• •
张长胜, 张健忠, 钱斌, 胡蓉
收稿日期:
2022-03-01
修回日期:
2022-07-19
出版日期:
2022-09-16
通讯作者:
作者简介:
基金资助:
ZHANG Chang-sheng, ZHANG Jian-zhong, QIAN Bin, HU Rong
Received:
2022-03-01
Revised:
2022-07-19
Online:
2022-09-16
Corresponding author:
摘要:
为了解决天鹰优化算法(Aquila Optimization algorithm,AO)易陷入局部最优及收敛速度慢的问题,本文提出一种多策略融合的改进天鹰优化算法(Multi-Strategy Integration Aquila Optimization algorithm,MSIAO).该算法采用结合Tent混沌映射的折射反向学习初始化种群以提高算法前期的搜索效率,根据种内互助及优化策略解决算法寻优停滞的缺陷,并通过基于Bernoulli混沌序列的自适应权重策略提高算法的收敛速度,引入了柯西-高斯变异算子增强算法迭代后期逃逸局部极值的能力.本文对10个基准函数、部分CEC2014测试函数集进行实验,并将MSIAO用于2个工程设计优化问题.结果表明,对于高维单峰、高维多峰以及固定维复杂多模态函数,MSIAO比AO具有更高的收敛精度和更快的收敛速度;MSIAO对压力容器与焊接梁优化设计的经济成本较AO分别节约4.62%、0.77%,验证了MSIAO对于处理机械工程问题的实用性和优越性.
中图分类号:
张长胜, 张健忠, 钱斌, 胡蓉. 多策略融合的改进天鹰优化算法[J]. 电子学报, DOI: 10.12263/DZXB.20220205.
ZHANG Chang-sheng, ZHANG Jian-zhong, QIAN Bin, HU Rong. Improved Aquila Optimization Based on Multi-Strategy Integration[J]. Acta Electronica Sinica, DOI: 10.12263/DZXB.20220205.
序号 | 基准测试函数 | 误差精度 |
---|---|---|
Sphere | 1.00E-3 | |
Schwefel'problem 2.22 | 1.00E-3 | |
Schwefel'problem 1.2 | 1.00E-3 | |
Schwefel'problem 2.21 | 1.00E-3 | |
Generalized Rosenbrock's Function | 1.00E-2 | |
Generalized Schwefel's problem 2.26 | 1.00E+2 | |
Ackley's Function | 1.00E-2 | |
Shekell's Foxholes Function | 1.00E-2 | |
Shekel's Family 3 | 1.00E-2 | |
Hatman's Function 2 | 1.00E-2 |
表1 测试函数
序号 | 基准测试函数 | 误差精度 |
---|---|---|
Sphere | 1.00E-3 | |
Schwefel'problem 2.22 | 1.00E-3 | |
Schwefel'problem 1.2 | 1.00E-3 | |
Schwefel'problem 2.21 | 1.00E-3 | |
Generalized Rosenbrock's Function | 1.00E-2 | |
Generalized Schwefel's problem 2.26 | 1.00E+2 | |
Ackley's Function | 1.00E-2 | |
Shekell's Foxholes Function | 1.00E-2 | |
Shekel's Family 3 | 1.00E-2 | |
Hatman's Function 2 | 1.00E-2 |
函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 | 函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 |
---|---|---|---|---|---|---|---|---|---|---|---|
AO | 1.88E-142 | 2.16E-132 | 7.83E-134 | 3.95E-133 | AO | -1.25E+04 | -3.51E+03 | -6.45E+03 | 2.09E+03 | ||
IPAO | 2.53E-156 | 1.18E-130 | 5.40E-132 | 2.28E-131 | IPAO | -1.26E+04 | -3.68E+03 | -9.32E+03 | 2.38E+03 | ||
IMAAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | IMAAO | -1.26E+04 | -1.13E+03 | -1.08E+04 | 1.59E+03 | ||
AWAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | AWAO | -1.26E+04 | -5.36E+03 | -9.70E+03 | 1.80E+03 | ||
CGAO | 2.83E-211 | 5.49E-166 | 1.92E-167 | 0.00E+00 | CGAO | -1.18E+04 | -3.73E+03 | -8.12E+03 | 2.69E+03 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.26E+04 | -8.09E+03 | -1.24E+04 | 9.27E+02 | ||
AO | 4.30E-72 | 6.23E-67 | 4.10E-68 | 1.19E-67 | AO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
IPAO | 5.62E-81 | 2.99E-58 | 9.96E-60 | 5.46E-59 | IPAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
IMAAO | 2.17E-196 | 6.09E-190 | 1.24E-170 | 0.00E+00 | IMAAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
AWAO | 2.76E-273 | 3.81E-253 | 1.29E-254 | 0.00E+00 | AWAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
CGAO | 7.10E-107 | 5.09E-84 | 3.54E-85 | 1.16E-84 | CGAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
AO | 2.83E-139 | 1.08E-127 | 3.94E-129 | 1.97E-128 | AO | 9.98E-01 | 1.27E+01 | 3.87E+00 | 4.24E+00 | ||
IPAO | 3.59E-155 | 1.00E-97 | 3.34E-99 | 1.83E-98 | IPAO | 9.98E-01 | 1.27E+01 | 3.19E+00 | 3.61E+00 | ||
IMAAO | 6.84.E-308 | 8.26E-301 | 9.90E-290 | 0.00E+00 | IMAAO | 9.98E-01 | 6.84E+00 | 2.89E+00 | 2.81E+00 | ||
AWAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | AWAO | 9.98E-01 | 5.93E+00 | 2.15E+00 | 1.19E+00 | ||
CGAO | 5.77E-206 | 2.69E-156 | 8.97E-158 | 4.91E-157 | CGAO | 9.98E-01 | 1.27E+01 | 3.55E+00 | 3.62E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 9.98E-01 | 9.98E-01 | 9.98E-01 | 9.59E-13 | ||
AO | 1.11E-71 | 1.58E-66 | 1.19E-67 | 3.03E-67 | AO | -1.05E+01 | -5.10E+00 | -8.92E+00 | 2.34E+00 | ||
IPAO | 2.54E-87 | 7.28E-56 | 2.43E-57 | 1.33E-56 | IPAO | -1.05E+01 | -1.04E+01 | -1.05E+01 | 4.43E-02 | ||
