EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于差分进化和RBF响应面的混合优化算法

邓凯文 陈海昕

邓凯文, 陈海昕. 基于差分进化和RBF响应面的混合优化算法[J]. 力学学报, 2017, 49(2): 441-455. doi: 10.6052/0459-1879-16-285
引用本文: 邓凯文, 陈海昕. 基于差分进化和RBF响应面的混合优化算法[J]. 力学学报, 2017, 49(2): 441-455. doi: 10.6052/0459-1879-16-285
Deng Kaiwen, Chen Haixin. HYBRID OPTIMIZATION ALGORITHM BASED ON DIFFERENTIAL EVOLUTION AND RBF RESPONSE SURFACE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 441-455. doi: 10.6052/0459-1879-16-285
Citation: Deng Kaiwen, Chen Haixin. HYBRID OPTIMIZATION ALGORITHM BASED ON DIFFERENTIAL EVOLUTION AND RBF RESPONSE SURFACE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 441-455. doi: 10.6052/0459-1879-16-285

基于差分进化和RBF响应面的混合优化算法

doi: 10.6052/0459-1879-16-285
基金项目: 

中航工业产学研专项 cxy2014QH14

清华大学自主科研计划 2015THZ0

详细信息
    通讯作者:

    2) 陈海昕, 教授, 主要研究方向:空气动力学, 计算流体力学.E-mail:chenhaixin@tsinghua.edu.cn

  • 中图分类号: V211.3

HYBRID OPTIMIZATION ALGORITHM BASED ON DIFFERENTIAL EVOLUTION AND RBF RESPONSE SURFACE

  • 摘要: 针对气动优化等昂贵优化问题,提出了一种基于差分进化和RBF响应面的混合优化算法HSADE,该方法结合了差分进化算法的强全局寻优能力和RBF响应面方法的快速局部搜索能力,能够同时有效地提高算法的局部搜索效率和全局寻优能力.对各子算法中的策略和逻辑进行了多项改进,提出和应用了基于双败淘汰赛的竞赛赛制和参数自适应等改进策略.对HSADE使用多个典型算例进行了测试,并横向对比了NSGA-Ⅱ,MOPSO和多目标差分进化算法.测试结果表明,在大多数问题中HSADE在以世代距离表征的局部搜索效率和以超体积比表征的全局寻优能力两项指标上都优于其他算法,证实了以上混合策略及算法改进的有效性.将该算法应用于一个翼型优化问题和一个二维超声速喷管膨胀面优化问题,并横向对比未经改良的差分进化算法DE和另一种混合算法NARSGA,结果表明在接近1 000次的函数评估下,HSADE能相对其他算法进一步对翼型减阻0.5 count,在喷管优化中HSADE得到的结果也好于其他两种算法,表明该方法具有较强工程应用价值.

     

  • 图  1  HSADE优化流程图

    Figure  1.  Optimization flow chart of HSADE

    图  2  一种典型的择优情景

    Figure  2.  A typical selection occasion

    图  3  种群信息辅助的择优逻辑

    Figure  3.  Population information enhanced selection logic

    图  4  优化进程

    Figure  4.  Optimization progress

    图  5  初始外形和3种算法得到的外形

    Figure  5.  Shapes of initial airfoil and optimal airfoils obtained by optimizers

    图  6  最优翼型表面压力分布形态

    Figure  6.  Surface pressure distribution of optimal airfoils

    图  7  3种算法的Pareto前缘对比

    Figure  7.  Comparisons of Pareto fronts obtained by HSADE, NARSGA and DE

    图  8  优化进程

    Figure  8.  Optimization progress

    图  9  喷管构型与3种算法获得的代表性个体外形

    Figure  9.  Nozzle concepts and representative optimal shapes obtained by HSADE, NARSGA and DE

