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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (7): 1346-1356    DOI: 10.3785/j.issn.1008-973X.2024.07.004
    
Elite coevolutionary mayfly algorithm
Huiling WU(),Sheng LIU*()
School of Management, Shanghai University of Engineering Science, Shanghai 201620, China
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Abstract  

An elite coevolutionary mayfly algorithm (ECMA) was proposed to resolve the small population diversity and the poor optimization performance of the mayfly algorithm. Firstly, male mayflies were divided into elite and ordinary members based on their fitness performance, then the elite individuals learned from itself to maintain the population diversity and achieve high-level global search, while the ordinary individuals flew toward a unified target for local development to improve the convergence speed of ECMA. Secondly, the position update of female mayflies was improved based on the marriage market theory, thus enhancing the optimization performance of ECMA. Thirdly, a new adaptive gravity coefficient was introduced to establish a balance between the global search and the local development to improve the convergence accuracy of ECMA. Finally, a jump-out strategy of Levy flight was introduced to avoid ECMA falling into a local optimum. Based on 20 benchmark test functions and CEC2019 test functions, the simulation optimization analysis of the algorithm was carried out. Compared with the mayfly algorithm and other excellent swarm intelligence algorithms, ECMA has greatly improved the optimization accuracy, convergence speed and stability.

Key words： mayfly algorithm      elite strategy      coevolution      Levy flight      marriage market theory     
Received: 01 June 2023      Published: 01 July 2024
CLC:  TP 301.6  
Fund:  国家自然科学基金资助项目（61673258，61075115）；上海市自然科学基金资助项目（19ZR1421600）.
Corresponding Authors: Sheng LIU     E-mail: 1156250694@qq.com;ls6601@163.com
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Huiling WU
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Cite this article:

Huiling WU,Sheng LIU. Elite coevolutionary mayfly algorithm. Journal of ZheJiang University (Engineering Science), 2024, 58(7): 1346-1356.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.07.004     OR     https://www.zjujournals.com/eng/Y2024/V58/I7/1346


精英协同进化的蜉蝣算法

蜉蝣算法的种群多样性低、寻优性能差，为此提出基于精英协同进化的蜉蝣算法（ECMA）. 将雄性蜉蝣种群根据自身种群适应度分为精英种群和普通种群，精英个体进行自我学习以保持种群的多样性，实现高水平的全局搜索；普通个体飞向统一目标进行局部开发，以提高ECMA的收敛速度. 根据婚姻市场理论改进雌性蜉蝣的位置更新，提高ECMA的寻优性能；引入新的自适应重力系数平衡全局搜索和局部开发能力，提高ECMA的收敛精度；引入莱维飞行的跳出策略，避免ECMA陷入局部最优. 基于20个基准测试函数和CEC2019测试函数进行算法的仿真优化分析，与蜉蝣算法以及其他优秀的群智能算法相比，ECMA在寻优精度、收敛速度和稳定性方面均有较大提升.