IMAAO | 3.98.E-298 | 3.64E-292 | 7.85E-280 | 4.30E-138 | IMAAO | -1.05E+01 | -1.05E+01 | -1.05E+01 | 2.92E-02 | ||
AWAO | 2.65E-276 | 1.94E-249 | 6.48E-251 | 0.00E+00 | AWAO | -1.05E+01 | -5.07E+00 | -8.24E+00 | 2.60E+00 | ||
CGAO | 4.32E-100 | 2.96E-83 | 1.45E-84 | 5.50E-84 | CGAO | -1.05E+01 | -9.72E+00 | -1.03E+01 | 1.87E-01 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.05E+01 | -1.03E+01 | -1.05E+01 | 2.16E-02 | ||
AO | 4.69E-05 | 1.44E-01 | 1.02E-02 | 2.61E-02 | AO | -3.28E+00 | -2.84E+00 | -3.12E+00 | 9.03E-02 | ||
IPAO | 8.97E-06 | 6.45E-02 | 5.25E-03 | 1.23E-02 | IPAO | -3.31E+00 | -2.98E+00 | -3.14E+00 | 9.18E-02 | ||
IMAAO | 3.34E-06 | 5.26E-04 | 6.55E-03 | 1.14E-02 | IMAAO | -3.08E+00 | -3.01E+00 | -2.92E+00 | 1.17E-01 | ||
AWAO | 1.03E-05 | 4.04E-02 | 8.56E-03 | 1.15E-02 | AWAO | -3.31E+00 | -2.95E+00 | -3.16E+00 | 8.65E-02 | ||
CGAO | 1.82E-04 | 1.38E-01 | 1.32E-02 | 2.78E-02 | CGAO | -3.32E+00 | -3.01E+00 | -3.15E+00 | 6.99E-02 | ||
MSIAO | 3.04E-07 | 4.60E-03 | 6.53E-05 | 1.17E-03 | MSIAO | -3.32E+00 | -2.85E+00 | -3.20E+00 | 7.24E-02 |
表2 不同改进策略实验结果
函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 | 函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 |
---|---|---|---|---|---|---|---|---|---|---|---|
AO | 1.88E-142 | 2.16E-132 | 7.83E-134 | 3.95E-133 | AO | -1.25E+04 | -3.51E+03 | -6.45E+03 | 2.09E+03 | ||
IPAO | 2.53E-156 | 1.18E-130 | 5.40E-132 | 2.28E-131 | IPAO | -1.26E+04 | -3.68E+03 | -9.32E+03 | 2.38E+03 | ||
IMAAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | IMAAO | -1.26E+04 | -1.13E+03 | -1.08E+04 | 1.59E+03 | ||
AWAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | AWAO | -1.26E+04 | -5.36E+03 | -9.70E+03 | 1.80E+03 | ||
CGAO | 2.83E-211 | 5.49E-166 | 1.92E-167 | 0.00E+00 | CGAO | -1.18E+04 | -3.73E+03 | -8.12E+03 | 2.69E+03 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.26E+04 | -8.09E+03 | -1.24E+04 | 9.27E+02 | ||
AO | 4.30E-72 | 6.23E-67 | 4.10E-68 | 1.19E-67 | AO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
IPAO | 5.62E-81 | 2.99E-58 | 9.96E-60 | 5.46E-59 | IPAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
IMAAO | 2.17E-196 | 6.09E-190 | 1.24E-170 | 0.00E+00 | IMAAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
AWAO | 2.76E-273 | 3.81E-253 | 1.29E-254 | 0.00E+00 | AWAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
CGAO | 7.10E-107 | 5.09E-84 | 3.54E-85 | 1.16E-84 | CGAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 8.88E-16 | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
AO | 2.83E-139 | 1.08E-127 | 3.94E-129 | 1.97E-128 | AO | 9.98E-01 | 1.27E+01 | 3.87E+00 | 4.24E+00 | ||
IPAO | 3.59E-155 | 1.00E-97 | 3.34E-99 | 1.83E-98 | IPAO | 9.98E-01 | 1.27E+01 | 3.19E+00 | 3.61E+00 | ||
IMAAO | 6.84.E-308 | 8.26E-301 | 9.90E-290 | 0.00E+00 | IMAAO | 9.98E-01 | 6.84E+00 | 2.89E+00 | 2.81E+00 | ||
AWAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | AWAO | 9.98E-01 | 5.93E+00 | 2.15E+00 | 1.19E+00 | ||
CGAO | 5.77E-206 | 2.69E-156 | 8.97E-158 | 4.91E-157 | CGAO | 9.98E-01 | 1.27E+01 | 3.55E+00 | 3.62E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 9.98E-01 | 9.98E-01 | 9.98E-01 | 9.59E-13 | ||
AO | 1.11E-71 | 1.58E-66 | 1.19E-67 | 3.03E-67 | AO | -1.05E+01 | -5.10E+00 | -8.92E+00 | 2.34E+00 | ||
IPAO | 2.54E-87 | 7.28E-56 | 2.43E-57 | 1.33E-56 | IPAO | -1.05E+01 | -1.04E+01 | -1.05E+01 | 4.43E-02 | ||
IMAAO | 3.98.E-298 | 3.64E-292 | 7.85E-280 | 4.30E-138 | IMAAO | -1.05E+01 | -1.05E+01 | -1.05E+01 | 2.92E-02 | ||
AWAO | 2.65E-276 | 1.94E-249 | 6.48E-251 | 0.00E+00 | AWAO | -1.05E+01 | -5.07E+00 | -8.24E+00 | 2.60E+00 | ||
CGAO | 4.32E-100 | 2.96E-83 | 1.45E-84 | 5.50E-84 | CGAO | -1.05E+01 | -9.72E+00 | -1.03E+01 | 1.87E-01 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.05E+01 | -1.03E+01 | -1.05E+01 | 2.16E-02 | ||
AO | 4.69E-05 | 1.44E-01 | 1.02E-02 | 2.61E-02 | AO | -3.28E+00 | -2.84E+00 | -3.12E+00 | 9.03E-02 | ||
