IEEE Computational Intelligence Magazine - May 2022 - 75

the single-task genetic algorithm (Singletask
GA) and CMAES [48], are also
selected, which can independently optimize
the expensive task. The performances
of the compared methods are
evaluated by five trials of 5-fold crossvalidation,
where the AUC values are
obtained by averaging over these 50
runs, as summarized in Tables V, VI,
and VII. Wins, ties, and losses of
EMTAUC with respect to all other
methods are reported in the last row of
Tables VI and VII. If the evaluation of an
algorithm cannot be obtained on each
dataset, its results are set to " − " . All
experimental studies are performed on a
Linux PC with Intel Core i7-10700K
CPU at 3.80 GHz and 32 GB RAM.
3) Parameter Settings: All the above
genetic operator-based algorithms
(ETriCM [16], MKnEA-AUC [20],
MFEAII, EMEA, SBGA, and Single-task
GA) employ the same SBX crossover
and PM mutation for a fair comparison,
where the distribution indexes of SBX
and PM are set to 15 and 15, respectively.
The probabilities of SBX and PM are
set to 1.0 and 1/d, respectively. Then the
population size of each task in EMEA,
SBGA, Single-task GA, SBCMAES, and
CMAES is set to 10, and the population
size in MFEAII is set to 20. For SBGA,
beneficial factor B and harmful factor H
are set to 0.25 and 0.5, respectively. For
EMEA, the interval of individual transfer
G and the number of transferred
individuals S are set to 5 and 2, respectively.
For MFEAII, the probability
model is configured as a variablewise
(marginal) normal distribution. To demonstrate
the effectiveness of the proposed
EMTAUC compared with the
single-task method,
d 30 ,=
m = -2 3
,
and the sample ratio s is set to 10%. The
maximum computational cost is set to
101000. The computational cost of a
function evaluation of the cheap task is
considered as 1, and that of a function
evaluation of the expensive task is regarded
as 1/s2, where s is the sampling rate.
Moreover, to compare with the MOEAs
and online learning methods, the population
size of each task in EMTAUC is
set to 100, the ratio s is set to 10%, and
the number of transferred individuals S
MAY 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 75
TABLE III The comparison of EMTAUC against single task methods in terms of AUC.
DATASET
diabetes
EMTAUC-MFEAII
8.26E−01(3.34E−03)+
fourclass
german_scale
splice
usps
australian
a9a
sonar
svmguide1
svmguide3
segment
ijcnn1
satimage
vowel
poker
w/t/l to single
8.34E−01(4.73E−04)+
7.84E−01(1.76E−03)+
8.19E−01(3.08E−03)+
9.50E−01(1.53E−03)+
9.22E−01(2.60E−03)+
8.90E−01(9.87E−04)+
8.44E−01(8.33E−03)+
9.82E−01(4.41E−03)+
7.42E−01(9.48E−03)+
9.70E−01(2.77E−03)+
8.30E−01(9.62E−03)+
9.97E−01(8.26E−04)+
7.99E−01(3.65E−03)+
5.21E−01(1.01E−03)+
15/0/0
EMTAUC-SBGA
8.21E−01(3.87E−03)+
8.29E−01(2.84E−03) .
7.71E−01(4.14E−03)+
7.87E−01(8.48E−03)+
9.37E−01(1.32E−03)+
9.23E−01(1.82E−03)+
8.79E−01(1.68E−03)+
8.40E−01(7.13E−03)+
9.83E−01(4.78E−03)+
7.31E−01(1.12E−02)+
9.66E−01(4.76E−03)+
7.75E−01(1.00E−02)+
9.97E−01(8.28E−04)+
8.01E−01(5.04E−03)+
5.11E−01(3.03E−03)+
14/1/0
EMTAUC-EMEA
SINGLE-TASK GA
8.17E−01(5.50E−03)+
8.30E−01(1.09E−03)+
7.72E−01(6.05E−03)+
7.82E−01(6.92E−03)+
9.31E−01(3.01E−03)+
9.21E−01(1.68E−03)+
8.72E−01(1.25E−03)+
8.39E−01(1.43E−02)+
9.81E−01(3.65E−03)+
7.27E−01(7.76E−03)+
9.58E−01(5.90E−03)+
7.80E−01(8.59E−03)+
9.97E−01(6.23E−04)+
8.01E−01(6.33E−03)+
5.11E−01(2.28E−03)+
15/0/0
8.08E−01(9.06E−03)
8.29E−01(4.65E−03)
7.61E−01(2.73E−03)
7.78E−01(7.45E−03)
9.29E−01(5.54E−03)
9.19E−01(1.02E−03)
8.69E−01(6.24E−03)
8.29E−01(1.09E−02)
9.77E−01(7.24E−03)
7.15E−01(4.64E−03)
9.54E−01(3.66E−03)
7.41E−01(2.48E−03)
9.96E−01(6.18E−04)
7.87E−01(7.38E−03)
5.09E−01(2.87E−03)
−
EMTAUC-SBCMAES
8.35E−01(8.00E−04)+
8.34E−01(8.90E−03)+
7.92E−01(3.30E−03)+
7.91E−01(2.76E−02)+
5.29E−01(8.00E−03)+
9.24E−01(2.80E−03) .
8.35E−01(6.12E−02)+
8.19E−01(2.40E−02)+
9.89E−01(1.00E−04) .
7.83E−01(3.40E−03)+
9.85E−01(2.00E−03) .
8.85E−01(8.90E−03)+
9.99E−01(8.00E−04)+
8.00E−01(3.50E−03)+
5.16E−01(4.00E−04)+
12/3/0
CMAES
8.27E−01(5.00E−04)
8.28E−01(3.07E−04)
7.83E−01(2.60E−03)
7.62E−01(1.41E−02)
4.86E−01(1.90E−02)
9.28E−01(1.70E−03)
5.47E−01(1.68E−02)
7.76E−01(2.35E−02)
9.89E−01(1.00E−04)
7.76E−01(4.60E−03)
9.84E−01(1.40E−03)
8.65E−01(1.86E−02)
9.98E−01(1.60E−03)
7.89E−01(4.60E−03)
5.06E−01(2.00E−04)
−
IEEE Computational Intelligence Magazine - May 2022

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