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粒子群优化算法的性能分析和参数选择

王东风 孟丽

王东风, 孟丽. 粒子群优化算法的性能分析和参数选择. 自动化学报, 2016, 42(10): 1552-1561. doi: 10.16383/j.aas.2016.c150774
引用本文: 王东风, 孟丽. 粒子群优化算法的性能分析和参数选择. 自动化学报, 2016, 42(10): 1552-1561. doi: 10.16383/j.aas.2016.c150774
WANG Dong-Feng, MENG Li. Performance Analysis and Parameter Selection of PSO Algorithms. ACTA AUTOMATICA SINICA, 2016, 42(10): 1552-1561. doi: 10.16383/j.aas.2016.c150774
Citation: WANG Dong-Feng, MENG Li. Performance Analysis and Parameter Selection of PSO Algorithms. ACTA AUTOMATICA SINICA, 2016, 42(10): 1552-1561. doi: 10.16383/j.aas.2016.c150774

粒子群优化算法的性能分析和参数选择

doi: 10.16383/j.aas.2016.c150774
基金项目: 

中央高校基本科研基金 20140139

国家自然科学基金 61203041

教育部高等学校博士学科点专项科研基金 20120036120013

详细信息
    作者简介:

    王东风   博士, 华北电力大学控制与计算机工程学院教授.主要研究方向为群智能优化算法和智能控制.E-mail:wangdongfeng@ncepu.edu.cn

    通讯作者:

    孟丽  华北电力大学控制与计算机工程学院博士研究生.主要研究方向为智能优化算法及其应用.本文通信作者.E-mail:mengli2014@163.com

Performance Analysis and Parameter Selection of PSO Algorithms

Funds: 

the Fundamental Research Funds for the Central Universities 20140139

National Natural Science Foundation of China 61203041

Specialized Research Fund for the Doctoral Program of Higher Education 20120036120013

More Information
    Author Bio:

      Ph. D., professor at the School of Control and Computer Engineering, North China Electric Power University. His research interest covers swarm intelligence-based optimization and intelligent control.E-mail:

    Corresponding author: MENG Li   Ph. D. candidate at the School of Control and Computer Engineering, North China Electric Power University. Her research interest covers swarm intelligence-based optimization and its application. Corresponding author of this paper.E-mail:mengli2014@163.com
  • 摘要: 惯性权重和加速因子是影响粒子群算法优化性能的重要参数.基于常用的12个测试函数,本文通过实验研究了不同参数组合下粒子的探索能力和算法的优化性能,在此基础上推荐了一组固定的参数组合.通过惯性权重和加速因子的不同变化策略组合对算法性能影响的实验分析,推荐了一种变化的参数设置方法.基于CEC2015发布的15个基准函数进一步验证了本文推荐的参数选取方法的有效性.最后讨论了粒子群优化(Particle swarm optimization,PSO)算法在连续优化和离散优化方面的应用问题.
  • 图  1  具有不同参数的种群优化函数Sphere时粒子的Pnum

    Fig.  1  The Pnum value of function Sphere optimized by PSO with different population scale

