Solid Mechanics and Vehicle Conceptual Design

Kriging?based mixed?integer optimization method using sample mapping mechanism for flight vehicle design

  • Haoda LI ,
  • Teng LONG ,
  • Renhe SHI ,
  • Nianhui YE
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  • School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China
    Key Laboratory of Dynamics and Control of Flight Vehicle of Ministry of Education,Beijing Institute of Technology,Beijing 100081,China
    Beijing Institute of Technology Chongqing Innovation Center,Chongqing 401121,China
E-mail: srenhe@163.com

Received date: 2023-03-21

  Revised date: 2023-04-25

  Accepted date: 2023-05-26

  Online published: 2023-06-02

Abstract

To deal with the problems of high computational cost and poor global convergence that often exist in discretecontinuous mixed optimization of complex flight vehicle systems, a Sample Mapping and Dynamic Kriging based Discrete-Continuous Mixed Optimization method (SMDK-DC) is proposed. In this method, time-consuming simulation model is replaced by Kriging surrogate model to reduce computational expenses. A sample point mapping mechanism based on generalized Manhattan distance criterion is also proposed to efficiently generate uniformly-distributed real sample points in continuous-discrete domain. Expected improvement criteria is combined with significant sampling space to identify new sample points,update Kriging continuously and dynamically, and guide the rapid convergence of the discrete-continuous optimization process. Benchmark cases show that compared with international methods such as SOMI and NOMAD, SMDK-DC has significant advantages in global convergence and robustness. Finally, SMDK-DC is used for solving a multidisciplinary design optimization problem of solid rocket motor. The method, on the premise of satisfying all the constraints of the combustion chamber and internal ballistic discipline, leads to a total impulse increase of at least 12. 92%, and the optimization yield is 1. 71% higher than that of SOMI, which verifying the effectiveness and engineering practicability of SMDK-DC.

Cite this article

Haoda LI , Teng LONG , Renhe SHI , Nianhui YE . Kriging?based mixed?integer optimization method using sample mapping mechanism for flight vehicle design[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(3) : 228726 -228726 . DOI: 10.7527/S1000-6893.2023.28726

