Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (2): 534-541.DOI: 10.11772/j.issn.1001-9081.2021020265
• Advanced computing • Previous Articles Next Articles
Mengjian ZHANG1, Deguang WANG1,2, Min WANG1, Jing YANG1,2()
Received:
2021-02-19
Revised:
2021-04-17
Accepted:
2021-04-22
Online:
2022-02-11
Published:
2022-02-10
Contact:
Jing YANG
About author:
ZHANG Mengjian, born in 1996, M. S. candidate. His research interests include swarm intelligent computing, wireless sensor network.Supported by:
通讯作者:
杨靖
作者简介:
张孟健(1996—),男,安徽芜湖人,硕士研究生,CCF会员,主要研究方向:群体智能计算、无线传感器网络;基金资助:
CLC Number:
Mengjian ZHANG, Deguang WANG, Min WANG, Jing YANG. Several novel intelligent optimization algorithms for solving constrained engineering problems and their prospects[J]. Journal of Computer Applications, 2022, 42(2): 534-541.
张孟健, 王德光, 汪敏, 杨靖. 求解工程约束问题的新型智能优化算法及展望[J]. 《计算机应用》唯一官方网站, 2022, 42(2): 534-541.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2021020265
函数 | 搜索范围 | 最优值 |
---|---|---|
[-100,100] | 0 | |
[-10,10] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-1.28, 1.28] | 0 | |
[-5.12,5.12] | 0 | |
[-32,32] | 0 | |
[-600,600] | 0 | |
[-5,5] | 0 |
Tab. 1 Benchmark functions
函数 | 搜索范围 | 最优值 |
---|---|---|
[-100,100] | 0 | |
[-10,10] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-100,100] | 0 | |
[-1.28, 1.28] | 0 | |
[-5.12,5.12] | 0 | |
[-32,32] | 0 | |
[-600,600] | 0 | |
[-5,5] | 0 |
算法 | 参数设置 |
---|---|
HHO | N=25 |
EO | N=25, a1=2, a2=1, GP=0.5, |
MPA | N=25, p=0.5, FADs=0.2 |
PO | N=25, parties = 5, lambda = 1.0 |
SMA | N=25, Vb=-1 to 1, Vc =1 to 0 |
HBO | N=25, [C, p1, p2] from corresponding equations |
Tab. 2 Parameter setting
算法 | 参数设置 |
---|---|
HHO | N=25 |
EO | N=25, a1=2, a2=1, GP=0.5, |
MPA | N=25, p=0.5, FADs=0.2 |
PO | N=25, parties = 5, lambda = 1.0 |
SMA | N=25, Vb=-1 to 1, Vc =1 to 0 |
HBO | N=25, [C, p1, p2] from corresponding equations |
算法 | 计算复杂度 |
---|---|
HHO | O(N×(T+T*D+1)) |
EO | O(1 + N*D + T*Cobj*N + T*N + T*N*D) |
MPA | O(T×(N*D + Cobj*N)) |
PO | O(T*N2*D + T*N2 + T*N2×Cobj + T*N*D) |
SMA | O(D + T*N×(1 + lgN + D)) |
HBO | O(T*N*D + T*N*Cobj + T*N*lg N) |
Tab. 3 Complexity comparison of different algorithms
算法 | 计算复杂度 |
---|---|
HHO | O(N×(T+T*D+1)) |
EO | O(1 + N*D + T*Cobj*N + T*N + T*N*D) |
MPA | O(T×(N*D + Cobj*N)) |
PO | O(T*N2*D + T*N2 + T*N2×Cobj + T*N*D) |
SMA | O(D + T*N×(1 + lgN + D)) |
HBO | O(T*N*D + T*N*Cobj + T*N*lg N) |
函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 | 寻优时间/s | 中位数 |
---|---|---|---|---|---|---|---|
F1 | HHO | 6.010 0E-198 | 3.140 0E-177 | 1.050 0E-178 | 0.000 0E-00 | 0.1622 | 7.220 0E-190 |
EO | 3.740 0E-72 | 5.370 0E-68 | 3.140 0E-69 | 9.880 0E-69 | 0.202 1 | 4.470 0E-70 | |
