The average performance score (APS) [52] [53], is also used as a metric to compare the performances of the algorithms. Considering the comparison ofM algorithms A1; .. . ; AM on K functions F1; ... ; FK,ifalgorithm Aj outperforms Ai on the k-th function Fk with statistical significance, dk i;j is set to be 1, otherwise 0. The performance score of algorithm Ai on function Fk P j2f1;...;Mgnfig dk is defined as: PSkðAiÞ¼ i;j. PSkðAiÞ represents the number of algorithms that outperform Ai on function Fk.The APS can TABLE IX Results on 50D test functions of CEC 2018. cDE MEAN F1 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20 F21 F22 F23 F24 F25 F26 F27 F28 F29 F30 BM y= =x 6.38e-03x 6.72e-08x 5.71e+01x 1.57e+02x 2.14e-03x 2.32e+02x 1.57e+02x 2.82e+00y 6.26e+03x 2.12e+02x 6.12e+04x 6.58e+03x 3.47e+02x 3.87e+02x 1.44e+03x 9.91e+02x 5.77e+03x 1.70e+02x 8.70e+02x 3.63e+02x 5.47e+03x 5.89e+02x 6.55e+02x 5.15e+02y 2.68e+03x 6.37e+02x 4.84e+02y 6.84e+02x 7.76e+05x 0(0) 3/0/26(3/0/21) STD 1.68e-02 1.05e-07 4.47e+01 1.39e+01 3.65e-03 1.55e+01 1.34e+01 4.09e+00 3.41e+02 6.41e+01 5.62e+04 9.15e+03 8.84e+01 2.07e+02 2.25e+02 2.16e+02 8.02e+03 4.30e+01 1.80e+02 1.44e+01 2.87e+03 1.58e+01 1.93e+01 4.30e+01 1.77e+02 6.21e+01 2.43e+01 1.67e+02 1.50e+05 MEAN 1.11e+04x 6.56e+00x 7.10e+01x 2.54e+02x 1.98e+00x 3.44e+02x 2.58e+02x 2.27e+02x 8.54e+03x 1.07e+02x 6.27e+03x 2.44e+02x 9.18e+01x 8.52e+01x 1.34e+03x 8.75e+02x 5.67e+01x 4.68e+01x 6.37e+02x 4.57e+02x 5.51e+03x 6.83e+02x 7.40e+02x 4.82e+02y 3.57e+03x 5.49e+02y 4.58e+02y 8.51e+02x 6.28e+05x 1(0) 3/0/26(3/0/21) then be computed as APSðAiÞ¼ 1 K PK sents better performance. Table XI shows the APS values obtained by cDE, CoBiDE, jSO, HSES, Q-HSES [8] (the conference version of this paper), and DQ-HSES k¼1 PSkðAiÞ. A smaller APS repreCoBiDE jSO STD 4.31e+03 2.73e+00 3.07e+01 1.38e+01 2.60e-01 1.71e+01 1.29e+01 1.01e+02 3.75e+02 7.78e+00 1.10e+03 2.00e+01 7.09e+00 8.08e+00 1.60e+02 1.14e+02 4.32e+00 4.33e+00 1.24e+02 1.30e+01 4.48e+03 1.32e+01 2.01e+01 5.91e+00 1.50e+02 1.56e+01 5.73e-02 9.93e+01 1.30e+04 MEAN 0.00e+00 0.00e+00 5.62e+01x 1.64e+01x 1.09e-06 6.64e+01x 1.69e+01x 0.00e+00y 3.13e+03x 2.79e+01x 1.68e+03x 3.05e+01y 2.49e+01x 2.38e+01x 4.50e+02y 2.82e+02y 2.42e+01x 1.41e+01x 1.40e+02x 2.19e+02x 1.48e+03 4.30e+02x 5.07e+02x 4.80e+02y 1.12e+03x 5.11e+02y 4.59e+02y 3.62e+02 6.01e+05 10(8) 7/6/16(7/4/13) STD 0.00e+00 0.00e+00 4.87e+01 3.46e+00 2.62e-06 3.47e+00 3.13e+00 0.00e+00 3.67e+02 3.32e+00 5.22e+02 2.12e+01 1.87e+00 2.48e+00 1.37e+02 8.61e+01 2.01e+00 2.26e+00 7.73e+01 3.76e+00 1.75e+03 6.23e+00 4.12e+00 2.79e+00 5.61e+01 1.10e+01 6.83e+00 1.31e+01 2.98e+04 MEAN 0.00e+00 0.00e+00 4.17e+01 7.60e-01 1.25e-06 5.51e+01 1.46e+00 1.61e+01 4.86e+02 2.25e+01 1.16e+02 4.76e+01 1.49e+01 1.76e+01 6.42e+02 5.05e+02 2.09e+01 1.02e+01 4.19e+01 2.04e+02 1.00e+02 4.23e+02 4.88e+02 5.45e+02 5.81e+02 5.69e+02 5.01e+02 5.02e+02 5.96e+05 20(16) DQ-HSES STD 0.00e+00 0.00e+00 4.95e+01 8.57e-01 2.16e-06 6.75e-01 1.11e+00 2.51e+01 4.31e+02 2.01e+00 1.25e+02 1.55e+01 9.14e+00 4.61e-01 2.60e+02 3.39e+02 1.34e-01 7.64e+00 5.44e+01 8.95e-01 1.48e-06 7.72e+00 2.85e+00 2.97e+01 1.64e+02 2.69e+01 1.36e+01 1.74e+02 1.13e+04 100 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | FEBRUARY 2023