    图  2  粒子探索能力与参数的关系

    Fig.  2  Relationship between particle exploration ability and its parameters

    图  3  算法成功率与参数的关系

    Fig.  3  Relationship between the algorithm success rate and particle parameters

    图  4  算法在12个测试函数上的性能总和

    Fig.  4  Total optimization performance on the 12 test functions

    图  5  c1所占比率对算法成功率的影响

    Fig.  5  The influence of ratio c1 on algorithm0s success rate

    图  6  变化的c1c2取值策略对算法成功率的影响

    Fig.  6  The influence of varying c1 and c2 on algorithm0s success rate

    表  1  5组参数的运行结果对比

    Table  1  Comparison of running results on 5 parameters

    函数PARAminmaxmean±stdSR
    Fun 111.47E-258.64E-226.32E-23±1.34E-221.00
    29.05E-365.64E-311.73E-32±7.16E-321.00
    31.98E-402.94E-341.31E-35±4.50E-351.00
    41.81E-572.84E-332.86E-35±2.84E-341.00
    51.63E-271.45E-232.71E-25±1.46E-241.00
    Fun 212.72E-027.29E+002.40E+00±1.43E+000.84
    23.18E-031.20E+023.75E+00±1.19E+010.76
    31.20E-038.27E+003.45E+00±1.96E+000.30
    46.03E-028.96E+004.30E+00±1.57E+000.07
    52.21E-028.45E+003.45E+00±1.40E+000.31
    Fun 316.55E-108.21E-081.38E-08±1.58E-081.00
    25.68E-141.07E-109.80E-12±1.70E-111.00
    32.98E-117.36E-098.82E-10±1.32E-091.00
    47.06E-124.01E-046.10E-06±4.09E-050.94
    51.23E-101.02E-081.63E-09±1.77E-091.00
    Fun 411.06E-141.00E+015.00E-01±2.19E+000.95
    27.73E-201.00E+011.00E-01±1.00E+000.99
    37.38E-237.89E-209.10E-21±1.60E-201.00
    48.37E-201.00E+011.00E-01±1.00E+000.98
    51.64E-151.12E-131.82E-14±1.87E-141.00
    Fun 511.14E-251.00E+042.00E+02±1.40E+030.00
    26.54E-351.82E-292.24E-31±1.82E-301.00
    31.74E-392.36E-331.04E-34±3.60E-341.00
    42.45E-546.74E-346.74E-36±6.74E-351.00
    51.44E-267.31E-245.72E-25±9.94E-250.32
    Fun 619.91E-131.39E+015.73E+00±3.06E+000.55
    29.94E-011.59E+016.61E+00±3.23E+000.43
    30.00E+001.39E+014.87E+00±2.94E+000.68
    49.94E-014.47E+019.87E+00±7.05E+000.23
    51.66E-137.95E+003.29E+00±1.84E+000.85
    Fun 711.47E-021.64E-017.49E-02±3.35E-020.83
    27.39E-031.84E-017.77E-02±3.52E-020.77
    31.47E-022.21E-017.94E-02±4.10E-020.74
    41.72E-023.05E-011.12E-01±5.99E-020.53
    51.11E-151.69E-016.15E-02±3.39E-020.86
    Fun 812.38E-131.99E+011.99E-01±1.99E+000.99
    23.55E-157.10E-153.94E-15±1.11E-151.00
    33.55E-157.10E-153.97E-15±1.16E-151.00
    43.55E-151.15E+001.15E-02±1.15E-010.97
    51.42E-146.18E-131.51E-13±1.19E-131.00
    Fun 910.00E+001.30E+036.41E+02±2.28E+020.35
    20.00E+001.42E+036.83E+02±2.86E+020.30
    31.18E+021.54E+036.41E+02±3.04E+020.44
    41.18E+001.19E+036.40E+02±2.51E+020.36
    50.00E+009.49E+024.48E+02±1.86E+020.67
    Fun 1013.55E-101.57E+001.46E-01±4.41E-010.86
    20.00E+003.07E+001.69E-01±5.28E-010.86
    30.00E+001.50E+006.00E-02±2.96E-010.96
    41.81E-133.00E+001.40E-01±4.50E-010.46
    50.00E+003.46E-023.46E-04±3.46E-030.99
    Fun 1115.76E-275.30E-215.90E-23±5.30E-221.00
    24.71E-321.90E-314.94E-32±1.53E-321.00
    34.71E-323.11E-011.55E-02±6.81E-020.95
    44.71E-323.11E-011.24E-02±6.12E-020.95
    55.16E-293.55E-245.37E-26±2.57E-251.00
    Fun 1216.86E-276.65E-222.13E-23±7.32E-231.00
    21.34E-324.65E-312.13E-32±4.68E-321.00
    31.34E-322.72E-265.45E-28±3.85E-271.00
    41.34E-324.23E-134.23E-15±4.26E-140.99
    52.78E-281.93E-232.82E-25±1.93E-241.00
    下载: 导出CSV