MPA | 4.710 0E-49 | 1.830 0E-45 | 2.180 0E-46 | 4.240 0E-46 | 0.386 0 | 4.290 0E-47 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.328 1 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 1.907 2 | 0.000 0E-00 | |
HBO | 6.560 0E-09 | 3.200 0E-06 | 5.570 0E-07 | 8.230 0E-07 | 0.201 9 | 1.200 0E-07 | |
F2 | HHO | 2.510 0E-104 | 2.000 0E-92 | 7.420 0E-94 | 3.660 0E-93 | 0.1553 | 8.620 0E-100 |
EO | 1.130 0E-41 | 9.660 0E-40 | 2.660 0E-40 | 2.290 0E-40 | 0.205 7 | 2.230 0E-40 | |
MPA | 1.800 0E-28 | 7.850 0E-26 | 1.130 0E-26 | 1.640 0E-26 | 0.378 9 | 4.770 0E-27 | |
PO | 0.000 0E-00 | 1.5609E-316 | 5.204 0E-318 | 0.000 0E-00 | 0.319 0 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 3.940 0E-173 | 1.310 0E-174 | 0.000 0E-00 | 1.8928 | 1.890 0E-237 | |
HBO | 1.990 0E-07 | 7.350 0E-05 | 9.130 0E-06 | 1.790 0E-05 | 0.292 6 | 1.330 0E-06 | |
F3 | HHO | 7.850 0E-175 | 1.540 0E-132 | 5.150 0E-134 | 2.820 0E-133 | 1.083 9 | 1.460 0E-151 |
EO | 6.580 0E-16 | 3.010 0E-10 | 3.100 0E-11 | 7.880 0E-11 | 0.5698 | 2.740 0E-13 | |
MPA | 6.690 0E-13 | 6.340 0E-05 | 4.410 0E-06 | 1.500 0E-05 | 1.155 2 | 1.200 0E-08 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.802 7 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 2.291 8 | 0.000 0E-00 | |
HBO | 3.630 0E+04 | 1.100 0E+05 | 8.290 0E+04 | 1.380 0E+04 | 0.585 1 | 8.610 0E+04 | |
F4 | HHO | 1.510 0E-102 | 5.760 0E-91 | 3.050 0E-92 | 1.170 0E-91 | 0.1991 | 1.600 0E-96 |
EO | 1.620 0E-16 | 1.350 0E-13 | 2.000 0E-14 | 3.890 0E-14 | 0.201 8 | 4.410 0E-15 | |
MPA | 2.100 0E-18 | 6.070 0E-17 | 1.460 0E-17 | 1.260 0E-17 | 0.377 3 | 1.030 0E-17 | |
PO | 2.8400E-303 | 1.3600E-269 | 4.5500E-271 | 0.000 0E-00 | 0.314 2 | 3.0800E-283 | |
SMA | 0.000 0E-00 | 1.050 0E-189 | 3.630 0E-191 | 0.000 0E-00 | 1.906 3 | 7.130 0E-237 | |
HBO | 1.910 0E+01 | 3.660 0E+01 | 2.840 0E+01 | 5.010 0E+00 | 0.196 2 | 2.850 0E+01 | |
F5 | HHO | 3.660 0E-08 | 3.420 0E-04 | 4.580 0E-05 | 7.260 0E-05 | 0.235 6 | 2.710 0E-05 |
EO | 1.260 0E-05 | 1.235 5E-04 | 5.150 0E-05 | 2.910 0E-05 | 0.2005 | 4.690 0E-05 | |
MPA | 8.080 0E-08 | 3.430 0E-01 | 3.710 0E-02 | 7.820 0E-02 | 0.364 4 | 1.950 0E-06 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.244 2 | 0.000 0E-00 | |
SMA | 7.110 0E-04 | 2.180 0E-02 | 1.080 0E-02 | 5.420 0E-03 | 2.108 2 | 1.080 0E-02 | |
HBO | 4.810 0E-09 | 9.640 0E-06 | 5.510 0E-07 | 1.760 0E-06 | 0.329 4 | 7.410 0E-08 |
Tab. 4 Results of benchmark functions (unimodal)
函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 | 寻优时间/s | 中位数 |
---|---|---|---|---|---|---|---|
F1 | HHO | 6.010 0E-198 | 3.140 0E-177 | 1.050 0E-178 | 0.000 0E-00 | 0.1622 | 7.220 0E-190 |