    图  10  3种算法的Pareto前缘

    Figure  10.  Pareto fronts obtained by HSADE, NARSGA and DE

    表  1  径向基函数类型

    Table  1.   Different types of radial basis functions

    表  2  几种响应面插值精度验证

    Table  2.   Examination of interpolation error of different response surfaces

    表  3  几种算法在测试问题上的收敛性指标结果

    Table  3.   Convergence criteria of competing algorithms upon tested problems

    表  4  几种算法在测试问题上的分布性指标结果

    Table  4.   Distribution criteria of competing algorithms upon tested problems

    表  5  翼型优化问题的优化变量、目标和约束

    Table  5.   Variables, targets and constraints of the airfoil optimization problem

    表  6  3种算法得到的最优翼型的性能参数和优化量

    Table  6.   Performance and optimization measurement of the optimal airfoils obtained by optimizers

    表  7  喷管设计变量范围

    Table  7.   Variable ranges of the nozzle design

    表  8  3种算法得到的代表个体的性能参数

    Table  8.   Performance of representative optimal shapes obtained by HSADE, NARSGA and DE

  • [1] Cheung S, Aaronson P, Edwards T. CFD optimization of a theoretical minimum-drag body. Journal of Aircraft, 2015, 32(1):193-198 https://www.researchgate.net/publication/234185918_CFD_optimization_of_a_theoretical_minimum-drag_body
    [2] 卢文书, 王帅培, 马元春.基于CFD/CSD与Kriging插值模型的大展弦比复合材料机翼静气动弹性优化设计.应用力学学报, 2015, 32(4):581-585 http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201504011.htm

    Lu Wenshu, Wang Shuaipei, Ma Yuanchun. Static aeroelastic optimization of a high-aspect-ratio composite wing based on CFD/CSD and Kriging model. Chinese Journal of Applied Mechanics, 2015, 32(4):581-585(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201504011.htm
    [3] Cazacu R, Grama L. Steel truss optimization using genetic algorithms and FEA. Procedia Technology, 2014, 12:339-346 doi: 10.1016/j.protcy.2013.12.496
    [4] Jones DR, Schonlau M, Welch WJ. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 1998, 13(4):455-492 doi: 10.1023/A:1008306431147
    [5] Su GS. Gaussian process assisted differential evolution algorithm for computationally expensive optimization problems//Bilof R ed. Pacific-Asia Workshop on Computational Intelligence and Industrial Application, PACIIA '08, Wuhan, 2008. Los Alamitos:IEEE, 2008. 272-276
    [6] Tabatabaei SME, Kadkhodaie-Ilkhchi A, Hosseini Z, et al. A hybrid stochastic-gradient optimization to estimating total organic carbon from petrophysical data:a case study from the Ahwaz Oilfield, SW Iran. Journal of Petroleum Science & Engineering, 2015, 127(1): 35-43 https://www.researchgate.net/publication/273401650_A_hybrid_stochastic-gradient_optimization_to_estimating_total_organic_carbon_from_petrophysical_data_A_case_study_from_the_Ahwaz_oilfield_SW_Iran
    [7] 孙美建, 詹浩. Kriging模型在机翼气动外形优化中的应用.空气动力学学报, 2011, 29(6):759-764 http://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201106013.htm

