Sequential RBF Surrogate-based Efficient Optimization Method for Engineering Design Problems with Expensive Black-Box Functions

• Published in: Chinese journal of mechanical engineering Vol. 27; no. 6; pp. 1099 - 1111
• Main Authors: Peng, Lei, Liu, Li, Long, Teng, Guo, Xiaosong
• Format: Journal Article
• Language: English
• Published: Beijing Chinese Mechanical Engineering Society 01.11.2014; Springer Nature B.V; Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing 100081, China
• Edition: English ed.
• Subjects: Algorithms; Computer simulation; Constraints; Design engineering; Design optimization; Efficiency; Electrical Machines and Networks; Electronics and Microelectronics; Engineering; Engineering design; Engineering Thermodynamics; Finite element method; Heat and Mass Transfer; Instrumentation; Machines; Manufacturing; Mathematical analysis; Mathematical models; Mechanical Engineering; Methods; Optimization; Power Electronics; Processes; Radial basis function; RBF; Theoretical and Applied Mechanics; 拉格朗日乘子法; 搜索引擎; 现代工程; 约束优化问题; 设计优化; 设计问题; 黑盒; surrogate-based optimization; adaptive surrogate; radial basis function; significant sampling space; global optimization
• ISSN: 1000-9345; 2192-8258
• DOI: 10.3901/CJME.2014.0820.138

As a promising technique, surrogate-based design and optimization（SBDO） has been widely used in modern engineering design optimizations. Currently, static surrogate-based optimization methods have been successfully applied to expensive optimization problems. However, due to the low efficiency and poor flexibility, static surrogate-based optimization methods are difficult to efficiently solve practical engineering cases. At the aim of enhancing efficiency, a novel surrogate-based efficient optimization method is developed by using sequential radial basis function（SEO-SRBF）. Moreover, augmented Lagrangian multiplier method is adopted to solve the problems involving expensive constraints. In order to study the performance of SEO-SRBF, several numerical benchmark functions and engineering problems are solved by SEO-SRBF and other well-known surrogate-based optimization methods including EGO, MPS, and IARSM. The optimal solutions, number of function evaluations, and algorithm execution time are recorded for comparison. The comparison results demonstrate that SEO-SRBF shows satisfactory performance in both optimization efficiency and global convergence capability. The CPU time required for running SEO-SRBF is dramatically less than that of other algorithms. In the torque arm optimization case using FEA simulation, SEO-SRBF further reduces 21% of thematerial volume compared with the solution from static-RBF subject to the stress constraint. This study provides the efficient strategy to solve expensive constrained optimization problems.