EO | 3.740 0E-72 | 5.370 0E-68 | 3.140 0E-69 | 9.880 0E-69 | 0.202 1 | 4.470 0E-70 | |
MPA | 4.710 0E-49 | 1.830 0E-45 | 2.180 0E-46 | 4.240 0E-46 | 0.386 0 | 4.290 0E-47 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.328 1 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 1.907 2 | 0.000 0E-00 | |
HBO | 6.560 0E-09 | 3.200 0E-06 | 5.570 0E-07 | 8.230 0E-07 | 0.201 9 | 1.200 0E-07 | |
F2 | HHO | 2.510 0E-104 | 2.000 0E-92 | 7.420 0E-94 | 3.660 0E-93 | 0.1553 | 8.620 0E-100 |
EO | 1.130 0E-41 | 9.660 0E-40 | 2.660 0E-40 | 2.290 0E-40 | 0.205 7 | 2.230 0E-40 | |
MPA | 1.800 0E-28 | 7.850 0E-26 | 1.130 0E-26 | 1.640 0E-26 | 0.378 9 | 4.770 0E-27 | |
PO | 0.000 0E-00 | 1.5609E-316 | 5.204 0E-318 | 0.000 0E-00 | 0.319 0 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 3.940 0E-173 | 1.310 0E-174 | 0.000 0E-00 | 1.8928 | 1.890 0E-237 | |
HBO | 1.990 0E-07 | 7.350 0E-05 | 9.130 0E-06 | 1.790 0E-05 | 0.292 6 | 1.330 0E-06 | |
F3 | HHO | 7.850 0E-175 | 1.540 0E-132 | 5.150 0E-134 | 2.820 0E-133 | 1.083 9 | 1.460 0E-151 |
EO | 6.580 0E-16 | 3.010 0E-10 | 3.100 0E-11 | 7.880 0E-11 | 0.5698 | 2.740 0E-13 | |
MPA | 6.690 0E-13 | 6.340 0E-05 | 4.410 0E-06 | 1.500 0E-05 | 1.155 2 | 1.200 0E-08 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.802 7 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 2.291 8 | 0.000 0E-00 | |
HBO | 3.630 0E+04 | 1.100 0E+05 | 8.290 0E+04 | 1.380 0E+04 | 0.585 1 | 8.610 0E+04 | |
F4 | HHO | 1.510 0E-102 | 5.760 0E-91 | 3.050 0E-92 | 1.170 0E-91 | 0.1991 | 1.600 0E-96 |
EO | 1.620 0E-16 | 1.350 0E-13 | 2.000 0E-14 | 3.890 0E-14 | 0.201 8 | 4.410 0E-15 | |
MPA | 2.100 0E-18 | 6.070 0E-17 | 1.460 0E-17 | 1.260 0E-17 | 0.377 3 | 1.030 0E-17 | |
PO | 2.8400E-303 | 1.3600E-269 | 4.5500E-271 | 0.000 0E-00 | 0.314 2 | 3.0800E-283 | |
SMA | 0.000 0E-00 | 1.050 0E-189 | 3.630 0E-191 | 0.000 0E-00 | 1.906 3 | 7.130 0E-237 | |
HBO | 1.910 0E+01 | 3.660 0E+01 | 2.840 0E+01 | 5.010 0E+00 | 0.196 2 | 2.850 0E+01 | |
F5 | HHO | 3.660 0E-08 | 3.420 0E-04 | 4.580 0E-05 | 7.260 0E-05 | 0.235 6 | 2.710 0E-05 |
EO | 1.260 0E-05 | 1.235 5E-04 | 5.150 0E-05 | 2.910 0E-05 | 0.2005 | 4.690 0E-05 | |
MPA | 8.080 0E-08 | 3.430 0E-01 | 3.710 0E-02 | 7.820 0E-02 | 0.364 4 | 1.950 0E-06 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.244 2 | 0.000 0E-00 | |
SMA | 7.110 0E-04 | 2.180 0E-02 | 1.080 0E-02 | 5.420 0E-03 | 2.108 2 | 1.080 0E-02 | |
HBO | 4.810 0E-09 | 9.640 0E-06 | 5.510 0E-07 | 1.760 0E-06 | 0.329 4 | 7.410 0E-08 |
函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 | 寻优时间/s | 中位数 |
---|---|---|---|---|---|---|---|
F6 | HHO | 6.6600E-08 | 5.8000E-04 | 1.0100E-04 | 1.0800E-04 | 0.570 0 | 8.2400E-05 |