    表  2  本文与文献[17]参数设置的优化结果比较

    Table  2  Comparison of optimization results between the parameters set in this paper and [17]

    函数MMethodminmaxmean±stdSR
    Fun 1Ours
    [17]
    3.91E-331.42E-291.20E-30±2.51E-301.00
    5.01E-336.95E-293.09E-30±9.83E-301.00
    Fun 2Ours
    [17]
    9.79E-022.26E+001.30E+00±5.31E-011.00
    1.00E+005.72E+002.40E+00±7.33E-010.84
    Fun 3Ours
    [17]
    5.90E-132.27E-102.13E-11±3.88E-111.00
    6.03E-132.48E-102.99E-11±4.90E-111.00
    Fun 4Ours
    [17]
    5.58E-187.20E-161.60E-16±1.52E-161.00
    8.12E-182.87E-136.86E-15±4.09E-141.00
    Fun 5Ours
    [17]
    7.24E-323.86E-281.60E-29±5.49E-291.00
    2.12E-323.44E-281.65E-29±5.70E-291.00
    Fun 6Ours
    [17]
    9.94E-017.95E+003.34E+00±1.55E+000.92
    1.98E+001.09E+015.49E+00±2.36E+000.54
    Fun 7Ours
    [17]
    0.00E+001.42E-015.20E-02±2.94E-020.96
    0.00E+001.84E-017.81E-02±3.58E-020.76
    Fun 8Ours
    [17]
    3.55E-157.10E-154.68E-15±1.67E-151.00
    3.55E-152.13E-147.81E-15±3.58E-151.00
    Fun 9Ours
    [17]
    1.18E+021.04E+034.71E+02±1.99E+020.64
    1.18E+021.19E+035.48E+02±2.16E+020.42
    Fun 10Ours
    [17]
    0.00E+001.44E-026.04E-04±2.51E-030.94
    0.00E+001.15E-013.03E-03±1.64E-020.84
    Fun 11Ours
    [17]
    4.71E-322.90E-279.03E-29±4.35E-281.00
    4.71E-321.34E-283.09E-30±1.90E-291.00
    Fun 12Ours
    [17]
    1.34E-326.16E-293.88E-30±9.45E-301.00
    1.34E-321.09E-022.19E-04±1.55E-030.98
    下载: 导出CSV

    表  3  本文给出的固定参数推荐值在CEC2015基准函数F1~F15上的运行结果

    Table  3  Running results on CEC2015 Benchmark functions F1~F15 with fixed parameters

    PARA F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15
    [6] 0.02 0.02 0.30 0.24 0.45 0.24 0.95 0.08 0.90 0.56 0.90 0.92 0.04 0.12 0.40
    [7] 0.08 0.12 0.40 0.14 0.40 0.10 1.00 0.30 0.85 0.68 0.80 0.91 0.02 0.16 0.48
    Ours 0.02 0.10 0.10 0.18 0.50 0.14 1.00 0.15 0.90 0.60 0.95 0.95 0.04 0.30 0.50
    下载: 导出CSV

    表  4  本文给出的时变参数设置方式在CEC2015基准函数F1~F15上的运行结果

    Table  4  Running results on CEC2015 Benchmark functions F1~F15 with time-varying parameters

    Method F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15
    Ours 0.70 0.26 0.30 0.94 1.00 0.64 1.00 0.50 1.00 0.95 1.00 1.00 0.25 0.40 0.96
    [17] 0.16 0.14 0.01 0.82 0.85 0.25 1.00 0.22 1.00 0.85 1.00 1.00 0.20 0.40 0.90
    下载: 导出CSV
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  • 收稿日期:  2015-11-18
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