约束自适应桁架优化设计方法

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (14) : 188-193.

论文

约束自适应桁架优化设计方法

肖阿阳1，王本利1，金耀初2

作者信息 +

A novel constraint adaptive truss optimization approach

XIAO A-yang1，WANG Ben-li1，JIN Yao-chu2

Author information +

文章历史 +

摘要

为求解多峰值、高度非线性桁架尺寸及形状优化问题，减少算法参数设置的盲目性，将Oracle罚函数与启发式算法相结合，提出可自适应处理约束列式的优化算法Ω-CMA-ES。该算法在处理各类复杂桁架优化问题时仅需设置一个参数Ω。测试算例表明，该算法对参数Ω具有良好的鲁棒性，可有效处理各类动态约束；且在探索全局最优解时体现出较高潜力，优化质量及收敛速度优于既有结果。

Abstract

A novel optimization algorithm named Ω-CMA-ES, which combines Oracle penalty function and metaheurastic, is proposed to solve a typical multi-modal and highly non-linear problem: truss sizing and shape optimization. This algorithm can alleviate the cumbersome burden of parameters setting, and thus adaptively handle the constraints of truss design. Only parameter Ω needs to be set manually while this algorithm is applied to handle various complex truss optimization problems. Numerical examples show the robustness of proposed algorithm to parameter Ω, for the algorithm can effectively handle various types of dynamic constrains; and the potential of proposed algorithm in finding global optimal solution, for the relevant performance indicators are better than the results published in the literature.

导出引用

肖阿阳1，王本利1，金耀初2. 约束自适应桁架优化设计方法[J]. 振动与冲击, 2015, 34(14): 188-193

XIAO A-yang1，WANG Ben-li1，JIN Yao-chu2. A novel constraint adaptive truss optimization approach[J]. Journal of Vibration and Shock, 2015, 34(14): 188-193

参考文献

[1] 王栋. 结构优化设计-探索与进展[M]. 北京: 国防工业出版社, 2013.
[2] Miguel L F F, Lopez R H, Miguel L F F. Multimodal size, shape, and topology optimisation of truss structures using the Firefly algorithm[J]. Advances in Engineering Software, Elsevier, 2013, 56: 23-37.
[3] Kaveh A, Zolghadr A. Shape and size optimization of truss structures with frequency constraints using enhanced charged system search algorithm[J]. Asian Journal of Civil Engineering (Building and Housing), 2011, 12(4):487-509.
[4] Kaveh A, Khayatazad M. Ray optimization for size and shape optimization of truss structures[J]. Computers & Structures, 2013, 117: 82-94.
[5] Runarsson T P, Yao X. Stochastic ranking for constrained evolutionary optimization[J]. Evolutionary Computation, IEEE Transactions on, 2000, 4(3): 284-294.
[6] Coello C A. Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(11): 1245-1287.
[7] Bendsoe M P, Sigmund O. Topology optimization: theory, methods and applications [M]. Springer, 2003.
[8] 程耿东, 顾元宪. 序列二次规划在结构动力优化中的应用[J]. 振动与冲击, 1986, 5(1): 12-20.
CHENG Geng-dong, GU Yuan-xian. Applications of SAP to structural dynamic optimization[J]. Journal of Vibration and Shock, 1986, 5(1): 12-20.
[9] Schlüter M, Gerdts M. The oracle penalty method [J]. Journal of Global Optimization, 2010, 47(2): 293-325.
[10] Jin Y, Olhofer M, Sendhoff B. A framework for evolutionary optimization with approximate fitness functions[J]. Evolutionary Computation, IEEE Transactions on, 2002, 6(5): 481-494.
[11] Hansen N, Ostermeier A. Completely derandomized self- adaptation in evolution strategies[J]. Evolutionary Computation, 2001, 9(2): 159-195.
[12] 唐文艳, 袁清珂. 改进的遗传算法求解桁架的形状优化[J]. 力学学报, 2006, 38(6): 843-849.
TANG Wen-yan, YUAN Qing-ke. Improved genetic algorithm for shape optimization of truss structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 843-849.
[13] 薛运虎,韦凌云,赵玫,等. 基于演化算法的带频率约束的桁架结构形状和尺寸优化[J]. 振动与冲击,2010,29(12):l3-17.
XUE Yun-hu, WEI Ling-yun, ZHAO Mei, et al. Truss optimization on shape and sizing with frequency constraints based on evolutionary algorithms[J]. Journal of Vibration and Shock, 2010, 29(12): l3-17.
[14] 孟艳,赵洪波,茹忠亮,等. GEP在桁架结构优化中的应用[J]. 工程力学, 2013, 30(1): 236-241.
MENG Yan, ZHAO Hong-bo, RU Zhong-liang, et al. The application of GEP in truss structure optimization[J]. Engineering Mechanics, 2013, 30(1): 236-241.
[15] 李峰,唐和生,许锐,等. 桁架结构优化设计的免疫克隆选择算法[J]. 同济大学学报(自然科学版),2010,38(9):1261-1265.
LI Feng, TANG He-sheng, XU Rui, et al. Immune clonal selection algorithm for truss structure optimal design[J]. Journal of Tongji University(Natural Science), 2010,38(9): 1261-1265.
[16] Camp C V. Design of space trusses using big bang-big crunch optimization[J]. Journal of Structural Engineering, 2007, 133(7): 999-1008.