IEEE Computational Intelligence Magazine - August 2022 - 42

[29], MOEA/D-DE [30], MOEA/
DVA [5], LMEA [6], WOF-SMPSO
[7], LSMOF-NSGA-II [8], IM-MOEA
[32], LMOCSO [11], SparseEA [20],
MOEA/PSL [22], and PM-MOEA
[27]. NSGA-II and MOEA/D-DE
stand for classical MOEAs, which generate
offspring solutions by using
genetic operators and differential evolution,
respectively. The next six
MOEAs are state-of-the-art algorithms
for solving large-scale MOPs, where
MOEA/DVA and LMEA are based on
variable grouping, WOF-SMPSO and
LSMOF-NSGA-II are based on
dimensionality reduction, and IMMOEA
and LMOCSO are based on
novel variation operators. The last three
MOEAs are tailored for large-scale
sparse MOPs, which search for sparse
Pareto optimal solutions by using bilevel
encoding, unsupervised neural
networks, and evolutionary pattern
mining, respectively. For MOEA/DDE,
the neighborhood size is set to 10,
the probability of choosing parents
locally is set to 0.9, and the maximum
number of solutions replaced by each
offspring solution is set to 2. For
MOEA/DVA, the number of sampling
solutions in variable analysis is set to
20 and the number of selected solutions
for variable interaction analysis is
set to 5. For LMEA, the number of
selected solutions for variable clustering
is set to 2, the number of perturbations
on each solution for variable
clustering is set to 4, and the number
of selected solutions for variable interaction
analysis is set to 5. For WOFSMPSO,
the number of groups is set
to 4, the number of evaluations for the
original problem is set to 1000, the
number of evaluations for the transformed
problem is set to 500, the
number of chosen solutions for weight
optimization is set to 3, and the fraction
of evaluations for weight optimization
is set to 0.5. For LSMOFNSGA-II,
the number of reference
solutions is set to 10 and the population
size of the transformed problem is
set to 30. For IM-MOEA, the number
of reference vectors is set to 10 and
the model group size is set to 3.
42 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2022
TABLE II Detailed settings of the large-scale sparse MOPs used in experiments (Cont.)
BENCHMARK PROBLEM
TYPE OF VARIABLES
CN3
CN4
Portfolio optimization
PO1
PO2
PO3
PO4
Knapsack problem
KP1
KP2
KP3
KP4
1.http://archive.ics.uci.edu/ml
2.https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi
3.http://featureselection.asu.edu/datasets.php
4.http://www-personal.umich.edu/%7emejn/netdata/
5.http://deim.urv.cat/%7ealexandre.arenas/data/welcome.htm
6.http://vlado.fmf.uni-lj.si/pub/networks/data/default.htm
7.https://www.metatrader5.com/en
Type of variables
Binary
Type of variables
Real
NO. OF VARIABLES
1000
5000
No. of variables
100
500
1000
5000
No. of variables
100
500
1000
5000
SPARSITY OF PARETO OPTIMAL
SOLUTIONS
BA1000
BA5000
Dataset
EURCHF7
EURCHF7
EURCHF7
EURCHF7
Dataset
Synthetic [52]
Synthetic [52]
Synthetic [52]
Synthetic [52]
NO. OF OBJECTIVES
1000
5000
No. of instruments
100
500
1000
5000
No. of items
100
500
1000
5000
999
4999
Length of each instrument
50
50
50
50
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