IPAO | 8.97E-06 | 6.45E-02 | 5.25E-03 | 1.23E-02 | IPAO | -3.31E+00 | -2.98E+00 | -3.14E+00 | 9.18E-02 | ||
IMAAO | 3.34E-06 | 5.26E-04 | 6.55E-03 | 1.14E-02 | IMAAO | -3.08E+00 | -3.01E+00 | -2.92E+00 | 1.17E-01 | ||
AWAO | 1.03E-05 | 4.04E-02 | 8.56E-03 | 1.15E-02 | AWAO | -3.31E+00 | -2.95E+00 | -3.16E+00 | 8.65E-02 | ||
CGAO | 1.82E-04 | 1.38E-01 | 1.32E-02 | 2.78E-02 | CGAO | -3.32E+00 | -3.01E+00 | -3.15E+00 | 6.99E-02 | ||
MSIAO | 3.04E-07 | 4.60E-03 | 6.53E-05 | 1.17E-03 | MSIAO | -3.32E+00 | -2.85E+00 | -3.20E+00 | 7.24E-02 |
函数 | 算法 | 最优值 | 平均值 | 标准差 | 时间 | 成功率 | 函数 | 算法 | 最优值 | 平均值 | 标准差 | 时间 | 成功率 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
GWO | 7.46E-33 | 9.96E-31 | 1.38E-30 | 0.14 | 100% | GWO | -7.77E+03 | -5.98E+03 | 1.53E+03 | 0.17 | 0 | ||
SSA | 2.99E-08 | 2.06E-07 | 4.37E-07 | 0.10 | 100% | SSA | -9.17E+03 | -7.56E+03 | 7.40E+02 | 0.12 | 0 | ||
WOA | 1.53E-88 | 4.62E-67 | 2.53E-66 | 0.09 | 100% | WOA | -1.26E+04 | -1.22E+04 | 7.02E+02 | 0.10 | 50% | ||
PSO | 1.86E+00 | 7.62E+00 | 2.90E+00 | 0.11 | 0 | PSO | -5.67E+03 | -3.37E+03 | 6.15E+02 | 0.14 | 0 | ||
AO | 4.07E-142 | 2.35E-133 | 9.09E-133 | 0.16 | 100% | AO | -1.25E+04 | -5.84E+03 | 1.57E+03 | 0.20 | 26.67% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.16 | 100% | MSIAO | -1.26E+04 | -1.25E+04 | 1.68E+02 | 0.22 | 100% | ||
GWO | 1.60E-19 | 2.17E-18 | 3.42E-18 | 0.14 | 100% | GWO | 1.51E-14 | 2.14E-14 | 3.81E-15 | 0.15 | 100% | ||
SSA | 2.50E-01 | 1.90E+00 | 1.22E+00 | 0.11 | 0 | SSA | 1.78E+00 | 2.60E+00 | 6.19E-01 | 0.12 | 0 | ||
WOA | 2.59E-59 | 7.28E-51 | 3.90E-50 | 0.09 | 100% | WOA | 8.88E-16 | 4.09E-15 | 2.16E-15 | 0.12 | 100% | ||
PSO | 6.25E+00 | 1.44E+01 | 6.01E+00 | 0.11 | 0 | PSO | 2.87E+00 | 4.58E+00 | 9.56E-01 | 0.12 | 0 | ||
AO | 1.87E-71 | 5.11E-68 | 1.25E-67 | 0.16 | 100% | AO | 8.88E-16 | 8.88E-16 | 0.00E+00 | 0.18 | 100% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.15 | 100% | MSIAO | 8.88E-16 | 8.88E-16 | 0.00E+00 | 0.20 | 100% | ||
GWO | 6.78E-06 | 4.25E-03 | 1.04E-02 | 0.32 | 43.33% | GWO | 9.98E-01 | 2.14E+00 | 2.60E+00 | 0.67 | 73.33% | ||
SSA | 3.71E+02 | 1.41E+03 | 9.57E+02 | 0.30 | 0 | SSA | 9.98E-01 | 1.23E+00 | 5.64E-01 | 0.61 | 70% | ||
WOA | 2.53E+04 | 4.98E+04 | 1.14E+04 | 0.23 | 0 | WOA | 9.98E-01 | 2.73E+00 | 3.03E+00 | 0.60 | 63.33% | ||
PSO | 1.95E+02 | 5.26E+02 | 2.59E+02 | 0.29 | 0 | PSO | 9.98E-01 | 1.68E+00 | 1.35E+00 | 0.67 | 80% | ||
AO | 3.93E-141 | 3.17E-124 | 1.73E-123 | 0.34 | 100% | AO | 9.98E-01 | 2.47E+00 | 2.67E+00 | 0.82 | 70% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.36 | 100% | MSIAO | 9.98E-01 | 9.98E-01 | 5.36E-16 | 0.84 | 100% | ||
GWO | 3.14E-06 | 4.26E-05 | 7.57E-05 | 0.14 | 100% | GWO | -1.05E+01 | -1.05E+01 | 1.84E-04 | 0.11 | 90% | ||
SSA | 5.53E+00 | 1.24E+01 | 4.06E+00 | 0.10 | 0 | SSA | -1.05E+01 | -8.75E+00 | 2.83E+00 | 0.72 | 76.67% | ||
WOA | 1.61E+01 | 5.65E+01 | 2.55E+01 | 0.08 | 0 | WOA | -1.05E+01 | -8.22E+00 | 3.60E+00 | 0.13 | 76.67% | ||
PSO | 3.77E+00 | 6.50E+00 | 1.44E+00 | 0.11 | 0 | PSO | -1.05E+01 | -5.24E+00 | 3.47E+00 | 0.14 | 73.33% | ||
AO | 5.82E-71 | 9.07E-68 | 2.50E-67 | 0.16 | 100% | AO | -1.05E+01 | -8.61E+00 | 2.51E+00 | 0.19 | 76.67% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.17 | 100% | MSIAO | -1.05E+01 | -1.05E+01 | 8.69E-02 | 0.21 | 100% | ||
GWO | 2.59E+01 | 2.66E+01 | 7.91E-01 | 0.17 | 0 | GWO | -3.32E+00 | -3.25E+00 | 7.24E-02 | 0.09 | 90% | ||
SSA | 1.68E+01 | 2.38E+02 | 4.90E+02 | 0.13 | 0 | SSA | -3.32E+00 | -3.23E+00 | 5.96E-02 | 0.09 | 86.67% | ||
WOA | 6.57E+00 | 2.72E+01 | 3.91E+00 | 0.12 | 0 | WOA | -3.32E+00 | -3.24E+00 | 1.65E-01 | 0.08 | 86.67% | ||
PSO | 3.60E+02 | 1.12E+03 | 1.03E+03 | 0.13 | 0 | PSO | -3.32E+00 | -3.21E+00 | 1.25E-01 | 0.10 | 86.67% | ||
AO | 3.28E-05 | 4.52E-03 | 5.88E-03 | 0.22 | 80% | AO | -3.30E+00 | -3.13E+00 | 9.04E-02 | 0.14 | 83.33% | ||
