Biomedical Engineering Reference
In-Depth Information
Table 5.12
Statistical.Results.of.Binary.ε-Indicator.in.Terms.of.the.Number.of.Occurrences.
in.Three.Different.Cases.for.Unconstrained.Test.Functions.with.Real.
Number Coding
TestFunction
Case
MOGA
NPGA2
NSGA2
SPEA2
PAES
MICROGA
ZIT1.(real)
Case.I
1,669
1,411
1,543
1,314
291
1,397
Case.II
0
0
0
0
21
0
Case.III
831
1,089
957
1,186
2,188
1,103
ZIT2.(real)
Case.I
1,634
1,674
1,707
1,951
1,110
1,438
Case.II
0
0
0
0
49
0
Case.III
866
826
793
549
1,341
1,062
ZIT3.(real)
Case.I
1,245
1,340
1,237
1,273
416
1,400
Case.II
0
2
0
0
14
0
Case.III
1,255
1,158
1,263
1,227
2,070
1,100
ZIT4.(real)
Case.I
1,670
2,078
1,308
2,294
1,422
2,500
Case.II
0
0
0
0
0
0
Case.III
830
422
1,192
206
1,078
0
ZIT6.(real)
Case.I
2,496
2,492
2,487
2,491
2,440
2,500
Case.II
0
2
2
4
11
0
Case.III
4
6
11
5
49
0
Source:
. Data.from.Chan,.T..M.,.Man,.K..F.,.Kwong,.S.,.Tang,.K..S.,.A.jumping.gene.para-
digm. for. evolutionary. multiobjective. optimization,.
IEEE Transactions on
EvolutionaryComputation
,.12(2),.143-159,.2008.
Note:
. The.best.result.for.each.case.is.marked.in.bold.
results.of.the.binary.ε-indicator.in.terms.of.the.number.of.occurrences.in.
three.different.cases.for.unconstrained.test.functions.with.binary.coding,.
with. real. number. coding,. and. constrained. test. functions,. respectively..
The.three.cases.were.specified.as.follows:
Case.I:.JG.is.better.than.the.compared.algorithm.
Case.II:.JG.is.worse.than.the.compared.algorithm.
Case.III:.They.are.incomparable.
The. effectiveness. of. the. JG. against. other. MOEAs. is. summarized. in.
Tables 5.14.
and
.5.15
..
The.JG.scored.58.favorable.marks.(X).and.20.inconclu-
sive.marks.(blanks).for.the.unconstrained.test.functions..For.the.constrained.
test. functions,. the. JG. scored. 17. favorable. marks. (X). and. 13. inconclusive.
marks.(blanks).
Moreover,. the. JG. had. better. search. performance. in. the. ZIT. series. for.
unconstrained.test.functions..This.may.indicate.that.JG.is.more.suitable.for.
solving. problems. with. longer. chromosome. lengths. and. real-number. cod-
ing.. Particularly,. the. JG. had. outstanding. performance. on. ZIT4,. which. has.
many.different.local.Pareto-optimal.fronts.in.the.search.space..JG.was.able.to.
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