神经网络辅助的多目标粒子群优化算法在复杂产品设计中的应用
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摘要
复杂产品有限元分析(Finite Element Analysis,FEA)费用很高,给多目标优化(Multi-Objective Optimization,MOO)带来很大困难。提出一种人工神经网络(Artificial Neural Network,ANN)辅助的多目标粒子群优化算法(Multi-Objective Particle Swarm Optimization,MOPSO)处理这类计算密集的设计问题:以基于噪声的虚拟样本丰富ANN的训练样本集,通过虚拟样本的控制参数和ANN模型参数的协同优化提高ANN泛化能力;以此ANN为代理模型支持多目标粒子群算法的进化,并采用基于网格邻域信息的拥挤指标提高Pareto前沿的收敛性、多样性及均匀性。最后,以航空发动机高压涡轮盘(High Pressure Turbine Disc,HPTD)多目标优化案例验证该策略的有效性和可用性。试验证明,这种面向成本的MOO方法降低了复杂产品多目标优化的工程应用难度,提高了设计质量。
Computational simulation of finite element analysis(FEA) for complex products is highly time-consuming, making it a great challenge to find a multi-objective optimization(MOO) solution. An artificial neural network(ANN) assisted multi-objective particle swarm optimization(MOPSO) was proposed in this paper to solve this computing intensive problem. The proposed approach has the following features. The size of training set for ANN is increased by noise-based virtual samples. The control parameters of virtual samples and neural model were optimized together to improve the generalization ability of ANN that is used as the fitness function of the MOPSO. The diversity, uniformity, and convergence of the proposed MOPSO are improved by exploiting the information of neighborhood grids. Finally, the feasibility and effectiveness of the MOPSO are validated by the MOO of high pressure turbine disc. The experiment shows that the engineering application difficulty of MOO is mitigated by this computation-efficient method.
Computational simulation of finite element analysis(FEA) for complex products is highly time-consuming, making it a great challenge to find a multi-objective optimization(MOO) solution. An artificial neural network(ANN) assisted multi-objective particle swarm optimization(MOPSO) was proposed in this paper to solve this computing intensive problem. The proposed approach has the following features. The size of training set for ANN is increased by noise-based virtual samples. The control parameters of virtual samples and neural model were optimized together to improve the generalization ability of ANN that is used as the fitness function of the MOPSO. The diversity, uniformity, and convergence of the proposed MOPSO are improved by exploiting the information of neighborhood grids. Finally, the feasibility and effectiveness of the MOPSO are validated by the MOO of high pressure turbine disc. The experiment shows that the engineering application difficulty of MOO is mitigated by this computation-efficient method.
引文
[1] 国家制造强国建设战略咨询委员会.中国制造2025蓝皮书(2016)[M].北京:电子工业出版社,2016.
[2] 冯国奇,崔东亮,王成恩,等.面向科学计算的复杂产品工程设计数据管理研究[J].计算机集成制造系统,2008,14(2):226-233.
[3] Steenackers G,Guillaume P,Vanlanduit S.Development of a regressive finite element model optimization technique making use of transmissibilities[J].Structural and Multidisciplinary Optimization,2009,39(1):47-62.
[4] Jin Y.Surrogate-assisted evolutionary computation:Recent advances and future challenges[J].Swarm and Evolutionary Computation,2011,1 (2):61-70.
[5] Mohan S C,Maiti D K.Structural optimization of rotating disk using response surface equation and genetic algorithm[J].International Journal for Computational Methods in Engineering Science and Mechanics,2013,14 (2):124-132.
[6] Garcia-Revillo F J,Jimenez-Octavio J R.Sanchez-Rebollo C,et al.Efficient multi-objective optimization for gas turbine discs[J].Advanced Structured Materials,2014,54:227-255.
[7] Li H,Water W,Zhu B,et al.Integrated high frequency coaxial transformer design platform using artificial neural network optimization and FEM simulation[J].IEEE Transactions on Magnetics,2015,51(3):1-4.
[8] Bakhtiari H,Karimi M,Rezazadeh S.Modeling,analysis and multi-objective optimization of twist extrusion process using predictive models and meta-heuristic approaches,based on finite element results[J].Journal of Intelligent Manufacturing,2016,27(2):463-473.
[9] 贺勇,廖诺,莫赞.基于PSO和ANN的采选品位智能约束优化[J].系统管理学报,2014(5):737-742.
[10] Tan C J,Lim C P,Cheah Y.A multi-objective evolutionary algorithm-based ensemble optimizer for feature selection and classification with neural network models[J].Neurocomputing,2014,125(3):217-228.
[11] Garud S S,Karimi I A,Kraft M.Smart sampling algorithm for surrogate model development[J].Computers & Chemical Engineering,2017,96:103-114.