MSIAO | 1.83E-07 | 8.32E-05 | 1.89E-04 | 0.24 | 93.33% | MSIAO | -3.32E+00 | -3.19E+00 | 7.66E-02 | 0.15 | 86.67% |
表3 各算法优化基准函数结果对比
函数 | 算法 | 最优值 | 平均值 | 标准差 | 时间 | 成功率 | 函数 | 算法 | 最优值 | 平均值 | 标准差 | 时间 | 成功率 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
GWO | 7.46E-33 | 9.96E-31 | 1.38E-30 | 0.14 | 100% | GWO | -7.77E+03 | -5.98E+03 | 1.53E+03 | 0.17 | 0 | ||
SSA | 2.99E-08 | 2.06E-07 | 4.37E-07 | 0.10 | 100% | SSA | -9.17E+03 | -7.56E+03 | 7.40E+02 | 0.12 | 0 | ||
WOA | 1.53E-88 | 4.62E-67 | 2.53E-66 | 0.09 | 100% | WOA | -1.26E+04 | -1.22E+04 | 7.02E+02 | 0.10 | 50% | ||
PSO | 1.86E+00 | 7.62E+00 | 2.90E+00 | 0.11 | 0 | PSO | -5.67E+03 | -3.37E+03 | 6.15E+02 | 0.14 | 0 | ||
AO | 4.07E-142 | 2.35E-133 | 9.09E-133 | 0.16 | 100% | AO | -1.25E+04 | -5.84E+03 | 1.57E+03 | 0.20 | 26.67% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.16 | 100% | MSIAO | -1.26E+04 | -1.25E+04 | 1.68E+02 | 0.22 | 100% | ||
GWO | 1.60E-19 | 2.17E-18 | 3.42E-18 | 0.14 | 100% | GWO | 1.51E-14 | 2.14E-14 | 3.81E-15 | 0.15 | 100% | ||
SSA | 2.50E-01 | 1.90E+00 | 1.22E+00 | 0.11 | 0 | SSA | 1.78E+00 | 2.60E+00 | 6.19E-01 | 0.12 | 0 | ||
WOA | 2.59E-59 | 7.28E-51 | 3.90E-50 | 0.09 | 100% | WOA | 8.88E-16 | 4.09E-15 | 2.16E-15 | 0.12 | 100% | ||
PSO | 6.25E+00 | 1.44E+01 | 6.01E+00 | 0.11 | 0 | PSO | 2.87E+00 | 4.58E+00 | 9.56E-01 | 0.12 | 0 | ||
AO | 1.87E-71 | 5.11E-68 | 1.25E-67 | 0.16 | 100% | AO | 8.88E-16 | 8.88E-16 | 0.00E+00 | 0.18 | 100% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.15 | 100% | MSIAO | 8.88E-16 | 8.88E-16 | 0.00E+00 | 0.20 | 100% | ||
GWO | 6.78E-06 | 4.25E-03 | 1.04E-02 | 0.32 | 43.33% | GWO | 9.98E-01 | 2.14E+00 | 2.60E+00 | 0.67 | 73.33% | ||
SSA | 3.71E+02 | 1.41E+03 | 9.57E+02 | 0.30 | 0 | SSA | 9.98E-01 | 1.23E+00 | 5.64E-01 | 0.61 | 70% | ||
WOA | 2.53E+04 | 4.98E+04 | 1.14E+04 | 0.23 | 0 | WOA | 9.98E-01 | 2.73E+00 | 3.03E+00 | 0.60 | 63.33% | ||
PSO | 1.95E+02 | 5.26E+02 | 2.59E+02 | 0.29 | 0 | PSO | 9.98E-01 | 1.68E+00 | 1.35E+00 | 0.67 | 80% | ||
AO | 3.93E-141 | 3.17E-124 | 1.73E-123 | 0.34 | 100% | AO | 9.98E-01 | 2.47E+00 | 2.67E+00 | 0.82 | 70% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.36 | 100% | MSIAO | 9.98E-01 | 9.98E-01 | 5.36E-16 | 0.84 | 100% | ||
GWO | 3.14E-06 | 4.26E-05 | 7.57E-05 | 0.14 | 100% | GWO | -1.05E+01 | -1.05E+01 | 1.84E-04 | 0.11 | 90% | ||
SSA | 5.53E+00 | 1.24E+01 | 4.06E+00 | 0.10 | 0 | SSA | -1.05E+01 | -8.75E+00 | 2.83E+00 | 0.72 | 76.67% | ||
WOA | 1.61E+01 | 5.65E+01 | 2.55E+01 | 0.08 | 0 | WOA | -1.05E+01 | -8.22E+00 | 3.60E+00 | 0.13 | 76.67% | ||
PSO | 3.77E+00 | 6.50E+00 | 1.44E+00 | 0.11 | 0 | PSO | -1.05E+01 | -5.24E+00 | 3.47E+00 | 0.14 | 73.33% | ||
AO | 5.82E-71 | 9.07E-68 | 2.50E-67 | 0.16 | 100% | AO | -1.05E+01 | -8.61E+00 | 2.51E+00 | 0.19 | 76.67% | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.17 | 100% | MSIAO | -1.05E+01 | -1.05E+01 | 8.69E-02 | 0.21 | 100% | ||
GWO | 2.59E+01 | 2.66E+01 | 7.91E-01 | 0.17 | 0 | GWO | -3.32E+00 | -3.25E+00 | 7.24E-02 | 0.09 | 90% | ||
SSA | 1.68E+01 | 2.38E+02 | 4.90E+02 | 0.13 | 0 | SSA | -3.32E+00 | -3.23E+00 | 5.96E-02 | 0.09 | 86.67% | ||
WOA | 6.57E+00 | 2.72E+01 | 3.91E+00 | 0.12 | 0 | WOA | -3.32E+00 | -3.24E+00 | 1.65E-01 | 0.08 | 86.67% | ||
PSO | 3.60E+02 | 1.12E+03 | 1.03E+03 | 0.13 | 0 | PSO | -3.32E+00 | -3.21E+00 | 1.25E-01 | 0.10 | 86.67% | ||
AO | 3.28E-05 | 4.52E-03 | 5.88E-03 | 0.22 | 80% | AO | -3.30E+00 | -3.13E+00 | 9.04E-02 | 0.14 | 83.33% | ||
MSIAO | 1.83E-07 | 8.32E-05 | 1.89E-04 | 0.24 | 93.33% | MSIAO | -3.32E+00 | -3.19E+00 | 7.66E-02 | 0.15 | 86.67% |
函数 | 算法 | 最优值 | 平均值 | 标准差 | 函数 | 算法 | 最优值 | 平均值 | 标准差 |
---|---|---|---|---|---|---|---|---|---|
TLSPSO | 9.86E-24 | 5.27E-19 | 8.64E-17 | TLSPSO | -4.98E+03 | -4.12E+03 | 4.35E+02 | ||
MDGWO | 6.37E-280 | 2.91E-272 | 0.00E+00 | MDGWO | -7.59E+03 | -6.53E+03 | 5.10E+02 | ||
ISMA | 0.00E+00 | 7.42E-117 | 4.06E-116 | ISMA | -1.26E+04 | -1.24E+04 | 3.52E+02 | ||
