A Improved Multi-objective Optimization Algorithm using Kriging Model
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摘要: 将基于模糊C均值聚类改进的多目标优化算法（A fuzzy c-means clustering based evolutionary algorithm，FCEA）与高价单目标优化算法（Efficient global optimization，EGO）进行融合，基于Kriging模型提出了一种改进的多目标优化算法（FCEA-EGO）。在FCEA-EGO算法寻优过程中，利用模糊C均值聚类算法从整个种群中选择相似个体进行遗传操作，引导算法进行寻优；基于EGO算法的校正点选择机制，逐步修正校正点，提高Kriging模型精度。实验结果表明，FCEA-EGO算法相对于典型的高价多目标优化算法MOEA/D-EGO、ParEGO、SMS-EGO具有更优异的求解能力。最后，基于FCEA-EGO算法对某轻型飞机的齿轮减速器进行了优化设计，验证了其求解实际工程优化问题的能力。Abstract: A fuzzy C-Means Clustering Based Evolutionary Algorithm (FCEA) is merged with Efficient Global Optimization (EGO), and a Kriging model is proposed to develop a multi-objective optimization algorithm (FCEA-EGO). In the optimization process of FCEA-EGO algorithm, the fuzzy C-means clustering algorithm is used to select similar individuals from the whole population for genetic operation, and the algorithm is guided to be optimized; Based on the EGO algorithm's correction point selection mechanism, the correction points are gradually corrected to improve the accuracy of the Kriging model. The experimental results show that the FCEA-EGO algorithm has better solving ability than the typical high-price multi-objective optimization algorithms MOEA/D-EGO, ParEGO and SMS-EGO. Finally, based on the FCEA-EGO algorithm, the gear reducer of a light aircraft is optimized, and its ability to solve practical engineering optimization problems is verified.
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表 1 IGD的平均值(标准差)
测试函数 FCEA-EGO MOEA/D-EGO SMS-EGO ParEGO ZDT1 1.524E-02(1.606E-02) 3.669E-02(1.208E-02) 8.089E-01(9.934E-02) 1.272E+01(1.632E+00) ZDT2 3.957E-02(1.452E-02) 3.791E-02(4.083E-03) 6.095E-01(9.100E-06) 1.441E+01(3.003E+00) ZDT3 7.435E-02(2.947E-02) 3.067E-01(1.225E-01) 7.654E-01(1.158E-01) 1.223E+01(2.119E+00) ZDT4 3.523E-01(1.047E-01) 1.882E+01(1.289E+01) 6.030E+01(1.148E+01) 5.263E+01(1.172E+01) ZDT6 1.852E-01(9.820E-02) 5.812E-01(1.122E-01) 1.521E+00(1.885E+00) 1.055E+01(3.007E-01) DTLZ2 3.137E-02(1.167E-03) 1.419E-01(1.035E-02) 1.428E-01(3.703E-02) 2.157E-01(1.532E-02) 
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表 2 HV的平均值(标准差)
测试函数 FCEA-EGO MOEA/D-EGO SMS-EGO ParEGO ZDT1 3.720E+00(3.807E-02) 3.605E+00(2.027E-02) 1.448E-01(1.099E-01) 0.000E+00(0.000E+00) ZDT2 3.413E+00(1.402E-01) 3.282E+00(6.652E-03) 1.100E-01(2.414E-05) 0.000E+00(0.000E+00) ZDT3 5.156E+00(1.517E+00) 3.349E+00(4.673E-01) 1.471E-01(1.126E-01) 0.000E+00(0.000E+00) ZDT4 3.863E+02(3.462E+02) 1.824E-02(5.770E-02) 0.000E+00(0.000E+00) 0.000E+00(0.000E+00) ZDT6 1.319E+01(1.875E+01) 1.280E+00(2.202E-01) 8.000E-02(8.896E-02) 0.000E+00(0.000E+00) DTLZ2 9.729E+00(7.861E-02) 7.299E+00(1.191E-02) 6.495E-01(5.788E-02) 3.511E-01(3.610E-02)
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