EO | 2.330 0E-04 | 2.490 0E-03 | 7.420 0E-04 | 4.600 0E-04 | 0.3631 | 6.700 0E-04 | |
MPA | 2.280 0E-04 | 1.600 0E-03 | 7.630 0E-04 | 3.600 0E-04 | 0.715 3 | 7.450 0E-04 | |
PO | 1.690 0E-05 | 7.120 0E-04 | 2.750 0E-04 | 1.950 0E-04 | 0.527 7 | 2.450 0E-04 | |
SMA | 1.080 0E-05 | 2.750 0E-04 | 1.160 0E-04 | 8.160 0E-05 | 2.293 0 | 9.020 0E-05 | |
HBO | 2.880 0E-02 | 7.930 0E-02 | 4.930 0E-02 | 1.350 0E-02 | 0.826 0 | 4.700 0E-02 | |
F7 | HHO | 8.8800E-16 | 8.8800E-16 | 8.8800E-16 | 0.000 0E-00 | 0.277 4 | 8.8800E-16 |
EO | 4.440 0E-15 | 7.990 0E-15 | 7.160 0E-15 | 1.530 0E-15 | 0.2137 | 7.990 0E-15 | |
MPA | 8.880 0E-16 | 4.440 0E-15 | 4.200 0E-15 | 9.010 0E-16 | 0.388 7 | 4.440 0E-15 | |
PO | 8.8800E-16 | 8.8800E-16 | 8.8800E-16 | 0.000 0E-00 | 0.320 0 | 8.8800E-16 | |
SMA | 8.8800E-16 | 8.8800E-16 | 8.8800E-16 | 0.000 0E-00 | 2.086 5 | 8.8800E-16 | |
HBO | 2.620 0E-06 | 9.420 0E-05 | 1.700 0E-05 | 2.220 0E-05 | 0.362 6 | 9.130 0E-06 | |
F8 | HHO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.324 4 | 0.000 0E-00 |
EO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.237 3 | 0.000 0E-00 | |
MPA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.436 1 | 0.000 0E-00 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.350 6 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 2.119 1 | 0.000 0E-00 | |
HBO | 9.260 0E-12 | 7.250 0E-07 | 3.700 0E-08 | 1.400 0E-07 | 0.2201 | 4.450 0E-10 | |
F9 | HHO | 1.850 0E-94 | 6.080 0E-09 | 2.030 0E-10 | 1.110 0E-09 | 0.566 1 | 1.310 0E-57 |
EO | 1.550 0E-104 | 7.740 0E-87 | 6.160 0E-88 | 1.940 0E-87 | 0.379 3 | 1.060 0E-95 | |
MPA | 1.370 0E-32 | 1.320 0E-19 | 8.890 0E-21 | 3.090 0E-20 | 0.761 9 | 2.780 0E-23 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.457 0 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 2.640 0E-301 | 8.820 0E-303 | 0.000 0E-00 | 2.243 6 | 0.000 0E-00 | |
HBO | 2.230 0E+43 | 7.020 0E+69 | 2.760 0E+68 | 1.290 0E+69 | 0.3523 | 1.340 0E+51 | |
F10 | HHO | 1.040 0E-10 | 6.160 0E-05 | 1.300 0E-05 | 1.660 0E-05 | 0.238 0 | 6.150 0E-06 |
EO | 7.400 0E-06 | 2.080 0E-04 | 4.310 0E-05 | 3.650 0E-05 | 0.199 2 | 3.580 0E-05 | |
MPA | 6.570 0E-08 | 1.060 0E-02 | 9.600 0E-04 | 2.390 0E-03 | 0.367 7 | 1.740 0E-07 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.240 4 | 0.000 0E-00 | |
SMA | 3.840 0E-07 | 6.440 0E-03 | 1.540 0E-03 | 1.610 0E-03 | 2.116 1 | 1.180 0E-03 | |
HBO | 1.570 0E-11 | 2.000 0E-08 | 1.440 0E-09 | 3.760 0E-09 | 0.1768 | 3.400 0E-10 |
Tab. 5 Results of benchmark functions (multimodal)
函数 | 算法 | 最优值 | 最差值 | 平均值 | 标准差 | 寻优时间/s | 中位数 |
---|---|---|---|---|---|---|---|