ACAO | 1.53E-270 | 1.65E-246 | 0.00E+00 | ACAO | -1.26E+04 | -1.25E+04 | 8.80E+02 | ||
IHAOHHO | 0.00E+00 | 0.00E+00 | 0.00E+00 | IHAOHHO | -5.66E+03 | -4.64E+03 | 3.43E+02 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.26E+04 | -1.25E+04 | 1.68E+02 | ||
TLSPSO | 8.61E-12 | 5.82E-10 | 6.49E-08 | TLSPSO | 6.86E-03 | 3.95E-02 | 8.53E-02 | ||
MDGWO | 8.62E-153 | 3.68E-151 | 3.65E-156 | MDGWO | 4.44E-15 | 7.88E-15 | 1.14E-15 | ||
ISMA | 1.62E-203 | 1.38E-54 | 7.51E-54 | ISMA | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
ACAO | 1.34E-135 | 5.89E-121 | 3.23E-120 | ACAO | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
IHAOHHO | 1.72E-173 | 5.09E-168 | 0.00E+00 | IHAOHHO | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
TLSPSO | 3.59E-29 | 9.16E-27 | 7.65E-25 | TLSPSO | 9.98E-01 | 9.98E-01 | 5.69E-02 | ||
MDGWO | 2.06E-276 | 4.01E-270 | 0.00E+00 | MDGWO | 9.98E-01 | 9.98E-01 | 1.13E-16 | ||
ISMA | 0.00E+00 | 1.96E-90 | 1.08E-89 | ISMA | 9.98E-01 | 9.98E-01 | 5.11E-16 | ||
ACAO | 1.09E-247 | 5.56E-219 | 0.00E+00 | ACAO | 9.98E-01 | 2.18E+00 | 2.19E+00 | ||
IHAOHHO | 7.76E-322 | 4.98E-310 | 0.00E+00 | IHAOHHO | 9.98E-01 | 9.98E-01 | 1.46E-03 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 9.98E-01 | 9.98E-01 | 5.36E-16 | ||
TLSPSO | 5.29E-16 | 4.89E-13 | 5.79E-11 | TLSPSO | -1.05E+01 | -6.01E+00 | 5.49E-01 | ||
MDGWO | 5.44E-148 | 1.98E-146 | 3.18E-141 | MDGWO | -1.05E+01 | -1.05E+01 | 1.95E-01 | ||
ISMA | 2.48E-209 | 5.84E-53 | 3.09E-52 | ISMA | -1.05E+01 | -1.05E+01 | 1.82E-01 | ||
ACAO | 6.05E-129 | 3.50E-118 | 1.92E-117 | ACAO | -1.04E+01 | -6.66E+00 | 2.23E+00 | ||
IHAOHHO | 1.87E-164 | 2.14E-159 | 4.47E-159 | IHAOHHO | -9.66E+00 | -5.84E+00 | 1.44E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.05E+01 | -1.05E+01 | 8.69E-02 | ||
TLSPSO | 9.69E-01 | 1.08E+00 | 1.01E+00 | TLSPSO | -3.32E+00 | -3.21E+00 | 8.55E-02 | ||
MDGWO | 2.56E+00 | 2.59E+00 | 1.50E+00 | MDGWO | -3.32E+00 | -3.29E+00 | 5.19E-02 | ||
ISMA | 6.55E-03 | 4.38E+00 | 8.96E+00 | ISMA | -3.32E+00 | -3.26E+00 | 5.35E-02 | ||
ACAO | 1.94E-06 | 3.93E-03 | 9.12E-03 | ACAO | -3.29E+00 | -3.08E+00 | 1.09E-01 | ||
IHAOHHO | 2.74E+01 | 2.80E+01 | 4.11E-01 | IHAOHHO | -3.19E+00 | -3.07E+00 | 8.04E-02 | ||
MSIAO | 1.83E-07 | 8.32E-05 | 1.89E-04 | MSIAO | -3.32E+00 | -3.19E+00 | 7.66E-02 |
表4 MSIAO与较新改进算法寻优结果对比
函数 | 算法 | 最优值 | 平均值 | 标准差 | 函数 | 算法 | 最优值 | 平均值 | 标准差 |
---|---|---|---|---|---|---|---|---|---|
TLSPSO | 9.86E-24 | 5.27E-19 | 8.64E-17 | TLSPSO | -4.98E+03 | -4.12E+03 | 4.35E+02 | ||
MDGWO | 6.37E-280 | 2.91E-272 | 0.00E+00 | MDGWO | -7.59E+03 | -6.53E+03 | 5.10E+02 | ||
ISMA | 0.00E+00 | 7.42E-117 | 4.06E-116 | ISMA | -1.26E+04 | -1.24E+04 | 3.52E+02 | ||
ACAO | 1.53E-270 | 1.65E-246 | 0.00E+00 | ACAO | -1.26E+04 | -1.25E+04 | 8.80E+02 | ||
IHAOHHO | 0.00E+00 | 0.00E+00 | 0.00E+00 | IHAOHHO | -5.66E+03 | -4.64E+03 | 3.43E+02 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.26E+04 | -1.25E+04 | 1.68E+02 | ||
TLSPSO | 8.61E-12 | 5.82E-10 | 6.49E-08 | TLSPSO | 6.86E-03 | 3.95E-02 | 8.53E-02 | ||
MDGWO | 8.62E-153 | 3.68E-151 | 3.65E-156 | MDGWO | 4.44E-15 | 7.88E-15 | 1.14E-15 | ||
ISMA | 1.62E-203 | 1.38E-54 | 7.51E-54 | ISMA | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
ACAO | 1.34E-135 | 5.89E-121 | 3.23E-120 | ACAO | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
IHAOHHO | 1.72E-173 | 5.09E-168 | 0.00E+00 | IHAOHHO | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 8.88E-16 | 8.88E-16 | 0.00E+00 | ||
TLSPSO | 3.59E-29 | 9.16E-27 | 7.65E-25 | TLSPSO | 9.98E-01 | 9.98E-01 | 5.69E-02 | ||
MDGWO | 2.06E-276 | 4.01E-270 | 0.00E+00 | MDGWO | 9.98E-01 | 9.98E-01 | 1.13E-16 | ||
ISMA | 0.00E+00 | 1.96E-90 | 1.08E-89 | ISMA | 9.98E-01 | 9.98E-01 | 5.11E-16 | ||
ACAO | 1.09E-247 | 5.56E-219 | 0.00E+00 | ACAO | 9.98E-01 | 2.18E+00 | 2.19E+00 | ||
