M-精英协同进化分子动理论优化算法

doi:10.11959/j.issn.1000-436x.2015200

摘要/Abstract

摘要：

提出了一种M-精英协同进化分子动理论优化算法(MECKMTOA,M-elite coevolutionary KMTOA)。该算法基于M个精英以尽量防止算法陷入按维早熟。测试结果表明，MECKMTOA在求解精度、算法稳定性、高维函数求解等方面均表现出避免发生错误引导，通过精英间的学习与协作提高算法的收敛精度，采用新型的波动算子良好性能。

关键词: 优化算法, 分子动理论优化算法, 函数优化, 精英策略, 协同进化

Abstract:

M-elite coevolutionary kinetic-molecular theory optimization algorithm (MECKMTOA) was proposed.MECKMTOA uses M elites to avoid misleading,improves the convergence precision by learning and collaboration among the elites,employs a new wave operator to prevent premature by dimension.The results show that MECKMTOA has good performance in precision and stability,and can solve the high-dimensional function optimization problems well.

Key words: optimization algorithm, kinetic-molecular theory optimization algorithm, function optimization, coevolution

范朝冬,章兢,易灵芝. M-精英协同进化分子动理论优化算法[J]. 通信学报, 2015, 36(7): 144-152.

Chao-dong FAN,Jing ZHANG,Ling-zhi YI. M-elite coevolutionary kinetic-molecular theory optimization algorithm[J]. Journal on Communications, 2015, 36(7): 144-152.

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参考文献 20

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M	平均值			标准差
M	F₅	F₆	F₉	F₅	F₆	F₉
3	3.778 7×10^-5	0.377 5	-1.170 7×10⁴	3.478 2×10^-5	1.176 7	6.434 0×10²
5	3.103 0×10^-5	0.165 3	-1.188 1×10⁵	2.765 7×10^-5	0.354 9	6.026 0×10²
10	4.108 8×10^-5	1.835 3	-1.166 8×10⁴	3.576 6×10^-5	11.117 6	6.469 1×10²
15	5.084 0×10^-5	1.760 0	-1.165 0×10⁴	5.105 3×10^-5	10.147 2	6.748 1×10²
20	5.322 4×10^-5	3.419 9	-1.149 0×10⁴	4.722 5×10^-5	15.570 3	7.025 3×10²
30	6.832 0×10^-5	3.545 2	-1.087 7×10⁴	6.793 3×10^-5	16.891 7	5.087 5×10²
40	9.264 3×10^-5	3.423 4	-1.088 3×10⁴	7.849 0×10^-5	16.299 9	6.268 7×10²
50	1.867 7×10^-5	5.017 7	-1.049 8×10⁴	1.874 0×10^-4	17.830 8	5.784 5×10²
70	4.982 3×10^-5	21.561 5	-1.001 4×10⁴	4.719 2×10^-4	11.072 5	4.894 7×10²
90	0.002 2	93.958 8	-9.092 9×10³	0.001 7	42.249 1	7.466 7×10²

M	平均值			标准差
M	F₅	F₆	F₉	F₅	F₆	F₉
1	4.556 5×10^-5	0.411 5	-1.162 7×10⁴	4.490 8×10^-5	1.122 1	7.112 7×10²
2	3.883 8×10^-5	0.472 0	-1.168 6×10⁴	2.661 7×10^-5	1.027 2	6.789 2×10²
3	3.778 7×10^-5	0.377 5	-1.170 7×10⁴	3.478 2×10^-5	1.176 7	6.434 0×10²
4	3.721 0×10^-5	0.301 5	-1.182 1×10⁴	4.407 2×10^-5	1.100 6	6.674 5×10²
5	3.103 0×10^-5	0.165 3	-1.188 1×10⁴	2.765 7×10^-5	0.354 9	5.868 1×10²
6	3.417 2×10^-5	0.410 2	-1.175 1×10⁴	3.105 1×10^-5	1.260 9	6.769 1×10²
7	3.717 1×10^-5	0.400 8	-1.173 7×10⁴	3.539 9×10^-5	1.003	6.052 4×10²
8	3.751 4×10^-5	0.444 0	-1.169 8×10⁴	4.550 1×10^-5	1.211 1	6.058 2×10²
9	3.868 8×10^-5	1.812 9	-1.167 0×10⁴	2.915 8×10^-5	11.183 9	6.533 2×10²
10	4.108 8×10^-5	1.835 3	-1.166 8×10⁴	3.576 6×10^-5	11.117 6	6.469 1×10²

