图共 6个 表共 4
    • 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

    • 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

      表 1  测试函数的多模性质

      Table 1.  Multimodal features of the 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

      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/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

      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

    • Indicator1/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

      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