    Sun Meijian, Zhan Hao. Application of Kriging surrogate model for aerodynamic shape optimization of wing. Acta Aerodynamica Sinica, 2011, 29(6):759-764(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201106013.htm
    [8] Huang D, Allen TT, Notz WI, et al. Global optimization of stochastic black-box systems via sequential kriging meta-models. Journal of Global Optimization, 2006, 34(3):441-466 doi: 10.1007/s10898-005-2454-3
    [9] Singh HK, Isaacs A, Ray T. A hybrid surrogate based algorithm (HSBA) to solve computationally expensive optimization problems. Evolutionary Computation, 2014:1069-1075 https://www.researchgate.net/publication/287021247_A_hybrid_surrogate_based_algorithm_HSBA_to_solve_computationally_expensive_optimization_problems
    [10] Elsayed SM, Ray T, Sarker RA. A surrogate-assisted differential evolution algorithm with dynamic parameters selection for solving expensive optimization problems. Evolutionary Computation, 2014: 1062-1068 https://www.researchgate.net/publication/266559265_A_surrogate-assisted_differential_evolution_algorithm_with_dynamic_parameters_selection_for_solving_expensive_optimization_problems
    [11] Liu B, Zhang QF, Gielen GGE. A Gaussian process surrogate model assisted evolutionary algorithm for medium scale expensive optimization problems. IEEE Transactions on Evolutionary Computation, 2014, 18(2):180-192 doi: 10.1109/TEVC.2013.2248012
    [12] Antunes AP, Azevedo JLF. Studies in aerodynamic optimization based on genetic algorithms. Journal of Aircraft, 2014, 51(3):1002-1012 doi: 10.2514/1.C032095
    [13] Nam T, Chakraborty I, Gross J, et al. Multidisciplinary design optimization of a truss-braced wing concept//14th AIAA Aviation Technology, Integration, and Operations Conference, Atlanta, 2014. Reston:AIAA, 2014
    [14] Gibertini G. Aerodynamic shape optimisation of a proprotor and its validation by means of CFD and experiments. Aeronautical Journal, 2015, 119(1120):1223-1251 https://www.researchgate.net/publication/283480981_Aerodynamic_shape_optimisation_of_a_proprotor_and_its_validation_by_means_of_CFD_and_experiments
    [15] Han ZH, Zimmerman R, Görtz S. Alternative cokriging method for variable-fidelity surrogate modeling. AIAA Journal, 2012, 50(5): 1205-1210 doi: 10.2514/1.J051243
    [16] Han ZH, Görtz S. Hierarchical Kriging model for variable-fidelity surrogate modeling. AIAA Journal, 2012, 50(9):1885-1896 doi: 10.2514/1.J051354
    [17] Zingg DW, Nemec M, Pulliam TH. A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization. European Journal of Computational Mechanics, 2008, 17(1-2):103-126 doi: 10.3166/remn.17.103-126?needAccess=true
    [18] Carrier G, Destarac D, Dumont A, et al. Gradient-based aerodynamic optimization with the elsA software//52nd Aerospace Sciences Meeting. 2014, 10:6.2014-0568
    [19] 白俊强, 王波, 孙智伟等.基于松散式代理模型管理框架的亚音速机翼优化设计方法研究.西北工业大学学报, 2011, 29(4):515-519 http://www.cnki.com.cn/Article/CJFDTOTAL-XBGD201104004.htm

    Bai Junqiang, Wang Bo, Sun Zhiwei, et al. Developing optimization design of subsonic wing with loose type of agent model. Journal of Northwestern Polytechnical University, 2011, 29(4): 515-519(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-XBGD201104004.htm
    [20] Kim HJ, Liou MS. Aerodynamic optimization using a hybrid moga-local search method//51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 18th AIAA/ASME/AHS Adaptive Structures Conference 12th, 2010: 2911
    [21] 倪昂修, 张宇飞, 陈海昕. NSGA-Ⅱ算法的改进及其在多段翼型缝道参数优化中的应用.空气动力学学报, 2014, 32(2):252-257 http://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201402019.htm

    Ni Angxiu, Zhang Yufei, Chen Haixin. An Improvement to NSGA-Ⅱ algorithm and its application in optimization design of multi-element airfoil. Acta Aerodynamica Sinica, 2014, 32(2):252-257(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201402019.htm
    [22] Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm:NSGA-Ⅱ. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197 doi: 10.1109/4235.996017
    [23] 公茂果, 焦李成, 杨咚咚等.进化多目标优化算法研究.软件学报, 2009, 20(2):271-289 http://www.cnki.com.cn/Article/CJFDTOTAL-RJXB200902009.htm

