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  • ISSN 1006-3080
  • CN 31-1691/TQ

基于空间学习和情感追踪的多模多目标群搜索算法

丁亚丹 冯翔 虞慧群

丁亚丹, 冯翔, 虞慧群. 基于空间学习和情感追踪的多模多目标群搜索算法[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20201022003
引用本文: 丁亚丹, 冯翔, 虞慧群. 基于空间学习和情感追踪的多模多目标群搜索算法[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20201022003
DING Yadan, FENG Xiang, YU Huiqun. A Spatial Learning Based SGSO with Emotional Tracking for Multimodal Multi-objective Optimization[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20201022003
Citation: DING Yadan, FENG Xiang, YU Huiqun. A Spatial Learning Based SGSO with Emotional Tracking for Multimodal Multi-objective Optimization[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20201022003

基于空间学习和情感追踪的多模多目标群搜索算法

doi: 10.14135/j.cnki.1006-3080.20201022003
基金项目: 国家自然科学基金(61772200;61772201,61602175);上海市浦江人才计划(17PJ1401900);上海市经信委“信息化发展专项资金”(201602008)
详细信息
    作者简介:

    丁亚丹(1997-),硕士生,主要研究方向为演化计算、人工智能。E-mail:dorisdingyd@126.com

    通讯作者:

    冯 翔,E-mail:xfeng@ecust.edu.cn

  • 中图分类号: TP18

A Spatial Learning Based SGSO with Emotional Tracking for Multimodal Multi-objective Optimization

  • 摘要: 为了解决多模态多目标优化问题,寻找与帕累托最优解等效的所有解,通过在基本的群搜索算法中引入社会行为,提出了一种新颖的基于空间学习机制和情感追踪行为的社会群搜索优化算法(MMO_LTSGSO)。首先,建立空间学习机制,根据学习到的个体自身位置与最佳个体位置的实时信息,对种群分布状态(离散态、聚合态)进行决策。当种群处于离散态时,采用追随和游走的方式增强算法空间探索能力;随着优化过程的进行,个体彼此影响交互,空间距离逐渐减小,此时种群逐渐聚合,采用动态步长的搜索策略更新个体位置,能实时勘探最优解周围的解,加快算法的收敛速度。其次,引入了情感因子,使一定的个体沿其偏好方向进行情感追踪移动行为,防止算法陷入停滞状态,提高算法求解精度;采用特殊的拥挤距离计算方式和引导进化策略保证算法在决策空间和目标空间的双重多样性。最后,从理论上证明了该算法的收敛性。使用15个多模态多目标优化测试基准函数验证算法的性能,并将其与现有的几个多模多目标优化算法进行性能对比,实验结果验证了本文算法能够有效求解多模多目标优化问题。

     

  • 图  1  解在决策空间和目标空间的分布

    Figure  1.  Distribution of solutions in decision space and target space

    图  2  3种搜索偏好行为

    Figure  2.  Three search preference behaviors

    图  3  情感因子追踪行为机制

    Figure  3.  Affective factor tracking behavior mechanism

    图  4  特殊的排序方式

    Figure  4.  Special sorting method

    图  5  MMO_LTSGSO在15个测试函数上的求得的PS与真实PS

    Figure  5.  The obtained PS by MMO_LTSGSO and the true PS on 15 test functions

    图  6  5个算法在15个测试函数上的Friedman排名

    Figure  6.  Friedman ranks of the optimization comprehensive performance for the five algorithms

    表  1  测试函数的多模性质

    Table  1.   Multimodal features of the test functions

    FunctionNumber of PSOverlap in every dimension
    MMF12No
    MMF22No
    MMF32Yes
    MMF44No
    MMF54No
    MMF64Yes
    MMF72No
    MMF84No
    MMF92No
    MMF102(1 Global+1 Local)No
    MMF112(1 Global+1 Local)No
    MMF128(4 Global+4 Local)Yes
    SYM-PART simple9Yes
    SYM-PART rotate9Yes
    Omni-test(n=3)27Yes
    下载: 导出CSV

    表  2  5个算法在15个多模多目标测试函数上的1/PSP值

    Table  2.   1/PSP value of five algorithms on 15 multimodal multi-objective test functions