References

1 MORRISON D R, JACOBSON S H, SAUPPE J J, et al. Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning[J]. Discrete Optimization201619: 79-102.
2 LIU W L, GONG Y J, CHEN W N, et al. Coordinated charging scheduling of electric vehicles: A mixed-variable differential evolution approach[J]. IEEE Transactions on Intelligent Transportation Systems202021(12): 5094-5109.
3 HANSEN P, MLADENOVI? N, MORENO PéREZ J A. Variable neighbourhood search: Methods and applications[J]. 4OR20086(4): 319-360.
4 NAKARIYAKUL S, CASASENT D P. Adaptive branch and bound algorithm for selecting optimal features[J]. Pattern Recognition Letters200728(12): 1415-1427.
5 HUSSIEN A G, HASSANIEN A E, HOUSSEIN E H, et al. New binary whale optimization algorithm for discrete optimization problems[J]. Engineering Optimization202052(6): 945-959.
6 LIU Y C, WANG H D. Surrogate-assisted hybrid evolutionary algorithm with local estimation of distribution for expensive mixed-variable optimization problems[J]. Applied Soft Computing2023133: 10995.
7 ABRAMSON M A, AUDET C, CHRISSIS J W, et al. Mesh adaptive direct search algorithms for mixed variable optimization[J]. Optimization Letters20093(1): 35-47.
8 龙腾, 刘建, WANG G G, 等. 基于计算试验设计与代理模型的飞行器近似优化策略探讨[J]. 机械工程学报201652(14): 79-105.
  LONG T, LIU J, WANG G G, et al. Discuss on approximate optimization strategies using design of computer experiments and metamodels for flight vehicle design[J]. Journal of Mechanical Engineering201652(14): 79-105 (in Chinese).
9 SHANOCK L R, BARAN B E, GENTRY W A, et al. Polynomial regression with response surface analysis: A powerful approach for examining moderation and overcoming limitations of difference scores[J]. Journal of Business and Psychology201025(4): 543-554.
10 BUHMANN M D. Radial basis functions: Theory and implementations[M]. Cambridge: Cambridge University Press, 2003.
11 SIMPSON T W, MAUERY T M, KORTE J, et al. Kriging models for global approximation in simulation-based multidisciplinary design optimization[J]. AIAA Journal200139: 2233-2241.
12 KLEIJNEN J P C. Kriging metamodeling in simulation: A review[J]. European Journal of Operational Research2009192(3): 707-716.
13 LI J, CHENG J H, SHI J Y, et al. Brief introduction of back propagation (BP) neural network algorithm and its improvement[C]∥ Advances in Computer Science and Information Engineering. Berlin: Springer, 2012: 553-558.
14 LIU Y, ZHAO G, LI G, et al. Analytical robust design optimization based on a hybrid surrogate model by combining polynomial chaos expansion and Gaussian kernel[J]. Structural and Multidisciplinary Optimization202265(11): 335.
15 JIN R, CHEN W, SIMPSON T W. Comparative studies of metamodelling techniques under multiple modelling criteria[J]. Structural and Multidisciplinary Optimization200123(1): 1-13.
16 LIU B, SUN N, ZHANG Q F, et al. A surrogate model assisted evolutionary algorithm for computationally expensive design optimization problems with discrete variables[C]∥ 2016 IEEE Congress on Evolutionary Computation (CEC). Piscataway: IEEE Press, 2016: 1650-1657.
17 HOLMSTR?M K, QUTTINEH N H, EDVALL M M. An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization[J]. Optimization and Engineering20089(4): 311-339.
18 ZHENG L, YANG Y P, FU G Q, et al. A surrogate-based optimization method with dynamic adaptation for high-dimensional mixed-integer problems[J]. Swarm and Evolutionary Computation202272: 101099.
19 MüLLER J, SHOEMAKER C A, PICHé R. SO-MI: A surrogate model algorithm for computationally expensive nonlinear mixed-integer black-box global optimization problems[J]. Computers & Operations Research201340(5): 1383-1400.
20 JIAO R W, ZENG S Y, LI C H, et al. A complete expected improvement criterion for Gaussian process assisted highly constrained expensive optimization[J]. Information Sciences2019471: 80-96.
21 JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization199813(4): 455-492.
22 PENG L, LIU L, LONG T, et al. Sequential RBF surrogate-based efficient optimization method for engineering design problems with expensive black-box functions[J]. Chinese Journal of Mechanical Engineering201427(6): 1099-1111.
23 PENG L, LIU L, LONG T, et al. Truss structure satellite bus geometry-structure optimization involving mixed variables and expensive models using metamodel-based optimization strategy[C]∥ Proceedings of the 15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Reston: AIAA, 2014.
24 韩忠华. Kriging模型及代理优化算法研究进展[J]. 航空学报201637(11): 3197-3225.
  HAN Z H. Kriging surrogate model and its application to design optimization: a review of recent progress[J]. Acta Aeronautica et Astronautica Sinica201637(11): 3197-3225 (in Chinese).
25 韩忠华, 许晨舟, 乔建领, 等. 基于代理模型的高效全局气动优化设计方法研究进展[J]. 航空学报202041(5): 623344.
  HAN Z H, XU C Z, QIAO J L, et al. Recent progress of efficient global aerodynamic shape optimization using surrogate-based approach[J]. Acta Aeronautica et Astronautica Sinica202041(5): 623344 (in Chinese).
26 YU X B, DUAN Y C, LUO W G. A knee-guided algorithm to solve multi-objective economic emission dispatch problem[J]. Energy2022259: 124876.
27 HALSTRUP M. Black-box optimization of mixed discrete-continuous optimization problems[D]. Dortmund: TU Dortmund University, 2016.
28 DATTA D, FIGUEIRA J R. A real-integer-discrete-coded differential evolution[J]. Applied Soft Computing201313(9): 3884-3893.
29 叶年辉, 胡少青, 李宏岩, 等. 考虑性能及成本的固体火箭发动机多学科设计优化[J]. 推进技术202243(7): 75-84.
  YE N H, HU S Q, LI H Y, et al. Multidisciplinary design optimization for solid rocket motor considering performance and cost[J]. Journal of Propulsion Technology202243(7): 75-84 (in Chinese).
30 鲍福廷, 侯晓. 固体火箭发动机设计[M]. 北京: 中国宇航出版社,2016.
  BAO F T, HOU X. Solid rocket motor design [M]. Beijing: China Astronautic Publishing House, 2016 (in Chinese).
31 WU Z P, WANG D H, ZHANG W H, et al. Solid-rocket-motor performance-matching design framework[J]. Journal of Spacecraft and Rockets201754(3): 698-707.
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