[12] Lindstrom M.Small data:The tiny clues that uncover huge trends[M].New York:St.Martin's Press,2016
[13] 李力,林懿伦,曹东璞,等.平行学习-机器学习的一个新型理论框架[J].自动化学报,2017,43(1):1-8.
[14] 王卫东,杨静宇.采用虚拟训练样本的二次判别分析方法[J].自动化学报,2008,34(4):400-407.
[15] Bishop C M.Training with noise is equivalent to Tikhonov regularization[J].Neural Computation,1995,7(1):108-116.
[16] Li D C,Lin L S,Peng L J.Improving learning accuracy by using synthetic samples for small datasets with non-linear attribute dependency[J].Decision Support Systems,2014,59(1):286-295.
[17] Li D C,Chen W C,Chang C J.et al.Practical information diffusion techniques to accelerate new product pilot runs[J].International Journal of Production Research,2015,53(17):5310-5319.
[18] Zitzler E,Laumanns M,Thiele L.SPEA2:Improving the strength Pareto evolutionary algorithm for multiobjective optimization[C]// Evolutionary Methods for Design,Optimization and Control with Applications to Industrial Problems.Proceedings of the Eurogen'2001.Athens,Greece:[s.n.],2001:95-100.
[19] Maashi M,?zcan E,Wenping M,et al.A multi-objective hyper-heuristic based on choice function[J].Expert Systems with Applications,2014,41(9):4475-4493.
[20] Jiao S,Maoguo G,Ma W,et al.A multipopulation coevolutionary strategy for multiobjective immune algorithm[J].the Scientific World Journal,2014:1-23.
[21] 雷雨,焦李成,公茂果,等.求解多目标考试时间表问题的NNIA改进算法[J].西安电子科技大学学报(自然科学版),2016,43(2):157-161.
[22] Deb K,Pratap A,Agarwal S,et al.A fast and elitist multiobjective genetic algorithm:NSGA-II[J].IEEE Transactions on Evolutionary Computation,2002,6(2):182-197.
[23] Coello C A C,Pulido G T,Lechuga M S.Handling multiple objectives with particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2004,8(3):256-279.
[24] Haykin S O.Neural networks and learning machines (3rd Edition)[M].New Jersey:Pearson Prentice Hall,2011.
[25] Zitzler E,Deb K,Thiele L.Comparison of multi-objective evolutionary algorithms:Empirical results.[J].Evolutionary Computation,2000,8(2):173-195.
[26] Deb K,Thiele L,Laumanns M,et al.Scalable test problems for evolutionary multiobjective optimization[C]//In:Abraham A,Jain L,Goldberg R.Eds.Evolutionary Multiobjective Optimization.Advanced Information and Knowledge Processing.London:Springer,2005.
[27] Huband S,Hingston P,Barone L,et al.A review of multi-objective test problems and a scalable test toolkit[J].IEEE Transactions on Evolutionary Computation,2006,10(5):477-506.
[28] Wang H,Jin Y,Yao X.Diversity assessment in many-objective optimization[J].IEEE Transactions on Cybernetics,2016,47(6):1-13.
[29] Joly M M,Verstraete T,Paniagua G.Differential evolution based soft optimization to attenuate vane-rotor shock interaction in high-pressure turbines[J].Applied Soft Computing,2013,13(4):1882-1891.
[30] Decastro J,Melcher K.A study on the requirements for fast active turbine tip clearance control systems[R].NASA technical reports,TM-2004-213121,Maryland,NASA,2004.
[31] 王成恩,崔东亮,曲荣霞等.传热与结构分析有限元法及应用[M].北京:科学出版社,2012.
[32] Abido M A.Multiobjective evolutionary algorithms for electric power dispatch problem[J].IEEE Transactions on Evolutionary Computation,2006,10(3):315-329.
[2] 冯国奇,崔东亮,王成恩,等.面向科学计算的复杂产品工程设计数据管理研究[J].计算机集成制造系统,2008,14(2):226-233.
[3] Steenackers G,Guillaume P,Vanlanduit S.Development of a regressive finite element model optimization technique making use of transmissibilities[J].Structural and Multidisciplinary Optimization,2009,39(1):47-62.
[4] Jin Y.Surrogate-assisted evolutionary computation:Recent advances and future challenges[J].Swarm and Evolutionary Computation,2011,1 (2):61-70.
[5] Mohan S C,Maiti D K.Structural optimization of rotating disk using response surface equation and genetic algorithm[J].International Journal for Computational Methods in Engineering Science and Mechanics,2013,14 (2):124-132.
[6] Garcia-Revillo F J,Jimenez-Octavio J R.Sanchez-Rebollo C,et al.Efficient multi-objective optimization for gas turbine discs[J].Advanced Structured Materials,2014,54:227-255.
