IEEE Computational Intelligence Magazine - November 2023 - 38
LGSEA demonstrates its capability to
scale up to large-scale decision
variables effectively.
suitable for LGSEA. In fact, the proposed LGSEAmay fail within
NSGA-II and MOEA/D, since Pareto-dominance shows slow
convergence to the optimal front while MOEA/D may suffer
from the fixed weight vectors on the complicated PF of GLT
test instances. Therefore, LGSEA with the optimal combination,
e.g., Operator 2 for offspring generation and S-metric method
for selection, is used in the subsequent parts.
2) Components Analysis
This experiment studies the role of the components, the mating
poolsM, in LGSEA, including the size ofMandMwith neighbors
or the global population. LGSEA with different settings ofK
(K 2f2; 4; 6; 8; 10g) is tested on the six GLT test instances. The
mean values and standard deviations ofthe IGDmetric ofthe final
populations obtained by LGSEA with different sizes of mating
pools are shown in Figure 5(a).This figure shows that the proposed
LGSEA is relatively insensitive to the settings of different
sizes of the mating pool, while LGSEA shows poor performance
with a small mating pool (K ¼ 2). The experimental results indicate
that a large size ofneighborhood mating pools is appropriate
for LGSEA, which is used in the following experiments, i.e.,
K ¼ 10.
Afterward, we further discuss the effect of neighborhood
mating in LGSEA. In several existing learning-based MOEAs,
such as the SMEA and OCEA, a mating restriction probability
(denoted as b) is adopted to balance the local and global search
with neighbors or random population solutions. The mean
and standard deviations ofthe IGD values obtained by LGSEA
with b ¼ 0:2; 0:4; 0:6; 0:8; 1:0on GLT1-GLT6 are shown in
Figure 5(b).AsseeninFigure 5(b), the mean IGD values
obtained by LGSEA for the other instances are not heavily
affected by b. Consequently, it may not be necessary to incorporate
an additional parameter in LGSEA.
TABLE III Statistical results (Mean(Std. Dev.)[rank]) obtained by AMEA, IM-MOEA, SMEA, RM-MEDA, MEA/GTM, and LGSEA over 30
independent runs on the GLT, LZ, IMF, WFG, and ZDT test suites in terms of the HV metrics.
38 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2023
IEEE Computational Intelligence Magazine - November 2023
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