结合黏菌觅食行为的改进多元宇宙算法

doi:10.13229/j.cnki.jdxbgxb20210649

Abstract

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

CLC Number:

TP393

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.

Figures/Tables 4

Table 1

Description of the benchmark functions"

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

Table 1

Table 2

Comparison results of SMVO and 10 similar algorithms"

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

Table 2

Fig.1

Fig.2

References 27

1	王伟, 何东之. 基于非线性和遗传变异的灰狼优化算法[J]. 合肥工业大学学报: 自然科学版, 2021, 44(2): 199-205.
	Wang Wei, He Dong-zhi. Gray wolf optimization algorithm based on nonlinearity and genetic variation[J]. Journal of Hefei University of Technology (Natural Science Edition), 2021, 44(2): 199-205.
2	Socha K, Dorigo M. Ant colony optimization for continuous domains[J]. European Journal of Operational Research, 2008, 185(3): 1155-1173.
3	Yang X S. A new metaheuristic bat-inspired algorithm[C]∥Nature inspired cooperative strategies for optimization (NICSO 2010), Springer, , HeidelbergBerlin, 2010: 65-74.
4	Storn R, Price K. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4): 341-359.
5	Yang X S. Firefly algorithms for multimodal optimization[C]∥International Symposium on Stochastic Algorithms, Springer, Berlin, Heidelberg, 2009: 169-178.
6	Mirjalili S. Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm[J]. Knowledge-Based Systems, 2015, 89: 228-249.
7	Poli R, Kennedy J, Blackwell T. Particle swarm optimization[J].Swarm Intelligence, 2007, 1(1): 33-57.
8	Mirjalili S. SCA: a sine cosine algorithm for solving optimization problems[J]. Knowledge-based Systems, 2016, 96: 120-133.
9	Mirjalili S, Gandomi A H, Mirjalili S Z, et al. Salp swarm algorithm: a bio-inspired optimizer for engineering design problems[J]. Advances in Engineering Software, 2017, 114: 163-191.
10	Pan W T. A new fruit fly optimization algorithm: taking the financial distress model as an example[J]. Knowledge-Based Systems, 2012, 26: 69-74.
11	Mirjalili S, Mirjalili S M, Hatamlou A. Multi-verse optimizer: a nature-inspired algorithm for global optimization[J]. Neural Computing and Applications, 2016, 27(2): 495-513.
12	熊保玉. 基于改进多元宇宙算法的零件平面度测量研究[J]. 光电子·激光, 2021, 32(3): 251-256.
	Xiong Bao-yu. Research on part flatness measurement based on improved multiverse algorithm[J]. Journal of Optoelectronics·Laser, 2021, 32(3): 251-256.
13	Yang X H, Chen W K, Li A Y, et al. A Hybrid machine‐learning method for oil‐immersed power transformer fault diagnosis[J]. IEEJ Transactions on Electrical and Electronic Engineering, 2020, 15(4): 501-507.
14	Zhu L, Lin J, Wang Z J. A discrete oppositional multi-verse optimization algorithm for multi-skill resource constrained project scheduling problem[J]. Applied Soft Computing, 2019, 85: No.105805.
15	Yildiz A R, Mirjalili S, Sait S, et al. The Harris hawks, grasshopper and multi-verse optimization algorithms for the selection of optimal machining parameters in manufacturing operations[J]. Materials Testing, 2019, 61(8): 725-733.
16	Singh A, Suhag S. Frequency regulation in an AC microgrid interconnected with thermal system employing multiverse-optimised fractional order-PID controller[J]. International Journal of Sustainable Energy, 2020, 39(3): 250-262.
17	Lin J, Zhu L, Wang Z J. A hybrid multi-verse optimization for the fuzzy flexible job-shop scheduling problem[J]. Computers & Industrial Engineering, 2019, 127: 1089-1100.
18	Li L L, Wen S Y, Wang C S, et al. Renewable energy prediction: a novel short-term prediction model of photovoltaic output power[J]. Journal of Cleaner Production, 2019, 228: 359-375.
19	Geng K F, Ye C M, Cao L, et al. Multi-objective reentrant hybrid flowshop scheduling with machines turning on and off control strategy using improved multi-verse optimizer algorithm[J]. Mathematical Problems in Engineering, 2019, 2019: 1-18.
20	Chauhan U, Rani A, Kumar B, et al. A multi verse optimization based MPPT controller for drift avoidance in solar system[J]. Journal of Intelligent & Fuzzy Systems, 2019, 36(3): 2175-2184.
21	Buch H, Trivedi I N. On the efficiency of metaheuristics for solving the optimal power flow[J]. Neural Computing and Applications, 2019, 31(9): 5609-5627.
22	Al-qaness M A A, Elaziz M A, Ewees A A, et al. A modified adaptive neuro-fuzzy inference system using multi-verse optimizer algorithm for oil consumption forecasting[J]. Electronics, 2019, 8(10): 1071.
23	Liu Xiao-long. Application of improved multiverse algorithm to large scale optimization problems[J]. Journal of Electronics & Information Technology, 2019, 41(7): 1666-1673.
24	Ewees A A, Abd El Aziz M, Hassanien A E. Chaotic multi-verse optimizer-based feature selection[J]. Neural Computing and Applications, 2019, 31(4): 991-1006.
25	Li S M, Chen H L, Wang M J. et al. Slime mould algorithm: A new method for stochastic optimization[J]. Future Generation Computer Systems, 2020, 111: 300-323.
26	García S, Fernández A, Luengo J, et al. Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power[J]. Information Sciences, 2010, 180(10): 2044-2064.
27	Derrac J, García S, Molina D, et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms[J]. Swarm and Evolutionary Computation, 2011, 1(1): 3-18.

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Improved multi⁃verse algorithm with combined slime mould foraging behavior

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