[7] Li H,Water W,Zhu B,et al.Integrated high frequency coaxial transformer design platform using artificial neural network optimization and FEM simulation[J].IEEE Transactions on Magnetics,2015,51(3):1-4.
[8] Bakhtiari H,Karimi M,Rezazadeh S.Modeling,analysis and multi-objective optimization of twist extrusion process using predictive models and meta-heuristic approaches,based on finite element results[J].Journal of Intelligent Manufacturing,2016,27(2):463-473.
[9] 贺勇,廖诺,莫赞.基于PSO和ANN的采选品位智能约束优化[J].系统管理学报,2014(5):737-742.
[10] Tan C J,Lim C P,Cheah Y.A multi-objective evolutionary algorithm-based ensemble optimizer for feature selection and classification with neural network models[J].Neurocomputing,2014,125(3):217-228.
[11] Garud S S,Karimi I A,Kraft M.Smart sampling algorithm for surrogate model development[J].Computers & Chemical Engineering,2017,96:103-114.
[12] Lindstrom M.Small data:The tiny clues that uncover huge trends[M].New York:St.Martin's Press,2016
[13] 李力,林懿伦,曹东璞,等.平行学习-机器学习的一个新型理论框架[J].自动化学报,2017,43(1):1-8.
[14] 王卫东,杨静宇.采用虚拟训练样本的二次判别分析方法[J].自动化学报,2008,34(4):400-407.
[15] Bishop C M.Training with noise is equivalent to Tikhonov regularization[J].Neural Computation,1995,7(1):108-116.
[16] Li D C,Lin L S,Peng L J.Improving learning accuracy by using synthetic samples for small datasets with non-linear attribute dependency[J].Decision Support Systems,2014,59(1):286-295.
[17] Li D C,Chen W C,Chang C J.et al.Practical information diffusion techniques to accelerate new product pilot runs[J].International Journal of Production Research,2015,53(17):5310-5319.
[18] Zitzler E,Laumanns M,Thiele L.SPEA2:Improving the strength Pareto evolutionary algorithm for multiobjective optimization[C]// Evolutionary Methods for Design,Optimization and Control with Applications to Industrial Problems.Proceedings of the Eurogen'2001.Athens,Greece:[s.n.],2001:95-100.
[19] Maashi M,?zcan E,Wenping M,et al.A multi-objective hyper-heuristic based on choice function[J].Expert Systems with Applications,2014,41(9):4475-4493.
[20] Jiao S,Maoguo G,Ma W,et al.A multipopulation coevolutionary strategy for multiobjective immune algorithm[J].the Scientific World Journal,2014:1-23.
[21] 雷雨,焦李成,公茂果,等.求解多目标考试时间表问题的NNIA改进算法[J].西安电子科技大学学报(自然科学版),2016,43(2):157-161.
[22] Deb K,Pratap A,Agarwal S,et al.A fast and elitist multiobjective genetic algorithm:NSGA-II[J].IEEE Transactions on Evolutionary Computation,2002,6(2):182-197.
[23] Coello C A C,Pulido G T,Lechuga M S.Handling multiple objectives with particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2004,8(3):256-279.
[24] Haykin S O.Neural networks and learning machines (3rd Edition)[M].New Jersey:Pearson Prentice Hall,2011.
[25] Zitzler E,Deb K,Thiele L.Comparison of multi-objective evolutionary algorithms:Empirical results.[J].Evolutionary Computation,2000,8(2):173-195.
[26] Deb K,Thiele L,Laumanns M,et al.Scalable test problems for evolutionary multiobjective optimization[C]//In:Abraham A,Jain L,Goldberg R.Eds.Evolutionary Multiobjective Optimization.Advanced Information and Knowledge Processing.London:Springer,2005.
[27] Huband S,Hingston P,Barone L,et al.A review of multi-objective test problems and a scalable test toolkit[J].IEEE Transactions on Evolutionary Computation,2006,10(5):477-506.
[28] Wang H,Jin Y,Yao X.Diversity assessment in many-objective optimization[J].IEEE Transactions on Cybernetics,2016,47(6):1-13.
[29] Joly M M,Verstraete T,Paniagua G.Differential evolution based soft optimization to attenuate vane-rotor shock interaction in high-pressure turbines[J].Applied Soft Computing,2013,13(4):1882-1891.
[30] Decastro J,Melcher K.A study on the requirements for fast active turbine tip clearance control systems[R].NASA technical reports,TM-2004-213121,Maryland,NASA,2004.
[31] 王成恩,崔东亮,曲荣霞等.传热与结构分析有限元法及应用[M].北京:科学出版社,2012.
[32] Abido M A.Multiobjective evolutionary algorithms for electric power dispatch problem[J].IEEE Transactions on Evolutionary Computation,2006,10(3):315-329.