    Gong Maoguo, Jiao Licheng, Yang Dongdong, et al. Research on evolutionary multi-objective optimization algorithms. Journal of Software, 2009, 20(20):271-289(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-RJXB200902009.htm
    [24] Zitzler E, Laumanns M, Thiele L. SPEA2:improving the strength pareto evolutionary algorithm. Eurogen, 2001, 3242(103):95-100 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.5073
    [25] Storn R, Price K. Differential evolution:a simple and efficient adaptive scheme for global optimization over continuous spaces. Journal of Global Optimization, 1995, 23(4):341-359 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.9696
    [26] Park J, Sandberg IW. Universal approximation using radial-basisfunction networks. Neural Computation, 1991, 3(2):246-257 doi: 10.1162/neco.1991.3.2.246
    [27] 穆雪峰, 姚卫星, 余雄庆等.多学科设计优化中常用代理模型的研究.计算力学学报, 2005, 22(5):608-612 http://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200505018.htm

    Mu Xuefeng, Yao Weixing, Yu Xiongqing, et al. A survey of surrogate models used in MDO. Chinese Journal of Computational Mechanics, 2005, 22(5): 608-612(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200505018.htm
    [28] Wang L, Huang FZ. Parameter analysis based on stochastic model for differential evolution algorithm. Applied Mathematics & Computation, 2010, 217(7):3263-3273
    [29] Brest J, Greiner S, Boskovic B, et al. Self-adapting control parameters in differential evolution:a comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation, 2007, 10(6):646-657 http://en.journals.sid.ir/Reference.aspx?ID=495582
    [30] Rippa S. An Algorithm for selecting a good value for the parameter c in radial basis function interpolation. Advances in Computational Mathematics, 1999, 11(2):193-210 http://citeseerx.ist.psu.edu/showciting?cid=191307
    [31] 吴亮红.动态差分进化算法及其应用.北京:科学出版社, 2014: 190-220

    Wu Lianghong. Dynamic Differential Evolution and its Application. Beijing:Science Press, 2014:190-220(in Chinese)
    [32] Nebro AJ, Luna F, Alba E, et al. Abyss:adapting scatter search to multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2008, 12(4):439-457 doi: 10.1109/TEVC.2007.913109
    [33] Deb K, Thiele L, Laumanns M, et al. Scalable test problems for evolutionary multiobjective optimization//Abraham A, Jain L, Goldberg R eds. Evolutionary Multiobjective Optimization. London:Springer London, 2005. 105-145
    [34] Coello CAC, Lechuga MS. MOPSO:a proposal for multiple objective particle swarm optimization//Proceedings of the 2002 Congress on Evolutionary Computation, CEC '02, Honolulu, Hawaii, 2002. Los Alamitos:IEEE, 2002. 2:1051-1056
    [35] Kulfan BM, Bussoletti JE. Fundamental parametric geometry representations for aircraft component shapes//11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, 2006. Reston:AIAA, 2006. 6948
    [36] Chen HX, Fu S, Li FW. Navier-Stokes simulations for transport aircraft wing/body high-lift configurations. Journal of Aircraft, 2003, 40(5):883-890 doi: 10.2514/2.6878
    [37] Zhang YF, Chen HX, Fu S. Improvement to patched grid technique with high-order conservative remapping method. Journal of Aircraft, 2012, 48(3):884-893 doi: 10.2514/1.C031093
    [38] 陈兵, 徐旭, 蔡国飙.二维超燃冲压发动机尾喷管优化设计.推进技术, 2002, 23(5):433-437 http://www.cnki.com.cn/Article/CJFDTOTAL-TJJS200205020.htm

    Chen Bing, Xu Xu, Cai Guobiao. Optimization design of two dimensional scramjet nozzle based on N-S equations. Journal of Propulsion Technology, 2002, 23(5):433-437(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-TJJS200205020.htm
  • 加载中
图(10) / 表(8)
计量
  • 文章访问数:  901
  • HTML全文浏览量:  126
  • PDF下载量:  639
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-10-17
  • 网络出版日期:  2017-01-20
  • 刊出日期:  2017-03-18

目录

    /

    返回文章
    返回