结合黏菌觅食行为的改进多元宇宙算法

doi:10.13229/j.cnki.jdxbgxb20210649

摘要/Abstract

摘要：

为提高多元宇宙优化算法求解实际问题的能力，提出了一种黏菌觅食的多元宇宙优化算法。该算法利用黏菌觅食行为在局部最优和全局最优之间寻求最优解。通过与其他10种同类算法在12个函数上的测试比较表明：本文算法收敛速度及解的质量优于其他算法，具有更好的求解能力和优化性能，可作为问题优化的有效工具。

关键词: 计算机应用, 细菌觅食行为, 多元宇宙优化算法, 函数优化

Abstract:

In order to improve the ability of multi-verse optimization algorithm to solve practical problems, a modified multi-verse optimization algorithm with slime mould foraging is proposed. The algorithm uses slime foraging behavior to further seek optimal solutions between local optimum and global optimum. By comparing with 10 other similar algorithms tested on 12 benchmark-functions, the results show that the convergence speed and solution quality of the proposed algorithm in this paper are better than other algorithms, with better solving ability and optimization performance, and can be used as an effective tool for problem optimization.

Key words: computer applications, slime mould foraging behavior, multi-verse optimization（MVO） algorithm, function optimization

中图分类号:

TP393

任丽莉,王志军,闫冬梅. 结合黏菌觅食行为的改进多元宇宙算法[J]. 吉林大学学报(工学版), 2021, 51(6): 2190-2197.

Li-li REN,Zhi-jun WANG,Dong-mei YAN. Improved multi⁃verse algorithm with combined slime mould foraging behavior[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(6): 2190-2197.

图/表 4

表 1

基准函数描述"

函数	函数公式	参数取值	最小值
F₁	$f 1 x = ∑ i = 1 n x i 2$		0
F₂	$f 2 x = x i + ∏ i = 1 n x i$		0
F₃	$f 3 x = ∑ i = 1 n ∑ j - 1 i x j 2$		0
F₄	$f 4 x = m a x i {x i, 1 ≤ i ≤ n}$		0
F₅	$f 5 x = ∑ i = 1 n - 1 [100 (x i + 1 - x i 2) 2 + (x i - 1) 2]$		0
F₆	$f 6 x = ∑ i = 1 n x i + 0.5 2$		0
F₇	$f 7 x = ∑ i = 1 n - x i s i n \| x i \|$		-418.9829×n
F₈	$f 8 x = ∑ i = 1 n [x i 2 - 10 c o s 2 π x i + 10]$	［-5.12，5.12］	0
F₉	$f 9 x = - 20 e x p - 0.2 1 n ∑ i = 1 n x i -$ $e x p 1 n ∑ i = 1 n c o s 2 π x i + 20 + e$		0
F₁₀	$f 10 x = 14000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s x i i + 1$		0
F₁₁	$f 11 x = π n 10 s i n a y 1 +$ $∑ i = 1 n - 1 (y i - 1) 2 [1 + 10 s i n 2 (π y i + 1)] +$ $???????????????? (y n - 1) 2 + ∑ i = 1 n μ (x i, 10,100,4)$ $y i = 1 + (x i + 1) / 4$ ； $μ x i, a, k, m = k x i - a m, ?????? x i > a 0, ?????? - a < x i < a k - x i - a m, ?????? x i < - a$		0
F₁₂	$f 12 x = 0.1 s i n 2 3 π x i +$ $∑ i = 1 n x i - 1 2 1 + s i n 2 3 π x i + 1 +$ $?????????? x n - 1) 2 1 + s i n 2 2 π x n +$ $∑ i = 1 n μ (x i, 5,100,4)$		0

表 1

表2

SMVO和10个同类算法的比较结果"