算法	平均值			标准差
算法	F₅	F₆	F₉	F₅	F₆	F₉
MECKMTOA1	5.4133	0.225 2	-1.151 4×10^-4	6.178 8×10^-5	0.581 9	6.794 9×10^-2
MECKMTOA2	4.645 6×10^-5	0.178 3	-1.185 6×10^-4	5.854 2×10^-5	0.387 3	6.533 2×10^-2
MECKMTOA3	5.922 7×10^-5	0.478 0	-1.135 8×10^-4	4.292 9×10^-5	1.292 6	5.114 2×10^-2
MECKMTOA	3.103 0×10^-5	0.165 3	-1.188 1×10^-4	2.765 7×10^-5	0.354 9	5.868 1×10^-2

函数	算法	最小值	最大值	平均值	标准差
F₁	KMTOA	0	0	0	0
F₁	MECKMTOA	0	0	0	0
F₂	KMTOA	7.903 5×10^-6	8.056 3×10^-5	2.374 3×10^-5	1.368 5×10^-5
F₂	MECKMTOA	2.153 3×10^-13	4.829 5×10^-10	6.494 6×10^-11	1.184 5×10^-10
F₃	KMTOA	0	0	0	0
F₃	MECKMTOA	0	0	0	0
F₄	KMTOA	0	0	0	0
F₄	MECKMTOA	0	0	0	0
F₅	KMTOA	3.680 2×10^-13	3.240 1×10^-4	8.346 8×10^-5	8.244 8×10^-5
F₅	MECKMTOA	9.474 7×10^-7	1.770 7×10^-4	3.103 0×10^-5	2.765 7×10^-5
F₆	KMTOA	1.731 7×10^-6	4.323 6	0.173 6	0.669 9
F₆	MECKMTOA	5.380 5×10^-28	1.035 8	0.165 3	0.354 9
F₇	KMTOA	0	0	0	0
F₇	MECKMTOA	0	0	0	0
F₈	KMTOA	0.397 9	0.397 9	0.397 9	3.364 5×10^-16
F₈	MECKMTOA	0.397 9	0.3979	0.397 9	3.364 5×10^-16
F₉	KMTOA	-1.256 9×10⁴	-1.067 3×10⁴	-1.156 2×10⁴	4.958 7×10²
F₉	MECKMTOA	-1.256 9×10⁴	-1.043 8×10⁴	-1.188 1×10⁴	5.868 1×10²
F₁₀	KMTOA	0	0	0	0
F₁₀	MECKMTOA	0	0	0	0
F₁₁	KMTOA	0	0	0	0
F₁₁	MECKMTOA	0	0	0	0
F₁₂	KMTOA	0	0	0	0
F₁₂	MECKMTOA	0	0	0	0
F₁₃	KMTOA	0	0	0	0
F₁₃	MECKMTOA	0	0	0	0
F₁₄	KMTOA	1.944 5×10^-8	1.961 9×10^-6	4.081 8×10^-7	3.598 8×10^-7
F₁₄	MECKMTOA	1.499 8×10^-3	2.175 1×10^-1	8.616 7×10^-14	3.826 2×10^-13
F₁₅	KMTOA	-1.867 3×10²	-1.867 3×10²	-1.867 3×10²	9.205 2×10^-14
F₁₅	MECKMTOA	-1.867 3×10²	-1.867 3×10²	-1.867 3×10²	2.842 2×10^-14

函数	平均值			标准差
函数	MECKMTOA	OEA	MECKMTOA	MECA	OEA
F₁	0	4.228×10^-183	2.481×10^-30	0	0	1.128×10^-29
F₃	0	1.845×10^-110	2.068×10^-13	0	3.113×10^-110	1.440×10^-12
F₄	0	3.274×10^-95	1.883×10^-9	0	2.313×10^-94	3.726×10^-9
F₅	3.103×10^-5	4.083×10^-4	3.297×10^-3	2.766×10^-5	3.800×10^-4	1.096×10^-3
F₉	-1.188×10⁴	-1.257×10⁴	-1.257×10⁴	5.868×10²	7.350×10^-12	5.555×10^-12
F₁₀	0	0	5.430×10^-17	0	0	1.683×10^-16
F₁₂	0	0	5.336×10^-14	0	0	2.945×10^-13
F₁₃	0	3.844×10^-3	1.317×10^-2	0	7.130×10^-3	1.561×10^-2