F6 | HHO | 6.6600E-08 | 5.8000E-04 | 1.0100E-04 | 1.0800E-04 | 0.570 0 | 8.2400E-05 |
EO | 2.330 0E-04 | 2.490 0E-03 | 7.420 0E-04 | 4.600 0E-04 | 0.3631 | 6.700 0E-04 | |
MPA | 2.280 0E-04 | 1.600 0E-03 | 7.630 0E-04 | 3.600 0E-04 | 0.715 3 | 7.450 0E-04 | |
PO | 1.690 0E-05 | 7.120 0E-04 | 2.750 0E-04 | 1.950 0E-04 | 0.527 7 | 2.450 0E-04 | |
SMA | 1.080 0E-05 | 2.750 0E-04 | 1.160 0E-04 | 8.160 0E-05 | 2.293 0 | 9.020 0E-05 | |
HBO | 2.880 0E-02 | 7.930 0E-02 | 4.930 0E-02 | 1.350 0E-02 | 0.826 0 | 4.700 0E-02 | |
F7 | HHO | 8.8800E-16 | 8.8800E-16 | 8.8800E-16 | 0.000 0E-00 | 0.277 4 | 8.8800E-16 |
EO | 4.440 0E-15 | 7.990 0E-15 | 7.160 0E-15 | 1.530 0E-15 | 0.2137 | 7.990 0E-15 | |
MPA | 8.880 0E-16 | 4.440 0E-15 | 4.200 0E-15 | 9.010 0E-16 | 0.388 7 | 4.440 0E-15 | |
PO | 8.8800E-16 | 8.8800E-16 | 8.8800E-16 | 0.000 0E-00 | 0.320 0 | 8.8800E-16 | |
SMA | 8.8800E-16 | 8.8800E-16 | 8.8800E-16 | 0.000 0E-00 | 2.086 5 | 8.8800E-16 | |
HBO | 2.620 0E-06 | 9.420 0E-05 | 1.700 0E-05 | 2.220 0E-05 | 0.362 6 | 9.130 0E-06 | |
F8 | HHO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.324 4 | 0.000 0E-00 |
EO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.237 3 | 0.000 0E-00 | |
MPA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.436 1 | 0.000 0E-00 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.350 6 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 2.119 1 | 0.000 0E-00 | |
HBO | 9.260 0E-12 | 7.250 0E-07 | 3.700 0E-08 | 1.400 0E-07 | 0.2201 | 4.450 0E-10 | |
F9 | HHO | 1.850 0E-94 | 6.080 0E-09 | 2.030 0E-10 | 1.110 0E-09 | 0.566 1 | 1.310 0E-57 |
EO | 1.550 0E-104 | 7.740 0E-87 | 6.160 0E-88 | 1.940 0E-87 | 0.379 3 | 1.060 0E-95 | |
MPA | 1.370 0E-32 | 1.320 0E-19 | 8.890 0E-21 | 3.090 0E-20 | 0.761 9 | 2.780 0E-23 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.457 0 | 0.000 0E-00 | |
SMA | 0.000 0E-00 | 2.640 0E-301 | 8.820 0E-303 | 0.000 0E-00 | 2.243 6 | 0.000 0E-00 | |
HBO | 2.230 0E+43 | 7.020 0E+69 | 2.760 0E+68 | 1.290 0E+69 | 0.3523 | 1.340 0E+51 | |
F10 | HHO | 1.040 0E-10 | 6.160 0E-05 | 1.300 0E-05 | 1.660 0E-05 | 0.238 0 | 6.150 0E-06 |
EO | 7.400 0E-06 | 2.080 0E-04 | 4.310 0E-05 | 3.650 0E-05 | 0.199 2 | 3.580 0E-05 | |
MPA | 6.570 0E-08 | 1.060 0E-02 | 9.600 0E-04 | 2.390 0E-03 | 0.367 7 | 1.740 0E-07 | |
PO | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.000 0E-00 | 0.240 4 | 0.000 0E-00 | |
SMA | 3.840 0E-07 | 6.440 0E-03 | 1.540 0E-03 | 1.610 0E-03 | 2.116 1 | 1.180 0E-03 | |
HBO | 1.570 0E-11 | 2.000 0E-08 | 1.440 0E-09 | 3.760 0E-09 | 0.1768 | 3.400 0E-10 |
算法 | 变量 | 挠度/cm | |||
---|---|---|---|---|---|
b | h | tw | tf | ||
HHO | 50 | 80 | 1.612 803 | 2.996 991 | 0.009 480 |