函数	指标	算法
函数	指标	SMVO	MVO	ACOR	BA	DE	FA	MFO	PSO	SCA	SSA	FOA
F₁	AVG	0.0000E+00	3.8821E-01	8.3333E+03	9.6820E-01	3.5921E-38	8.9258E+04	1.7885E+04	1.0215E+03	9.2607E+01	7.1331E-08	8.3400E-09
F₁	STD	0.0000E+00	5.7880E-02	7.4664E+03	5.6898E-01	2.3499E-38	4.2672E+03	1.6008E+04	5.5314E+01	2.0806E+02	8.6630E-09	2.4030E-11
F₂	AVG	0.0000E+00	6.8669E+03	9.6333E+01	9.4976E+13	3.0648E-24	1.3083E+16	1.4633E+02	3.7238E+25	1.0159E-10	6.5869E+00	9.1360E-04
F₂	STD	0.0000E+00	3.5845E+04	2.4280E+01	3.7080E+14	1.3807E-24	3.4100E+16	5.1427E+01	2.0365E+26	3.4747E-10	3.4193E+00	1.3357E-06
F₃	AVG	0.0000E+00	2.6883E+03	1.4986E+05	1.7049E+01	2.9061E+05	2.3464E+05	1.3382E+05	1.0788E+04	9.5811E+04	1.9569E+03	2.8263E-05
F₃	STD	0.0000E+00	4.0873E+02	2.8063E+04	2.2746E+01	1.8556E+04	1.9245E+04	6.3781E+04	1.7024E+03	2.6538E+04	8.4069E+02	6.8662E-08
F₄	AVG	0.0000E+00	1.2104E+01	9.6771E+01	3.3869E+01	5.5452E+00	9.2689E+01	9.3025E+01	9.9060E+00	6.9119E+01	2.2962E+01	9.1370E-06
F₄	STD	0.0000E+00	4.5201E+00	1.4074E+00	9.0360E+00	6.6624E-01	3.8012E+00	2.3997E+00	1.1529E+00	4.3507E+00	3.4007E+00	1.3417E-08
F₅	AVG	1.5835E-02	4.9426E+02	1.3349E+07	2.8592E+02	1.0187E+02	1.7606E+08	2.9936E+07	3.1949E+06	3.2992E+06	1.6356E+02	9.8000E+01
F₅	STD	3.7012E-02	6.9841E+02	3.6869E+07	3.5499E+02	1.9726E+01	1.5717E+07	5.3247E+07	3.7002E+05	4.5742E+06	8.3286E+01	9.0545E-05
F₆	AVG	9.0036E-04	3.9619E-01	1.0350E+04	1.1715E+00	0.0000E+00	8.9748E+04	1.8681E+04	1.0071E+03	2.4174E+02	6.9710E-08	2.5001E+01
F₆	STD	1.6295E-03	6.2888E-02	1.0695E+04	7.2217E-01	0.0000E+00	4.6417E+03	1.4721E+04	6.6866E+01	5.5760E+02	6.6761E-09	1.6127E-06
F₇	AVG	-4.1898 E+04	-2.6001 E+04	-2.7968 E+04	-2.3691 E+04	-3.0562 E+04	-7.4199 E+03	-2.4779 E+04	-2.1629 E+04	-8.2331 E+03	-2.5007 E+04	-3.8652 E+02
F₇	STD	2.2476E-03	1.1331E+03	9.8801E+02	1.3029E+03	3.4339E+03	3.3381E+02	3.2373E+03	2.6617E+03	5.2180E+02	1.4100E+03	1.0746E+02
F₈	AVG	0.0000E+00	5.5830E+02	8.1668E+02	1.1135E+03	4.5580E+02	1.1000E+03	6.1028E+02	1.5153E+03	1.1892E+02	1.9594E+02	1.6559E-06
F₈	STD	0.0000E+00	7.9842E+01	2.6996E+02	8.4706E+01	1.5662E+01	2.6471E+01	9.1932E+01	6.0336E+01	7.1792E+01	4.2158E+01	5.8328E-09
F₉	AVG	8.8818E-16	5.8807E+00	2.0469E+01	4.4138E+00	2.7060E-14	1.8817E+01	1.9839E+01	1.1143E+01	1.8607E+01	3.6859E+00	3.6561E-05
F₉	STD	0.0000E+00	7.6754E+00	3.4023E-01	4.2681E+00	2.7174E-15	1.3307E-01	2.6975E-01	1.9434E-01	5.9012E+00	7.5550E-01	5.4312E-08
F₁₀	AVG	0.0000E+00	4.3777E-01	1.0842E+02	1.8523E+01	0.0000E+00	8.0778E+02	1.5486E+02	1.2549E+00	2.3668E+00	2.6268E-03	2.1868E-10
F₁₀	STD	0.0000E+00	5.6867E-02	1.1457E+02	2.2898E+01	0.0000E+00	4.3289E+01	1.2573E+02	1.6028E-02	5.9518E+00	5.6705E-03	6.5896E-13
F₁₁	AVG	9.5530E-07	4.2929E+00	3.4150E+07	1.4669E+01	4.7116E-33	2.4717E+08	8.6413E+07	1.9446E+01	6.7238E+06	1.0379E+01	1.3254E+00
F₁₁	STD	1.4455E-06	1.2730E+00	8.8505E+07	3.3454E+00	1.3918E-48	3.6377E+07	1.3942E+08	6.6756E+00	1.0208E+07	2.4541E+00	4.7128E-08

表2

图1

图2

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