IHAOHHO | 7.76E-322 | 4.98E-310 | 0.00E+00 | IHAOHHO | 9.98E-01 | 9.98E-01 | 1.46E-03 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | 9.98E-01 | 9.98E-01 | 5.36E-16 | ||
TLSPSO | 5.29E-16 | 4.89E-13 | 5.79E-11 | TLSPSO | -1.05E+01 | -6.01E+00 | 5.49E-01 | ||
MDGWO | 5.44E-148 | 1.98E-146 | 3.18E-141 | MDGWO | -1.05E+01 | -1.05E+01 | 1.95E-01 | ||
ISMA | 2.48E-209 | 5.84E-53 | 3.09E-52 | ISMA | -1.05E+01 | -1.05E+01 | 1.82E-01 | ||
ACAO | 6.05E-129 | 3.50E-118 | 1.92E-117 | ACAO | -1.04E+01 | -6.66E+00 | 2.23E+00 | ||
IHAOHHO | 1.87E-164 | 2.14E-159 | 4.47E-159 | IHAOHHO | -9.66E+00 | -5.84E+00 | 1.44E+00 | ||
MSIAO | 0.00E+00 | 0.00E+00 | 0.00E+00 | MSIAO | -1.05E+01 | -1.05E+01 | 8.69E-02 | ||
TLSPSO | 9.69E-01 | 1.08E+00 | 1.01E+00 | TLSPSO | -3.32E+00 | -3.21E+00 | 8.55E-02 | ||
MDGWO | 2.56E+00 | 2.59E+00 | 1.50E+00 | MDGWO | -3.32E+00 | -3.29E+00 | 5.19E-02 | ||
ISMA | 6.55E-03 | 4.38E+00 | 8.96E+00 | ISMA | -3.32E+00 | -3.26E+00 | 5.35E-02 | ||
ACAO | 1.94E-06 | 3.93E-03 | 9.12E-03 | ACAO | -3.29E+00 | -3.08E+00 | 1.09E-01 | ||
IHAOHHO | 2.74E+01 | 2.80E+01 | 4.11E-01 | IHAOHHO | -3.19E+00 | -3.07E+00 | 8.04E-02 | ||
MSIAO | 1.83E-07 | 8.32E-05 | 1.89E-04 | MSIAO | -3.32E+00 | -3.19E+00 | 7.66E-02 |
函数 | 维度 | 特征 | 定义域 | 最佳值 |
---|---|---|---|---|
CEC03 | 30 | UN | [-100,100] | 300 |
CEC05 | 30 | MF | [-100,100] | 500 |
CEC10 | 30 | MF | [-100,100] | 1000 |
CEC15 | 30 | MF | [-100,100] | 1500 |
CEC19 | 30 | HF | [-100,100] | 1900 |
CEC22 | 30 | HF | [-100,100] | 2200 |
CEC25 | 30 | CF | [-100,100] | 2500 |
CEC28 | 30 | CF | [-100,100] | 2800 |
表5 CEC2014函数
函数 | 维度 | 特征 | 定义域 | 最佳值 |
---|---|---|---|---|
CEC03 | 30 | UN | [-100,100] | 300 |
CEC05 | 30 | MF | [-100,100] | 500 |
CEC10 | 30 | MF | [-100,100] | 1000 |
CEC15 | 30 | MF | [-100,100] | 1500 |
CEC19 | 30 | HF | [-100,100] | 1900 |
CEC22 | 30 | HF | [-100,100] | 2200 |
CEC25 | 30 | CF | [-100,100] | 2500 |
CEC28 | 30 | CF | [-100,100] | 2800 |
函数 | 指标 | CEC03 | CEC05 | CEC10 | CEC15 | CEC19 | CEC22 | CEC25 | CEC28 |
---|---|---|---|---|---|---|---|---|---|
GWO | 平均值 | 9.98E+03 | 5.21E+02 | 3.50E+03 | 1.52E+03 | 1.92E+03 | 2.52E+03 | 2.71E+03 | 3.78E+03 |
标准差 | 4.39E+03 | 4.07E-02 | 1.55E+03 | 2.57E+01 | 1.69E+01 | 1.86E+02 | 2.51E+00 | 1.32E+02 | |
SSA | 平均值 | 2.41E+04 | 5.20E+02 | 4.90E+03 | 1.51E+03 | 1.92E+03 | 2.73E+03 | 2.71E+03 | 3.93E+03 |
标准差 | 6.46E+03 | 8.30E-02 | 6.40E+02 | 2.95E+00 | 1.16E+01 | 2.18E+02 | 3.75E+00 | 2.29E+02 | |
WOA | 平均值 | 6.57E+04 | 5.20E+02 | 5.42E+03 | 1.59E+03 | 1.96E+03 | 3.06E+03 | 2.72E+03 | 5.07E+03 |
标准差 | 3.74E+04 | 1.64E-01 | 7.36E+02 | 2.45E+01 | 4.44E+01 | 2.16E+02 | 1.59E+01 | 5.83E+02 | |
PSO | 平均值 | 3.55E+03 | 5.21E+02 | 1.73E+03 | 1.51E+03 | 1.92E+03 | 2.49E+03 | 2.71E+03 | 4.27E+03 |
标准差 | 3.00E+03 | 6.49E-02 | 2.87E+02 | 2.81E+00 | 2.09E+01 | 1.67E+02 | 2.13E+00 | 4.99E+02 | |
AO | 平均值 | 3.90E+04 | 5.21E+02 | 3.81E+03 | 1.53E+03 | 1.92E+03 | 2.90E+03 | 2.70E+03 | 3.00E+03 |
标准差 | 8.17E+03 | 1.30E-01 | 7.34E+02 | 6.65E+00 | 2.25E+01 | 1.74E+02 | 0.00E+00 | 0.00E+00 | |
MSIAO | 平均值 | 3.69E+03 | 5.06E+02 | 2.83E+03 | 1.51E+03 | 1.91E+03 | 2.65E+03 | 2.66E+03 | 2.91E+03 |
标准差 | 8.56E+02 | 3.59E-02 | 2.75E+02 | 2.63E+00 | 1.03E+01 | 1.96E+02 | 0.00E+00 | 0.00E+00 |
表6 CEC2014函数优化结果对比
函数 | 指标 | CEC03 | CEC05 | CEC10 | CEC15 | CEC19 | CEC22 | CEC25 | CEC28 |
---|---|---|---|---|---|---|---|---|---|
GWO | 平均值 | 9.98E+03 | 5.21E+02 | 3.50E+03 | 1.52E+03 | 1.92E+03 | 2.52E+03 | 2.71E+03 | 3.78E+03 |
标准差 | 4.39E+03 | 4.07E-02 | 1.55E+03 | 2.57E+01 | 1.69E+01 | 1.86E+02 | 2.51E+00 | 1.32E+02 | |
SSA | 平均值 | 2.41E+04 | 5.20E+02 | 4.90E+03 | 1.51E+03 | 1.92E+03 | 2.73E+03 | 2.71E+03 | 3.93E+03 |
标准差 | 6.46E+03 | 8.30E-02 | 6.40E+02 | 2.95E+00 | 1.16E+01 | 2.18E+02 | 3.75E+00 | 2.29E+02 | |
WOA | 平均值 | 6.57E+04 | 5.20E+02 | 5.42E+03 | 1.59E+03 | 1.96E+03 | 3.06E+03 | 2.72E+03 | 5.07E+03 |
标准差 | 3.74E+04 | 1.64E-01 | 7.36E+02 | 2.45E+01 | 4.44E+01 | 2.16E+02 | 1.59E+01 | 5.83E+02 | |