EO | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 349 |
MPA | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 349 |
PO | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 348 |
SMA | 50 | 80 | 1.608 409 | 3.259 853 | 0.009 349 |
HBO | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 349 |
Tab. 6 Comparison of best results of I-beam design
算法 | 变量 | 挠度/cm | |||
---|---|---|---|---|---|
b | h | tw | tf | ||
HHO | 50 | 80 | 1.612 803 | 2.996 991 | 0.009 480 |
EO | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 349 |
MPA | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 349 |
PO | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 348 |
SMA | 50 | 80 | 1.608 409 | 3.259 853 | 0.009 349 |
HBO | 50 | 80 | 1.608 409 | 3.259 855 | 0.009 349 |
算法 | 最优值 | 最差值 | 均值 | 标准差 | 寻优时间/s |
---|---|---|---|---|---|
HHO | 0.009 480 | 0.010 704 | 0.009 851 | 2.50E-04 | 0.528 0 |
EO | 0.009 349 | 0.009 349 | 0.009 349 | 7.15E-13 | 0.309 2 |
MPA | 0.009 349 | 0.009 349 | 0.009 349 | 2.93E-15 | 0.535 3 |
PO | 0.009 348 | 0.024 567 | 0.010 957 | 3.92E-03 | 0.290 5 |
SMA | 0.009 349 | 0.009 349 | 0.009 349 | 6.51E-09 | 0.539 4 |
HBO | 0.009 349 | 0.024 204 | 0.013 310 | 6.68E-03 | 0.246 7 |
Tab. 7 Comparison of the statistical results of I-beam design
算法 | 最优值 | 最差值 | 均值 | 标准差 | 寻优时间/s |
---|---|---|---|---|---|
HHO | 0.009 480 | 0.010 704 | 0.009 851 | 2.50E-04 | 0.528 0 |
EO | 0.009 349 | 0.009 349 | 0.009 349 | 7.15E-13 | 0.309 2 |
MPA | 0.009 349 | 0.009 349 | 0.009 349 | 2.93E-15 | 0.535 3 |
PO | 0.009 348 | 0.024 567 | 0.010 957 | 3.92E-03 | 0.290 5 |
SMA | 0.009 349 | 0.009 349 | 0.009 349 | 6.51E-09 | 0.539 4 |
HBO | 0.009 349 | 0.024 204 | 0.013 310 | 6.68E-03 | 0.246 7 |
算法 | 变量 | 横截面积/cm2 | |
---|---|---|---|
A1 | A2 | ||
HHO | 0.777 64 | 0.440 38 | 263.895 9 |
EO | 0.788 57 | 0.408 54 | 263.895 8 |
MPA | 0.777 64 | 0.440 38 | 263.895 8 |
PO | 0.806 61 | 0.389 04 | 264.244 9 |
SMA | 0.832 04 | 0.328 08 | 265.153 7 |
HBO | 0.788 67 | 0.408 25 | 263.895 9 |
Tab. 8 Comparison of best results of three-bar truss design
算法 | 变量 | 横截面积/cm2 | |
---|---|---|---|
A1 | A2 | ||
HHO | 0.777 64 | 0.440 38 | 263.895 9 |
EO | 0.788 57 | 0.408 54 | 263.895 8 |
MPA | 0.777 64 | 0.440 38 | 263.895 8 |
PO | 0.806 61 | 0.389 04 | 264.244 9 |
SMA | 0.832 04 | 0.328 08 | 265.153 7 |
HBO | 0.788 67 | 0.408 25 | 263.895 9 |
算法 | 最佳值 | 最差值 | 均值 | 标准差 | 寻优时间/s |
---|---|---|---|---|---|
HHO | 263.895 9 | 264.227 6 | 263.995 4 | 0.105 58 | 0.492 8 |
EO | 263.895 8 | 263.897 0 | 263.896 0 | 0.000 29 | 0.290 9 |
MPA | 263.895 8 | 263.919 0 | 263.897 4 | 0.004 31 | 0.501 3 |
PO | 264.244 9 | 270.708 9 | 268.765 3 | 2.053 70 | 0.272 6 |
