Synthesis of Sparse Rectangular Planar Arrays with Multiple Constraints Based on Dynamic Parameters Differential Evolution Algorithm
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摘要:
针对多约束条件下稀布矩形平面阵列天线的优化问题，该文提出一种基于动态参数差分进化(DPDE)算法的方向图综合方法。首先，对差分进化(DE)算法中的缩放因子和交叉概率引入动态变化控制策略，提高搜索效率和搜索精度。其次，改进矩阵映射方法，重新定义映射法则，改善现有方法随机性强和搜索精度低的不足。最后，为检验所提方法的有效性进行仿真实验，实验数据表明，该方法可以提高天线优化性能，有效降低天线的峰值旁瓣电平。
Abstract:For solving the problem of the synthesis of sparse rectangular planar arrays with multiple constraints, this paper proposes a Dynamic Parameters Differential Evolution (DPDE) based algorithm. Firstly, to improve searching efficiency and accuracy of Differential Evolution (DE), the proposed method introduces dynamically changing strategies to the scaling factor and the crossover probability of the traditional Differential Evolution algorithm. Secondly, a modified matrix mapping method and the redefinition of mapping principles are presented to make up the defects of strong randomness and low accuracy in existing methods. Finally, simulation experiments of antenna arrays are performed to validate the effectiveness of the proposed method, and the results demonstrate that the proposed method performs out the existing methods in the respect of reducing peak sidelobe level of antenna arrays.
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表 1 标准测试函数
函数 变量取值范围 最小值 f1 $\displaystyle\sum\limits_{i = 1}^n {x_i^2} $ [–100, 100] 0 f2 $\displaystyle\sum\limits_{i = 1}^n {\left| {{x_i}} \right|} + \prod\limits_{i = 1}^n {{x_i}} $ [–10, 10] 0 f3 ${\displaystyle\sum\limits_{i = 1}^n {\left( {\displaystyle\sum\limits_{j = 1}^i {{x_j}} } \right)} ^2}$ [–100, 100] 0 f4 $\displaystyle\sum\limits_{i = 1}^D {{{\left( {\left| {{x_i} + 0.5} \right|} \right)}^2}\quad } $ [–100, 100] 0 f5 $\displaystyle\sum\limits_{i = 1}^D {\left[ {x_i^2 - 10\cos \left( {2\pi {x_i}} \right) + 10} \right]} $ [–5.12，5.12] 0 f6 $ - 20{ {\rm{e} }^{ - 0.2\sqrt {\dfrac{1}{D}\displaystyle\sum\limits_{i = 1}^D {x_i^2} } } } - { {\rm{e} }^{\dfrac{1}{D}\displaystyle\sum\limits_{i = 1}^D {\cos \left( {2\pi {x_i} } \right)} } } + 20 + {\rm{e} }$ [–32, 32] 0 f7 $\dfrac{1}{ {400} }\displaystyle\sum\limits_{i = 1}^D {x_i^2} - \prod\limits_{i = 1}^D {\cos \left( {\frac{ { {x_i} } }{ {\sqrt i } } } \right)} + 1$ [–600, 600] 0 
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表 2 实验参数设置
缩放因子 交叉概率Cr 种群规模NP 迭代次数NI 变量维度D 缩放因子F 变异概率Mr DPDE $1/\sqrt t $ 自适应 50 10000 100/200 0.5 0.5 DE (无) 0.5
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表 3 DPDE和DE的实验结果对比(较好的以*标出)
DPDE (D=100) DE (D=100) DPDE (D=200) DE (D=200) MEAN SD PSR(%) MEAN SD PSR(%) MEAN SD PSR(%) MEAN SD PSR(%) f1 2.72E-28* 5.23E-56 100 1.86E-14 5.94E-29 100 5.16E-17* 6.17E-34 100 1.87E+01 7.91E+00 0 f2 1.87E-14* 5.83E-29 100 7.97E-09 2.65E-18 0 1.01E-08* 9.34E-18 0 4.73E+00 3.23E-01 0 f3 1.41E+00* 3.61E-02 0 3.39E+05 5.07E+08 0 9.04E+00* 1.32E+00 0 1.33E+06 1.02E+10 0 f4 9.25E-28* 9.62E-55 100 1.99E-14 6.35E-29 100 1.97E-16* 1.01E-32 100 1.92E+01 1.12E+01 0 f5 3.72E+01* 1.77E+02 0 7.67E+02 3.69E+02 0 2.11E+02* 2.14E+03 0 2.04E+03 8.78E+02 0 f6 1.54E-14* 3.52E-30 100 2.80E-08 3.13E-17 0 1.68E-09* 2.27E-19 0 2.05E+00 9.44E-01 0 f7 8.66E-17* 2.16E-33 100 1.08E-14 1.55E-29 100 2.33E-16* 1.64E-33 100 2.74E+00 1.12E-01 0
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表 4 仿真实验结果对比(dB)
实验 方法 最优值 均值 最差值 方差 实验1 本文方法 –62.093 –60.395 –58.141 0.898 MGA –45.456 – –43.864 – MMM –51.499 – –49.269 – AMM –61.454 –58.922 – – 实验2 本文方法 –22.753 –21.287 –19.038 0.363 MGA –18.840 – – – MMM –20.384 – – – AMM –21.886 –20.456 – –
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