Thinned array optimization based on genetic model improved artificial bee colony algorithm
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摘要: 人工蜂群算法作为一种新兴的群体智能算法，在解决复杂连续问题时表现突出。但是由于算法本身内在运行机制的原因，算法在搜索上表现出优异的性能，却疏于开发。为了平衡搜索和开发二者之间的矛盾，提出了一种基于遗传模型改进的人工蜂群算法，并成功运用到了阵列综合领域。算法先将全局最优解引入邻域搜索过程，指导蜂群寻找最佳蜜源，加速算法收敛。为了避免人工蜂群算法陷入局部最优，需要提高其开发能力，通过借鉴遗传算法中的进化机制，建立了遗传模型，对采取最佳保留后的蜜源进行遗传操作，丰富蜜源的多样性。在一组广泛使用的数值函数上对改进人工蜂群算法进行了测试，实验数据表明，该算法相较于其他算法具有很强的竞争力。将该算法运用于线性阵列的稀疏优化，旨在降低阵列的峰值旁瓣电平，在同样的阵列约束下与其他算法进行了优化对比，仿真结果进一步证明了算法的有效性。Abstract: To solve the problem that artificial bee colony algorithm is good at exploration and neglect exploitation, this paper proposes an improved artificial bee colony algorithm based on genetic model, which has been successfully applied to array synthesis. Firstly, the global optimal solution is introduced into the neighborhood search process to guide the bees to find the best nectar source thus to accelerate the convergence of the algorithm. Secondly, to avoid the local optimization of the algorithm, the exploitation ability of artificial bee colony algorithm must be improved. The evolutionary mechanism of genetic algorithm is used for reference, and a genetic model is established to carry out genetic operation on the honey source after adopting the optimal retention, to enrich the diversity of honey source. The improved artificial bee colony algorithm is tested on a set of widely used numerical functions, and the experimental data show that the proposed algorithm has strong competitiveness compared with other algorithms. Then, the algorithm is applied to the sparse optimization of the linear array to reduce the peak sidelobe level of the array. The optimization is compared with other algorithms under the same array constraints. The simulation results further prove the effectiveness of the algorithm.
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图 3 标准人工蜂群算法邻域搜索方式
Figure 3. Neighborhood search method of artificial bee colony algorithm
图 4 全局邻域搜索方式
Figure 4. Global artificial bee colony algorithm neighborhood search method
图 5 不同稀疏率下GMIABC算法优化结果
Figure 5. Optimization results of GMIABC algorithm at different sparsity rates
图 6 稀疏率η=70%时GMIABC与GA,ABC算法的阵列稀疏优化对比
Figure 6. Comparison of array sparsity optimization between GMIABC, GA and ABC algorithms when sparsity rate η=70%
表 1 基准数值函数
Table 1. Benchmark numerical functions
function expression range minimum value Sphere $ {f}_{1}\left(x\right)={\displaystyle\sum }_{i=1}^{D}{x}_{i}^{2} $ $ {\left[-\mathrm{100,100}\right]}^{D} $ 0 Elliptic $ {f}_{2}\left(x\right)={\displaystyle\sum }_{i=1}^{D}{{\left({10}^{6}\right)}^{\tfrac{i-1}{D-1}}}x_{i}^{2} $ $ {\left[-\mathrm{100,100}\right]}^{D} $ 0 SumSquare $ {f}_{3}\left(x\right)={\displaystyle\sum }_{i=1}^{D}{ix}_{i}^{2} $ $ {\left[-\mathrm{10,10}\right]}^{D} $ 0 Exponential ${f}_{4}\left(x\right)=\mathrm{e}\mathrm{x}\mathrm{p}\left(0.5 {\displaystyle\sum }_{i=1}^{D}{x}_{i}\right)$ $ {\left[-\mathrm{10,10}\right]}^{D} $ 0 Rosenbrock $ {f}_{5}\left(x\right)={\displaystyle\sum }_{i}^{D-1}\left[{100\left({x}_{i+1}-{x}_{i}^{2}\right)}^{2}-{\left({x}_{i}-1\right)}^{2}\right] $ $ {\left[-\mathrm{5,10}\right]}^{D} $ 0 Rastrigin $ {f}_{6}\left(x\right)={\displaystyle\sum }_{i}^{D}\left[{x}_{i}^{2}-10\mathrm{cos}\left(2\pi {x}_{i}\right)+10\right] $ $ {\left[-\mathrm{5.12,5.12}\right]}^{D} $ 0 Himmelblau $ {f}_{7}\left(x\right)=1/\mathrm{D}{\displaystyle\sum }_{i}^{D}\left[{x}_{i}^{4}-16{x}_{i}^{2}+5{x}_{i}\right] $ $ {\left[-\mathrm{5,5}\right]}^{D} $ −78.33236 
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表 2 GMIABC与ABC，GABC算法比较
Table 2. Comparison of GMIABC, ABC and GABC algorithms
algorithm $ {f}_{1}\left(x\right) $ $ {f}_{2}\left(x\right) $ $ {f}_{3}\left(x\right) $ $ {f}_{4}\left(x\right) $ $ {f}_{5}\left(x\right) $ $ {f}_{6}\left(x\right) $ $ {f}_{7}\left(x\right) $ ABC mean 2.42e−15 4.52e−8 7.32e–15 7.18e−21 4.75e−01 1.34e−13 −78.332 std 3.20e−15 4.83e−8 8.18e−15 7.21e−21 5.81e−01 1.97e−13 0 GABC mean 5.12e−16 4.19e−16 5.25e–15 7.18e−23 9.71e−02 0 −78.332 std 4.35e−17 4.25e−16 6.18e−15 7.07e−23 1.01e−01 0 3.13e−15 GA mean 1.23e−13 4.47e−12 8.10e−11 0 4.1675e−05 0 −78.332 std 1.63e−13 5.77e−12 7.82e−11 0 5.0100e−05 0 1.0974e−14 GMIABC mean 3.73e−23 4.99e−21 3.57e−20 0 1.910158e−07 0 −78.33233 std 4.16e−23 1.21e−20 6.93e−20 0 2.110158e−07 0 0
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表 3 GMIABC与GA, ABC,ABCSIM算法阵列稀疏优化比较
Table 3. Comparison of sparsity optimization between GMIABC and GA, ABC and ABCSIM algorithms
algorithm min/dB mean/dB std min/dB mean/dB std min/dB mean/dB std min/dB mean/dB std η=50%（Nt= 50） η=60%（Nt =60） η=70%（Nt =70） η=80%（Nt =80） GA −15.935 −15.677 0.189 −18.121 −17.521 0.353 −19.378 −19.110 0.187 −20.941 −20.752 0.178 ABC −15.330 −15.061 0.237 −16.806 −16.563 0.207 −18.386 −17.722 0.423 −19.836 −18.430 0.967 ABCSIM −17.211 −16.863 0.262 −17.426 −17.158 0.217 −18.202 −17.588 0.429 −18.172 −17.764 0.331 GMIABC min/dB −18.541 −18.281 0.227 −19.368 −19.200 0.135 −21.365 −20.892 0.171 −21.338 −21.573 0.175
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