Rapid Mode Pursuing Sampling Method for High Dimensional Optimization Problems

WU Yufei¹, LONG Teng^1,2, SHI Renhe¹, WANG G Gary³

1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081;
2. Key Laboratory of Dynamics and Control of Flight Vehicle of Ministry of Education, Beijing Institute of Technology, Beijing 100081;
3. School of Mechatronic Systems Engineering, Simon Fraser University, Surrey, BC V3T 0A3, Canada

Received:2018-03-21 Revised:2018-10-23 Online:2019-02-05 Published:2019-02-05

摘要/Abstract

摘要： 基于计算试验设计和代理模型的近似优化策略在现代复杂系统工程设计中得到了广泛应用，其中追峰采样方法（Mode pursuing sampling，MPS）是一种代表性的近似优化策略。分析并针对MPS处理高维优化问题时效率低下的缺陷，提出了基于重点设计空间的快速追峰采样方法（RMPS-SDS），将重点设计空间的思想引入MPS框架，定制了一套样本点分配策略以增强MPS的局部搜索能力与收敛速度，从而提高求解高维优化问题的效率。采用一系列标准数值测试问题和工程设计问题检验RMPS-SDS方法的性能，并与MPS和GA进行了对比研究。研究结果表明，在相同模型调用次数前提下，RMPS-SDS的优化结果更接近理论全局最优解，且鲁棒性更好。与标准MPS相比，RMPS-SDS方法求解高维优化问题的效率、收敛性和鲁棒性都具有明显优势，更具有工程实用性。

关键词: 近似优化, 全局优化, 重点设计空间, 追峰采样, 自适应代理模型

Abstract: Approximate optimization strategies using design of computer experiments (DoCE) and metamodels have been widely applied in design of modern complex engineering systems. Mode pursuing sampling method (MPS) is a representative of such optimization algorithms. A rapid mode pursuing sampling method using significant design space concept (notated as RMPS-SDS) is proposed in this work to alleviate the low efficiency problem of MPS in solving high dimensional optimization problems. The idea of significant design space is incorporated into the MPS framework, and a sample point allocation strategy is designed to enhance the local search capability and convergence speed of MPS. RMPS-SDS is tested on a number of standard numerical benchmark problems and two engineering design problems and compared with MPS and GA. The comparison results indicate that with the same computational budget (i.e., the same number of function evaluations), results of RMPS-SDS are much closer to the theoretical global optima with lower standard deviation for multiple runs. It is thus demonstrated that the proposed RMPS-SDS outperforms the standard MPS in terms of efficiency, convergence, and robustness in solving high dimensional optimization problems, which is more promising for engineering practices.

Key words: adaptive metamodel, approximate optimization, global optimization, mode pursuing sampling, significant design space

中图分类号:

V221

武宇飞, 龙腾, 史人赫, WANG G Gary. 针对高维优化问题的快速追峰采样方法[J]. 机械工程学报, 2019, 55(3): 138-146.

WU Yufei, LONG Teng, SHI Renhe, WANG G Gary. A Rapid Mode Pursuing Sampling Method for High Dimensional Optimization Problems[J]. Journal of Mechanical Engineering, 2019, 55(3): 138-146.

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针对高维优化问题的快速追峰采样方法

A Rapid Mode Pursuing Sampling Method for High Dimensional Optimization Problems

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