Performance Measures on Jumping Gene - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 108

diverse.nondominated.solutions.for.the.test.functions.BEL.and.SRIN..Also,.the.
difference.between.its.score.and.that.of.the.winner.was.tiny.for.other.test.func-
tions..Hence,.the.JG.obtained.good.diversity.performance.based.on.these.results.

5.7.2.3 Diversity Evaluation Using Extreme
Nondominated Solution Generation

Tables 5.9. and .5.10. list.the.total.number.of.extreme.nondominated.solutions.
found.by.various.MOEAs.for.different.unconstrained.and.constrained.test.
functions,.respectively..For.each.test.function,.50.nondominated.solution.sets.
were.obtained.after.50.simulation.runs.for.each.MOEA.
Furthermore,.an.initial.value.of.a.scaling.factor.for.each.test.function.was.arbi-
trarily.chosen.as. μ = 0.01.according.to. Equations.(5.11). a nd . (5.12) .. If.no.extreme.
nondominated.solution.was.counted.in.all.the.MOEAs,.comparison.could.not.
be.made..In.this.case,.the.value.of.the.scaling.factor.was.repetitively.increased.
by.a.step.(0.01).until.at.least.one.nonzero.value.was.found.in.any.of.the.MOEAs.
From . Table 5.9, .the.results.indicated.that.the.JG.acquired.the.largest.num-
ber. of. extreme. nondominated. solutions. for. most. unconstrained. test. func-
tions..Similar.outcomes.were.observed.for.the.constrained.test.functions,.as.
shown.in . Table 5.10 .

5.7.2.4 Statistical Test Using Binary ε -Indicator

To. make. a. direct. comparison. in. the. performance. of. the. algorithms,. the.
binary. ε-indicator. was. adopted.. Tables 5.11 - 5.13 . show. the. statistical.

Table 5.9
Total.Numbers.of.Extreme.Nondominated.Solutions.for.Unconstrained.Test.Functions

Scaling
Factor TestFunction MOGA NPGA2 NSGA2 SPEA2 PAES MICROGA JG

0.01 SCH 15 43 60 62 264 0 72

0.01 FON 16 22 22 17 0 6 26

0.01 POL 32 46 82 45 106 34 93

0.01 ZIT1.(binary) 9 17 30 20 4 0 32

0.03 ZIT2.(binary) 0 0 0 0 5 0 12

0.01 ZIT3.(binary) 1 12 10 0 10 0 5

0.7 ZIT4.(binary) 59 0 0 26 0 0 81

0.01 ZIT6.(binary) 0 114 57 87 562 0 145

0.01 ZIT1.(real) 0 0 0 0 0 0 13

0.03 ZIT2.(real) 0 0 0 0 0 0 3

0.01 ZIT3.(real) 0 0 0 0 3 0 10

0.01 ZIT4.(real) 0 0 0 0 0 0 54

0.01 ZIT6.(real) 0 0 0 0 0 0 9

Note: . The.best.result.for.each.test.function.is.marked.in.bold.