PSO | 平均值 | 3.55E+03 | 5.21E+02 | 1.73E+03 | 1.51E+03 | 1.92E+03 | 2.49E+03 | 2.71E+03 | 4.27E+03 |
标准差 | 3.00E+03 | 6.49E-02 | 2.87E+02 | 2.81E+00 | 2.09E+01 | 1.67E+02 | 2.13E+00 | 4.99E+02 | |
AO | 平均值 | 3.90E+04 | 5.21E+02 | 3.81E+03 | 1.53E+03 | 1.92E+03 | 2.90E+03 | 2.70E+03 | 3.00E+03 |
标准差 | 8.17E+03 | 1.30E-01 | 7.34E+02 | 6.65E+00 | 2.25E+01 | 1.74E+02 | 0.00E+00 | 0.00E+00 | |
MSIAO | 平均值 | 3.69E+03 | 5.06E+02 | 2.83E+03 | 1.51E+03 | 1.91E+03 | 2.65E+03 | 2.66E+03 | 2.91E+03 |
标准差 | 8.56E+02 | 3.59E-02 | 2.75E+02 | 2.63E+00 | 1.03E+01 | 1.96E+02 | 0.00E+00 | 0.00E+00 |
算法 | 变量最优值 | 开销 平均值 | 时间 /s | |||
---|---|---|---|---|---|---|
PSO | 0.8833 | 0.4562 | 45.9623 | 170.6321 | 7763.3523 | 0.17 |
WOA | 0.8330 | 0.5613 | 45.6175 | 178.6594 | 7860.2788 | 0.14 |
SSA | 0.8799 | 0.4349 | 45.5917 | 140.1964 | 7588.1924 | 0.14 |
GWO | 0.8392 | 0.4053 | 45.6371 | 179.6354 | 7296.5341 | 0.15 |
SCA | 1.1563 | 0.6859 | 45.6217 | 82.6172 | 7315.3926 | 0.13 |
SMA | 0.9216 | 0.7635 | 49.6217 | 98.5243 | 7529.6874 | 0.15 |
ChOA | 1.2162 | 0.6329 | 62.2593 | 25.4475 | 8582.4655 | 0.20 |
AO | 1.1534 | 0.3692 | 48.6871 | 96.8699 | 7140.9473 | 0.14 |
IAO | 0.8629 | 0.5091 | 42.6427 | 162.9673 | 6825.3564 | 0.16 |
表7 压力容器设计问题结果对比
算法 | 变量最优值 | 开销 平均值 | 时间 /s | |||
---|---|---|---|---|---|---|
PSO | 0.8833 | 0.4562 | 45.9623 | 170.6321 | 7763.3523 | 0.17 |
WOA | 0.8330 | 0.5613 | 45.6175 | 178.6594 | 7860.2788 | 0.14 |
SSA | 0.8799 | 0.4349 | 45.5917 | 140.1964 | 7588.1924 | 0.14 |
GWO | 0.8392 | 0.4053 | 45.6371 | 179.6354 | 7296.5341 | 0.15 |
SCA | 1.1563 | 0.6859 | 45.6217 | 82.6172 | 7315.3926 | 0.13 |
SMA | 0.9216 | 0.7635 | 49.6217 | 98.5243 | 7529.6874 | 0.15 |
ChOA | 1.2162 | 0.6329 | 62.2593 | 25.4475 | 8582.4655 | 0.20 |
AO | 1.1534 | 0.3692 | 48.6871 | 96.8699 | 7140.9473 | 0.14 |
IAO | 0.8629 | 0.5091 | 42.6427 | 162.9673 | 6825.3564 | 0.16 |
算法 | 变量最优值 | 开销 平均值 | 时间 /s | |||
---|---|---|---|---|---|---|
PSO | 0.2059 | 2.4193 | 9.3362 | 0.2297 | 1.8169 | 0.21 |
WOA | 0.2653 | 1.7926 | 7.9579 | 0.2653 | 1.7489 | 0.18 |
SSA | 0.1735 | 3.5334 | 9.2095 | 0.2105 | 1.7663 | 0.20 |
GWO | 0.1250 | 4.5368 | 9.0624 | 0.2056 | 1.7456 | 0.20 |
SCA | 0.1570 | 4.0850 | 9.0993 | 0.2108 | 1.7968 | 0.27 |
SMA | 0.1250 | 4.5166 | 9.0366 | 0.2057 | 1.7492 | 0.25 |
ChOA | 0.1577 | 4.1055 | 8.8791 | 0.2153 | 1.7826 | 0.62 |
AO | 0.1559 | 3.5328 | 8.7646 | 0.2187 | 1.7216 | 0.22 |
MSIAO | 0.1507 | 3.2561 | 8.6311 | 0.2262 | 1.7085 | 0.22 |
表8 焊接梁设计问题结果对比
算法 | 变量最优值 | 开销 平均值 | 时间 /s | |||
---|---|---|---|---|---|---|
PSO | 0.2059 | 2.4193 | 9.3362 | 0.2297 | 1.8169 | 0.21 |
WOA | 0.2653 | 1.7926 | 7.9579 | 0.2653 | 1.7489 | 0.18 |
SSA | 0.1735 | 3.5334 | 9.2095 | 0.2105 | 1.7663 | 0.20 |
GWO | 0.1250 | 4.5368 | 9.0624 | 0.2056 | 1.7456 | 0.20 |
SCA | 0.1570 | 4.0850 | 9.0993 | 0.2108 | 1.7968 | 0.27 |
SMA | 0.1250 | 4.5166 | 9.0366 | 0.2057 | 1.7492 | 0.25 |
ChOA | 0.1577 | 4.1055 | 8.8791 | 0.2153 | 1.7826 | 0.62 |
AO | 0.1559 | 3.5328 | 8.7646 | 0.2187 | 1.7216 | 0.22 |
MSIAO | 0.1507 | 3.2561 | 8.6311 | 0.2262 | 1.7085 | 0.22 |
1 | ABUALIGAH L, YOUSRI D, ELAZIZ M ABD, et al. Aquila optimizer: a novel meta-heuristic optimization algorithm[J]. Computers & Industrial Engineering, 2021, 157: 107250. |
2 | ALRASSAS A M, AL-QANESS M A A, EWEES A A, et al. Optimized ANFIS model using aquila optimizer for oil production forecasting[J]. Processes, 2021, 9(7): 1194. |
3 | KANDAN M, KRISHNAMURTHY A, SELVI S, et al. Quasi oppositional aquila optimizer-based task scheduling approach in an IoT enabled cloud environment[J]. The Journal of Supercomputing, 2022, 78(7): 10176-10190. |
4 | WANG S, JIA H, ABUALIGAH L, et al. An improved hybrid aquila optimizer and Harris hawks algorithm for solving industrial engineering optimization problems[J]. Processes, 2021, 9(9): 1551. |
5 | AL-QANESS M A A, EWEES A A, FAN H, et al. Modified aquila optimizer for forecasting oil production[J/OL]. Geo-Spatial Information Science. DOI: 10.1080/10095020. 2022. 2068385 . |
