IEEE Computational Intelligence Magazine - May 2022 - 76
is set to 5. All algorithms are stopped
until the algorithms converge. For
EMTAUC, the interval d of the dynamic
adjustment strategy is chosen from
{5:5:40} with the best performance. All
other parameters of the comparison algorithm
are tuned for the current problems.
Five-fold cross-validation is executed on
training sets to decide the learning rate
l 2 :12 10
d -6
penalty parameter md -6
@ for online algorithms and
@ for all
2 :110
algorithms. For OAMseq, OAMinf, and
OAMgra, the buffer sizes are fixed to be
100, as suggested in [21]. For ETriCM
and MKnEA-AUC, the population size
is set to 100. CHIM-based sorting and
EAE-selection strategy are employed to
choose individuals in ETriCM [16].
B. Results and Discussion
This section first studies the effectiveness
of the EMTAUC framework compared
with the single task framework. The
results are reported in Table III. The
symbols " − " , " ≈ " and " + " imply that the
corresponding compared method is significantly
worse, similar, and better than
the Single-task GA or CMAES on the
Wilcoxon rank-sum test with a 95%
confidence level, respectively. On each of
the 15 real-world datasets, the AUC of
EMTAUC matches or exceeds that of the
single-task method in all cases. EMTAUCSBGA
outperforms the single task in 13
of 14 cases and matches the single task on
the fourclass dataset. EMTAUC-MFEAII
and EMTAUC-EMEA are superior to
Single-task GA in all cases. Compared to
CMAES, EMTAUC-CMAES performs
better on 12 and ties 3 out of 15 cases in
terms of the AUC. In EMTAUC, practical
knowledge is transferred between
the cheap task and the expensive task to
improve the performance of the AUC
optimization problem. Since EMTAUC
has the same basic evolutionary solver
of the inexpensive task and expensive
task as the single-task method, the
-1.5
-2
-2.5
-2
02468 10
Costs
(a)
-0.8
-0.72
-1.6
-1.4
-1.2
-1
02468 10
Costs
(c)
EMTAUC-MFEAII
× 104
EMTAUC-SBGA
-0.73
-0.74
-0.75
02468 10
× 104
Costs
(d)
EMTAUC-EMEA
Single-Task GA
FIGURE 4 The convergence curve of EMTAUC-MFEAII, EMTAUC-SBGA, EMTAUC-EMEA, and Single-task GA on four representative datasets,
(a) usps, (b) a9a, (c) ijcnn1, and (d) poker.
× 104
0246 810
× 104
Costs
(b)
-1.8
-1.6
-1.4
-1.2
76 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2022
log (Averaged Objective Value)
log (Averaged Objective Value)
log (Averaged Objective Value)
log (Averaged Objective Value)
IEEE Computational Intelligence Magazine - May 2022
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