关键词： 蜉蝣算法,  精英策略,  协同进化,  莱维飞行,  婚姻市场理论 
Fig.1 Gravity coefficient curve of elite coevolutionary mayfly algorithm
Fig.2 Flow chart of elite coevolutionary mayfly algorithm
类型编号名称维度取值范围最优值
单峰函数F1sphere30[?100,100]0
F2Schwefel’s problem 2.2230[10,10]0
F3Schwefel’s problem 1.230[?100,100]0
F4Schwefel’s problem 2.2130[?100,100]0
F5generalized Rosenbrock’s function30[?30,30]0
F6Step function30[?100,100]0
F7Quartic function30[?1.28,1.28]0
多峰函数F8generalized Schwefel’s problem 2.2630[?500,500]?418.9829d
F9generalized Rastrigin’s function30[?5.12,5.12]0
F10Ackley’s function30[?32,32]0
F11generalized Griewank function30[?600,600]0
F12generalized penalized function30[?50,50]0
F13generalized penalized function30[?50,50]0
F14Shekel’s foxholes function2[?65,65]1
F15Kowalik’s function4[–5,5]0.00030
F16six-hump camel-back function2[?5,5]?1.0316
F17Branin function2[?5,5]0.398
F18Goldstein-Price function2[?2,2]3
F19Hartman’s function3[1,3]?3.86
F20Shekel’s family4[0,10]?10.1532
Tab.1 Benchmark function
Fig.3 Performance presentation of different parameter combinations
Fig.4 Mean ranking of mayfly algorithms with different improvement in benchmark test function
算法函数avgstd函数avgstd函数avgstd函数avgstd
ECMAF100F200F300F400
MA7.02×10?192.33×10?181.24×10?92.41×10?92.49×10?62.56×10?65.21×10?11.89×10?1
WOA8.76×10?1484.79×10?1472.97×10?1041.07×10?1032.27×1041.01×1043.69×1012.94×101
GWO1.53×10?585.75×10?581.32×10?341.69×10?342.34×10?141.13×10?131.29×10?141.88×10?14
PSO1.18×10?85.87×10?89.27×10?21.41×10?14.97×1012.47×1025.92×10?13.59×10?1
SCA1.48×10?23.46×10?21.78×10?53.54×10?53.77×1032.98×1031.91×1011.19×101
ECMAF52.70×1018.15×10?1F62.00×10?12.19×10?1F74.55×10?53.63×10?5F8?9.30×1035.33×102
MA2.92×1012.15×1013.26×10?198.91×10?191.26×10?24.86×10?3?9.55×1035.45×102
WOA2.72×1015.32×10?18.79×10?21.08×10?12.34×10?32.79×10?3?1.15×1041.46×103
GWO2.70×1018.14×10?17.25×10?14.22×10?18.04×10?44.37×10?4?5.89×1039.99×102
PSO4.55×1013.99×1017.95×10?73.62×10?61.86×10?28.72×10?3?6.33×1038.90×102
SCA8.95×1021.64×1034.716.51×10?14.75×10?26.90×10?2?3.93×1032.86×102
ECMAF900F108.88×10?160F1100F127.58×10?36.35×10?3
MA8.694.321.973.77×10?11.19×10?21.06×10?24.15×10?25.84×10?2
WOA003.02×10?152.40×10?151.65×10?39.03×10?38.25×10?31.16×10?2
GWO5.46×10?11.821.60×10?143.22×10?153.50×10?36.81×10?33.95×10?22.44×10?2
PSO5.38×1011.48×1011.258.51×10?14.37×10?23.78×10?21.56×10?12.53×10?1
SCA1.56×1012.12×1011.24×1019.592.32×10?12.23×10?13.555.65
ECMAF132.152.80×10?1F149.98×10?15.39×10?10F153.16×10?43.84×10?5F16?1.036.45×10?16
MA2.54×10?25.74×10?29.98×10?14.12×10?179.76×10?43.66×10?3?1.036.58×10?16
WOA2.11×10?11.64×10?11.821.896.26×10?43.07×10?4?1.036.29×10?11
GWO4.93×10?11.77×10?14.914.573.06×10?36.91×10?3?1.035.61×10?9
PSO1.22×10?13.10×10?14.633.501.07×10?33.66×10?3?1.036.78×10?16
SCA2.47×1038.76×1031.538.92×10?19.50×10?43.46×10?4?1.032.56×10?5
ECMAF173.98×10?10F183.002.03×10?3F19?3.862.68×10?15F20?3.313.63×10?2
MA3.98×10?103.001.14×10?15?3.862.71×10?15?3.295.35×10?2
WOA3.98×10?12.20×10?63.001.97×10?5?3.862.77×10?3?3.241.18×10?1
GWO3.98×10?19.06×10?73.001.23×10?5?3.862.40×10?3?3.249.24×10?2
PSO3.98×10?103.001.08×10?15?3.862.71×10?15?3.275.99×10?2
SCA3.98×10?11.31×10?33.002.62×10?5?3.851.40×10?3?3.041.02×10?1
Tab.2 Optimization results of different swarm intelligence algorithms in benchmark test functions
Fig.5 Convergence comparison effect of different algorithms in benchmark test function
函数维度avgstd
MAECMAMAECMA
F15002.41×1027.85×10?2672.87×1010
F110007.95×1031.20×10?2489.83×1020
F25009.36×1011.17×10?1748.150
F21000NaN3.80×10?136NaN2.08×10?135
F45002.96×1011.11×10?1422.276.08×10?142
F410003.36×1015.351.721.25×101
F55002.69×1044.98×1023.34×1033.16×10?1
F510006.66×1059.98×1027.57×1043.08×10?1
F75001.25×1021.13×10?41.87×1011.22×10?4
F710001.21×1028.66×10?51.30×1018.15×10?5
F95004.88×1021.653.32×1013.05
F910002.05×1033.631.47×1024.66
F105001.06×1012.19×10?153.45×10?11.74×10?15
F1010001.19×1013.49×10?153.23×10?11.60×10?15
F115002.31×1021.04×10?13.88×1013.23×10?1
F1110008.25×1023.931.48×1024.96
F125002.73×1018.25×10?13.648.02×10?2
F1210002.71×1018.30×10?14.727.58×10?2
Tab.3 Comparison results of two mayfly algorithms in high-dimension benchmark test functions
算法函数avgstd函数avgstd
ECMAF215.11×1046.92×103F221.72×1016.60×10-2
MA2.32×10103.95×10102.08×1011.10×101
WOA5.74×10104.70×10101.74×1016.19×10?3
GWO1.07×1081.51×1081.73×1011.40×10?4
PSO8.04×10128.20×10111.23×1043.02×103
SCA4.61×1094.22×1091.75×1014.61×10?2
ECMAF231.27×1011.22×10-10F242.33×1021.01×102
MA1.27×1013.61×10-153.06×1021.19×102
WOA1.27×1017.43×10?75.89×1022.83×102
GWO1.27×1011.79×10?65.40×1012.22×101
PSO1.27×10102.33×1011.04×101
SCA1.27×1018.14×10?51.98×1039.63×102
ECMAF251.664.35×10?1F268.061.56
MA1.694.44×10?18.712.40
WOA1.762.43×10-19.641.15
GWO2.391.97×10?11.16×1012.40×10?1
PSO1.481.59×10?19.989.32×10?1
SCA2.341.87×10?11.11×1017.51×10?1
ECMAF272.40×1021.10×102F284.776.09×10?1
MA2.63×1021.53×1024.828.00×10?1
WOA8.06×1022.53×1025.934.82×10-1
GWO3.53×1022.29×1026.184.47×10-1
PSO5.03×1023.33×1025.231.05
SCA8.50×1022.24×1025.028.29×10-1
ECMAF294.045.49×10?1F301.96×1012.59
MA2.402.30×10?11.98×1012.62
WOA4.839.21×10?12.03×1011.02×10?1
GWO1.12×1029.35×1012.05×1014.52×10?2
PSO4.407.46×10?12.04×1012.02×10?1
SCA2.393.16×10?22.05×1015.89×10?2
Tab.4 Optimization results of different swarm intelligence algorithms in CEC2019 function
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