SMA | 265.153 7 | 272.717 6 | 270.360 4 | 1.834 30 | 0.463 1 |
HBO | 263.895 9 | 263.905 8 | 263.897 5 | 0.002 18 | 0.228 0 |
Tab. 9 Comparison of the statistical results of three-bar truss design
算法 | 最佳值 | 最差值 | 均值 | 标准差 | 寻优时间/s |
---|---|---|---|---|---|
HHO | 263.895 9 | 264.227 6 | 263.995 4 | 0.105 58 | 0.492 8 |
EO | 263.895 8 | 263.897 0 | 263.896 0 | 0.000 29 | 0.290 9 |
MPA | 263.895 8 | 263.919 0 | 263.897 4 | 0.004 31 | 0.501 3 |
PO | 264.244 9 | 270.708 9 | 268.765 3 | 2.053 70 | 0.272 6 |
SMA | 265.153 7 | 272.717 6 | 270.360 4 | 1.834 30 | 0.463 1 |
HBO | 263.895 9 | 263.905 8 | 263.897 5 | 0.002 18 | 0.228 0 |
算法 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | 质量/kg |
---|---|---|---|---|---|---|---|---|
HHO | 3.510 9 | 0.700 0 | 17.705 | 7.628 6 | 7.800 2 | 3.460 3 | 5.245 3 | 3 000.133 |
EO | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
MPA | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
PO | 3.600 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
SMA | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
HBO | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
Tab. 10 Comparison of best results of speed reducer design
算法 | x1 | x2 | x3 | x4 | x5 | x6 | x7 | 质量/kg |
---|---|---|---|---|---|---|---|---|
HHO | 3.510 9 | 0.700 0 | 17.705 | 7.628 6 | 7.800 2 | 3.460 3 | 5.245 3 | 3 000.133 |
EO | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
MPA | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
PO | 3.600 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
SMA | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
HBO | 3.500 0 | 0.700 0 | 17.000 | 7.300 0 | 7.800 0 | 3.458 4 | 5.245 9 | 2 999.037 |
算法 | 最优值 | 最差值 | 均值 | 标准差 | 寻优时间/s |
---|---|---|---|---|---|
HHO | 3 000.133 | 4 130.480 | 3 307.517 | 3.19E+02 | 1.262 2 |
EO | 2 999.037 | 2 999.037 | 2 999.037 | 1.34E-12 | 0.361 0 |
MPA | 2 999.037 | 2 999.037 | 2 999.037 | 1.90E-05 | 1.302 9 |
PO | 2 999.037 | 3 038.268 | 3 023.883 | 1.92E+01 | 0.351 7 |
SMA | 2 999.037 | 2 999.040 | 2 999.038 | 7.98E-04 | 0.677 4 |
HBO | 2 999.037 | 2 999.037 | 2 999.037 | 1.39E-12 | 0.291 7 |
Tab. 11 Comparison of the statistical results of speed reducer design
算法 | 最优值 | 最差值 | 均值 | 标准差 | 寻优时间/s |
---|---|---|---|---|---|
HHO | 3 000.133 | 4 130.480 | 3 307.517 | 3.19E+02 | 1.262 2 |
EO | 2 999.037 | 2 999.037 | 2 999.037 | 1.34E-12 | 0.361 0 |
MPA | 2 999.037 | 2 999.037 | 2 999.037 | 1.90E-05 | 1.302 9 |
PO | 2 999.037 | 3 038.268 | 3 023.883 | 1.92E+01 | 0.351 7 |
SMA | 2 999.037 | 2 999.040 | 2 999.038 | 7.98E-04 | 0.677 4 |
HBO | 2 999.037 | 2 999.037 | 2 999.037 | 1.39E-12 | 0.291 7 |
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