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摘要:
针对麻雀搜索算法(SSA)在接近全局最优时，种群多样性减少，易陷入局部最优解等问题，提出了一种混沌麻雀搜索优化算法(CSSOA)。首先，通过改进Tent混沌序列初始化种群，提高初始解的质量，增强算法的全局搜索能力。其次，引入高斯变异的方法，加强局部搜索能力，提高搜索精度；同时以搜索停滞的解为基础产生Tent混沌序列，用此混沌序列对部分陷入局部最优的个体进行混沌扰动，促使算法跳出限制继续搜索。最后，对12个基准函数进行仿真实验。结果表明：所提算法能够克服SSA易陷入局部最优的缺点，提高算法的搜索精度、收敛速度和稳定性。同时，将CSSOA应用到简单图像分割问题，验证了CSSOA应用于实际工程问题的可行性。
Abstract:Aimed at the problem that when the Sparrow Search Algorithm (SSA) is close to the global optimum, the population diversity decreases, and it is easy to fall into the local optimal solution. A Chaotic Sparrow Search Optimization Algorithm (CSSOA) is proposed. Firstly, the population was initialized by improving the Tent chaotic sequence, the quality of the initial solution was improved, and the global search ability of the algorithm was strengthened. Secondly, the method of Gaussian mutation was introduced to strengthen the local search ability and improve the search accuracy. At the same time, a Tent chaotic sequence was generated based on the search stagnation solution, and this chaotic sequence was used to chaotically disturb some individuals who were partially trapped in the local optimum, prompting the algorithm to jump out of the limit and continue the search. Finally, through simulations of 12 benchmark functions, the results show that the proposed algorithm can overcome the shortcomings of SSA being easily trapped in local optimum, and improve the search accuracy, convergence speed and stability of the algorithm. Meanwhile, CSSOA is applied to the simple image segmentation problem, which verifies the feasibility of applying CSSOA to practical engineering problems.
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图 2 5种算法在基准函数上的收敛曲线比较
Figure 2. Comparison of convergence curves of 5 algorithms obtained on benchmark functions
表 1 基准函数
Table 1. Benchmark functions
函数类型 基准测试函数 维度 搜索空间 最优值 高维单峰 
30 [-100, 100]n 0 
30 [-10, 10]n 0 
30 [-100, 100]n 0 
30 [-100, 100]n 0 
30 [-1.28, 1.28]n 0 高维多峰 
30 [-500, 500]n －418.982 9n 
30 [-5.12, 5.12]n 0 
30 [-32, 32]n 0 
30 [-600, 600]n 0 低维多峰 
2 [-65, 65]2 1 
6 [0, 1]4 -3.32 
4 [0, 10]10 -10.536 
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表 2 基准函数优化结果比较
Table 2. Optimization result comparison of benchmark functions
类型 函数 PSO GWO WOA SSA CSSOA 平均值 标准差 平均值 标准差 平均值 标准差 平均值 标准差 平均值 标准差 高维单峰 F1 5.073 1.718 1.587×10-2 9.820×10-3 3.136×10-11 8.830×10-11 3.757×10-24 2.058×10-23 6.186×10-78 3.195×10-77 F2 6.920 2.727 2.516×10-2 9.797×10-3 1.637×10-8 4.417×10-8 1.673×10-13 7.279×10-13 1.745×10-40 4.160×10-40 F3 1.429×103 6.541×102 2.654×10-2 2.405×102 1.019×105 2.836×104 6.526×10-14 3.313×10-13 3.292×10-65 1.283×10-64 F4 5.159 1.412 1.503 6.449×10-1 6.399×10 2.410×10 6.980×10-16 3.278×10-15 5.188×10-39 2.247×10-38 F5 1.271×10 9.092 1.935×10-2 8.231×10-3 1.579×10-2 1.533×10-2 4.250×10-3 4.383×10-3 7.229×10-4 6.384×10-4 高维多峰 F6 -3.211×103 4.485×102 -5.466×103 9.532×102 -9.034×103 1.675×103 -8.513×103 6.873×102 -1.109×104 7.128×102 F7 1.896×102 4.051×101 4.288×101 1.779×10 3.923×10-1 1.271 2.266×102 3.867×10 0 0 F8 3.035 3.845×10-1 2.553×10-2 9.419×10-3 4.154×10-7 6.556×10-7 1.480×10-15 1.885×10-15 8.882×10-16 0 F9 2.977×101 8.579 2.474×10-1 1.233×10-1 8.940×10-2 2.365×10-1 4.736×10 5.372×10 0 0 低维多峰 F10 3.565 2.217 5.700 4.123 3.396 2.921 5.552 5.217 1.164 5.265×10-1 F11 -3.274 5.924×10-2 -3.228 8.406×10-2 -3.190 8.603×10-2 -3.267 6.033×10-2 -3.306 4.111×10-2 F12 -8.554 3.376 -9.778 2.227 -5.023 2.705 -7.647 2.738 -1.054×10 1.281×10-5
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表 3 基准函数的优化结果比较
Table 3. Optimization result comparison of benchmark functions
函数 PSO GWO WOA SSA CSSOA 迭代次数 时间/s 迭代次数 时间/s 迭代次数 时间/s 迭代次数 时间/s 迭代次数 时间/s F1 100 0.033 100 0.061 100 0.190 95 0.128 6 0.021 F2 100 0.024 100 0.048 100 0.185 100 0.118 6 0.011 F3 100 0.193 100 0.225 100 0.351 100 0.417 7 0.054 F4 100 0.033 100 0.058 100 0.192 100 0.137 6 0.018 F5 100 0.035 100 0.061 100 0.192 100 0.139 4 0.014 F6 100 0.027 100 0.045 100 0.184 100 0.121 3 0.011 F7 100 0.036 100 0.068 100 0.196 42 0.067 5 0.024 F8 100 0.042 100 0.068 100 0.199 100 0.151 6 0.023 F9 100 0.049 100 0.073 100 0.206 41 0.066 5 0.017 F10 77 0.177 89 0.227 69 0.173 100 0.480 5 0.040 F11 82 0.036 85 0.055 98 0.087 100 0.174 9 0.027 F12 97 0.080 100 0.106 100 0.120 100 0.230 4 0.019
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表 4 图像分割阈值
Table 4. Image segmentation threshold
类型 图像 最大值 最小值 平均值 标准差 标准测试图像 Lena 118 116 117.033 0.490 Man 91 88 89.067 0.450 舰船SAR图像 图像1 124 121 123.067 0.583 图像2 126 124 125.100 0.403
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