基于α-stable分布的多目标粒子群算法研究及应用
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摘要
多目标的粒子群算法(MOPSO)在各个领域的优化设计中得到了广泛应用及改进,但是目前仍然存在着在进化后期容易陷入局部最优导致收敛精度低、解的多样性差等问题。引入α-stable分布理论,发展建立了一种新的基于α-stable动态变异的多目标粒子群优化算法(ASMOPSO)。通过α-stable分布生成随机数对PSO算法的种群进行变异操作,增加种群的多样性,在算法中动态调整稳定性系数α实现变异范围和幅度的变化,从而使得改进的ASMOPSO算法具有兼顾计算精度和全局寻优的能力。使用ZDT系列无约束函数和带约束的Tanaka及Srinivas函数对改进前后的算法进行了测试,结果显示出了ASMOPSO算法的快速全局寻优性能。将改进后的算法应用到RAE2822跨音速翼型的减阻和力矩绝对值不增大的综合优化中,得到了较好的多目标气动优化结果。
The multi-objective particle swarm optimization algorithm(MOPSO) has been applied and modified for optimal designs in various engineering fields. However, the intimal algorithm is still has the problems of low accuracy and poor diversity of solutions as it is easy to fall into local optimum in the later evolution stage. A new dynamic mutation operator has been established based on the α-stable distribution theory and incorporated with multi-objective particle swarm optimization algorithm(ASMOPSO). By using random Numbers which generated by the α-stable distribution, the population of PSO algorithm was mutated. And this mutate operation increases the diversity of the population. Because the stability coefficient in the ASMOPSO algorithm can change the range and amplitude of the mutation. This operation makes the new algorithm has the ability to balance the calculation accuracy and global optimization. Several benchmark functions test show that the ASMOPSO algorithm has fast global optimization ability. The proposed algorithm is applied to the multi-objective aerodynamic optimization design of RAE2822 transonic airfoil. The comparison results also show that ASMOPSO algorithm is more excellent than the basic MOPSO algorithm.
The multi-objective particle swarm optimization algorithm(MOPSO) has been applied and modified for optimal designs in various engineering fields. However, the intimal algorithm is still has the problems of low accuracy and poor diversity of solutions as it is easy to fall into local optimum in the later evolution stage. A new dynamic mutation operator has been established based on the α-stable distribution theory and incorporated with multi-objective particle swarm optimization algorithm(ASMOPSO). By using random Numbers which generated by the α-stable distribution, the population of PSO algorithm was mutated. And this mutate operation increases the diversity of the population. Because the stability coefficient in the ASMOPSO algorithm can change the range and amplitude of the mutation. This operation makes the new algorithm has the ability to balance the calculation accuracy and global optimization. Several benchmark functions test show that the ASMOPSO algorithm has fast global optimization ability. The proposed algorithm is applied to the multi-objective aerodynamic optimization design of RAE2822 transonic airfoil. The comparison results also show that ASMOPSO algorithm is more excellent than the basic MOPSO algorithm.
引文
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[2] LEIFSSON L,KOZIEL S,TESFAHUNEGN Y A.Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates[J].AIAA Journal,2016,54:531-541
[3] EBRAHIMI M,JAHANGIRIAN A.Accelerating Global Optimization of Aerodynamic Shapes Using a New Surrogate-Assisted Parallel Genetic Algorithm[J].Engineering Optimization,2017,49(12):1-16
[4] CAO L,ZHANG D.Aerodynamic Configuration Optimization for Hypersonic Gliding Vehicle Based on Improved Hybrid Multi-Objective PSO Algorithm[C]//IEEE International Conference on Signal Processing,Communications and Computing,2015:1-5
[5] SONG L,LUO C,LI J,et al.Aerodynamic Optimization of Axial Turbomachinery Blades Using Parallel Adaptive Range Differential Evolution and Reynolds-Averaged Navier-Stokes Solutions[J].International Journal for Numerical Methods in Biomedical Engineering,2011,27(2):283-303
[6] WEISHUANG L U,TIAN Y,LIU P.Aerodynamic Optimization and Mechanism Design of Flexible Variable Camber Trailing-Edge Flap[J].Chinese Journal of Aeronautics,2017,30(3):988-1003
[7] KOO D,ZINGG D W.Investigation into Aerodynamic Shape Optimization of Planar and Nonplanar Wings[J].AIAA Journal,2017,56(1):1-14
[8] 李丁,夏露.一种混合粒子群优化算法在翼型设计中的应用[J].航空计算技术,2010,40(6):66-71LI Ding,XIA Lu.Application of a Hybrid Particle Swarm Optimization to Airfoil Design[J].Aeronautical Computing Technique,2010,40(6):66-71 (in Chinese)
[9] 陈进,郭小锋,孙振业,等.基于改进多目标粒子群算法的风力机大厚度翼型优化设计[J].东北大学学报,2016,37(2):232-236CHEN Jin,GUO Xiaofeng,SUN Zhenye,et al.Optimization of Wind Turbine Thick Airfoils Using Improved Multi-Objective Particle Swarm Algorithm[J].Journal of Northeastern University,2016,37(2):232-236 (in Chinese)
[10] 李鑫,屈转利,李耿,等.高效低噪的二维翼型优化设计[J].振动与冲击,2017,36(4):66-72LI Xin,QU Zhuanli,LI Geng,et al.A Numerical Optimization for High Efficiency and Low Noise Airfoils[J].Journal of Vibration and Shock,2017,36(4):66-72 (in Chinese)
[11] WERON A,WERON R.Computer Simulation of Levy-α Stable Variables and Processes[M].Poland,Springer,Berlin Heidelberg,1995:379-392
[12] KOGON S M,MANOLAKIS D G.Signal Modeling with Self-Similar α Stable Processes:The Fractional Levy Stable Motion Model[J].IEEE Trans on Signal Processing,1996,44(4):1006-1010
[13] WEI J L,JAMBEK A B,NEOH S C.Kursawe and ZDT Functions Optimization Using Hybrid Micro Genetic Algorithm(HMGA)[J].Soft Computing-a Fusion of Foundations,Methodologies and Applications,2015,19(12):3571-3580
[14] LI X.Better Spread and Convergence:Particle Swarm Multiobjective Optimization Using the Maximin Fitness Function[C]//Genetic and Evolutionary Computation Conference,2004:117-128
[15] PENG H,LI R,CAO L L,et al.Multiple Swarms Multi-Objective Particle Swarm Optimization Based on Decomposition[J].Procedia Engineering,2011,15(2):3371-3375
[16] PENG X,LIU D,SHAN J,et al.Airfoil Aerodynamic Optimization Based on an Improved Genetic Algorithm[C]//International Conference on Intelligent Systems Design & Engineering Applications,2014:133-137
[17] Uoigne Alan Le,Qin Ning.Variable-Fidelity Aerodynamic Optimization for Turbulent Flows Using a Discrete Adjoint Formulation[J].AIAA Journal,2004,42(42):1281-1292
[18] LAURENCEAU J,MEAUX M,MONTAGNAC M,et al.Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers[J].AIAA Journal,2010,48(5):981-994
[19] DEB K,PRATAP A,AGARWAL S,et al.A Fast and Elitist Multi-Objective Genetic Algorithm:NSGA-II [J].IEEE Trans on Evolutionary Computation,2002,6(2):182-197