    Test functions1/PSP(mean±std)
    MMO_LTSGSOMO_Ring_PSO_SCDDN_NSGAIIMMOEA_GDMMOPIO
    MMF10.0411±0.00130.0455±0.00190.0741±0.02000.0436±0.00280.0361±0.0018
    MMF20.0177±0.00590.0283±0.01200.0577±0.13010.011±0.00440.0267±0.0065
    MMF30.0148±0.00200.0223±0.00870.0477±0.03020.022±0.00480.0175±0.0054
    MMF40.0222±0.00220.0251±0.00200.0554±0.01810.0217±0.00110.0195±0.0027
    MMF50.0743±0.00510.0810±0.00410.1517±0.01980.0747±0.00320.0745±0.0048
    MMF60.0658±0.00380.0679±0.00430.1143±0.01700.0660±0.00230.0658±0.0060
    MMF70.0204±0.00080.0232±0.00170.0366±0.00950.0205±0.00210.0158±0.0017
    MMF80.0621±0.01250.0598±0.00470.1236±0.14150.0590±0.00610.0743±0.0112
    MMF90.0054±0.00030.0070±0.00040.0135±0.00810.0056±0.00020.0025±0.0001
    MMF100.1599±1.56100.1029±0.02070.1030±3.13310.1118±0.10201.8053±2.2440
    MMF110.1880±0.56160.1884±0.34251.4972±0.14900.1889±0.41181.6055±0.3832
    MMF120.1428±0.52340.1433±0.50500.1954±0.68920.1731±0.54971.6757±0.4923
    SYM_PART_simple0.0777±0.01400.1443±0.03711.1423±1.34140.1248±0.01480.0778±0.0073
    SYM_PART_rotated0.0947±0.01900.1560±0.04592.2009±11.4240.1351±0.01950.2210±0.3609
    Omni_test0.0870±0.02580.3086±0.07981.2623±0.36090.9491±0.01230.3950±0.0598
    下载: 导出CSV

    表  3  5个算法在15个多模多目标测试函数上的1/Hv值

    Table  3.   1/Hv value of five algorithms on 15 multimodal multi-objective test functions

    Test functions1/Hv(mean±std)
    MMO_LTSGSOMO_Ring_PSO_SCDDN_NSGAIIMMOEA_GDMMOPIO
    MMF11.1462±0.00021.1480±0.00031.1481±0.00151.1488±0.00351.1459±0.0004
    MMF21.1629±0.00361.1707±0.00971.1590±0.02731.1967±0.01901.1686±0.0030
    MMF31.1630±0.00321.1647±0.00601.1633±0.01771.1678±0.01311.1657±0.0044
    MMF41.8552±0.00121.8585±0.00191.8567±0.00071.8594±0.00811.8556±0.0012
    MMF51.1459±0.00031.1476±0.00061.1470±0.00131.1471±0.00411.1455±0.0003
    MMF61.1461±0.00041.1476±0.00121.1475±0.00081.1462±0.02191.1463±0.0005
    MMF71.1462±0.00041.1475±0.00041.1480±0.00121.1463±0.00111.1430±0.0001
    MMF82.3752±0.01132.3889±0.03612.3762±0.00322.3834±0.00612.3756±0.0019
    MMF90.1032±0.00030.1033±0.00030.1033±0.00030.1035±0.00020.1033±0.0009
    MMF100.0777±0.00070.0791±0.00060.0778±0.00300.0820±0.00340.0779±0.0009
    MMF110.0689±0.00010.0690±0.00030.0689±0.00140.0690±0.00010.0671±0.0001
    MMF120.6360±0.00020.6373±0.00110.6357±0.05620.6596±0.06650.6368±0.0003
    SYM_PART_simple0.0601±0.00070.0604±0.00060.0601±0.00010.0591±0.00940.0601±0.0001
    SYM_PART_rotated0.0601±0.00010.0605±0.00070.0601±0.00020.0699±0.00910.0602±0.0002
    Omni_test0.0189±0.00020.0190±0.00010.0189±0.00080.0288±0.00080.0190±0.0004
    下载: 导出CSV

    表  4  5个优化算法在决策空间和目标空间的平均排名

    Table  4.   Average ranking of five optimization algorithms on decision space and objective space

    Algorithim1/PSP1/HvComprehensive
    MMO_LTSGSO1.871.531.7
    MO_Ring_PSO_SCD3.473.933.7
    DN_NSGAII4.472.733.6
    MMOEA_GD2.734.133.43
    MMOPIO2.472.672.57
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-10-22
  • 网络出版日期:  2021-01-07

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