6 | SINGH S, BANSAL J C. Mutation-driven grey wolf optimizer with modified search mechanism[J]. Expert Systems with Applications, 2022, 194: 116450. |
7 | BAIRATHI D, GOPALANI D. An improved salp swarm algorithm for complex multi-modal problems[J]. Soft Computing, 2021, 25(15): 10441-10465. |
8 | CHAKRABORTY S, SAHA A K, CHAKRABORTY R, et al. An enhanced whale optimization algorithm for large scale optimization problems[J]. Knowledge-Based Systems, 2021, 233: 107543. |
9 | ZHANG X, LIN Q. Three-learning strategy particle swarm algorithm for global optimization problems[J]. Information Sciences, 2022, 593: 289-313. |
10 | LI X, MOBAYEN S. Optimal design of a PEMFC-based combined cooling, heating and power system based on an improved version of aquila optimizer[J]. Concurrency and Computation-Practice & Experience, 2022, 34(15): e6976. |
11 | WANG S, MA J, LI W, et al. An optimal configuration for hybrid SOFC, gas turbine, and proton exchange membrane electrolyzer using a developed aquila optimizer[J]. International Journal of Hydrogen Energy, 2022, 47(14): 8943-8955. |
12 | MA L, LI J, ZHAO Y. Ma L, Li J, Zhao Y. Population forecast of China's rural community based on CFANGBM and improved aquila optimizer algorithm[J]. Fractal and Fractional, 2021, 5(4): 190. |
13 | WANG S, JIA H, LIU Q, et al. An improved hybrid aquila optimizer and Harris hawks optimization for global optimization[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 7076-7109. |
14 | EWEES A A, ALGAMAL Z Y, ABUALIGAH L, et al. A cox proportional-hazards model based on an improved aquila optimizer with whale optimization algorithm operators[J]. Mathematics, 2022, 10(8): 1273. |
15 | 杜彦斌, 周志杰, 许磊, 等. 基于灰色关联分析与自适应混沌差分进化算法的激光熔覆工艺参数优化方法[J]. 计算机集成制造系统, 2022, 28(01): 149-160. |
DU Y B, ZHOU Z J, XU L, et al. Laser cladding process parameter optimization method based on grey relational analysis and ACDE algorithm[J]. Computer Integrated Manufacturing Systems, 2022, 28(01): 149-160. (in Chinese) | |
16 | 周鹏, 董朝轶, 陈晓艳, 等. 基于阶梯式Tent混沌和模拟退火的樽海鞘群算法[J]. 电子学报, 2021, 49(9): 1724-1735. |
ZHOU P, DONG C Y, CHEN X Y, et al. A salp swarm algorithm based on stepped Tent chaos and simulated annealing[J]. Acta Electronica Sinica, 2021, 49(09): 1724-1735. (in Chinese) | |
17 | 龙文, 伍铁斌, 唐明珠, 等. 基于透镜成像学习策略的灰狼优化算法[J]. 自动化学报, 2020, 46(10): 2148-2164. |
LONG W, WU T B, TANG M Z, et al. Grey wolf optimizer algorithm based on lens imaging learning strategy[J]. Acta Automatica Sinica, 2020, 46(10): 2148-2164. (in Chinese) | |
18 | TSUNEDA A. Orthogonal chaotic binary sequences based on Bernoulli map and Walsh functions[J]. Entropy, 2019, 21(10): 930. |
19 | 褚鼎立, 陈红, 王旭光. 基于自适应权重和模拟退火的鲸鱼优化算法[J]. 电子学报, 2019, 47(05): 992-999. |
CHU D L, CHEN H, WANG X G. Whale optimization algorithm based on adaptive weight and simulated annealing[J]. Acta Electronica Sinica, 2019, 47(05): 992-999. (in Chinese) | |
20 | 付华, 刘昊. 多策略融合的改进麻雀搜索算法及其应用[J]. 控制与决策, 2021, 37(1): 87-96. |
FU H, LIU H. Improved sparrow search algorithm with multi-strategy integration and its application[J]. Control and Decision, 2021, 37(01): 87-96. (in Chinese) | |
21 | 刘成汉, 何庆. 融合多策略的黄金正弦黑猩猩优化算法[J/OL]. 自动化学报. DOI:10.16383/j.aas.c210313 . |
LIU C H, HE Q. Golden sine chimp optimization algorithm integrating multiple strategies[J/OL]. Acta Automatica Sinica, 2022. DOI:10.16383/j.aas.c210313. (in Chinese) | |
22 | DHAWALE D, KAMBOJ V K, ANAND P. An effective solution to numerical and multi-disciplinary design optimization problems using chaotic slime mold algorithm[J/OL]. Engineering with Computers. DOI: 10.1007/s00366-021-01409-4 . |
23 | LONG W, WU T, LIANG X, et al. Solving high-dimensional global optimization problems using an improved sine cosine algorithm[J]. Expert Systems with Applications, 2019, 123: 108-126. |
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