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ÏÏ
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
f_1
1
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1
0.35
0
0
−1
x1
x2
x3
x4
x5
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1.2
1.2
Mean global front
1
1
0.6
0.4
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
f_1
0
1
89;:=<?>@<BA /'"CDE"$6E*GFBDE#'1.H6+IJDEK?6+I;D+6E"C.H6
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1
0.8
0.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
f_1
1
0.6
x_2
Global front
solutions
0.4
0
89J:B<O>P<RQTS 2UVXW0W3DEK#1'.H6YI;DE6ZI[D\6E"C.H6
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1
0.6
x_2
NSGA−II
0.2
Orig. global front
0
0.6
0.4
Original
local front
0.2
Theory
(Robust front)
0.8
Mean local front
(Robust front)
f_2
f_2
0.8
0.4
Local front
solutions
Global front
solutions
0.2
0.2
0
0
−0.15
−0.15
0
0.2
0.4
0.6
0.8
1
x_1
89;:=<?>^<OQS 2UV_W0W'.0KG16E*GK.`I6E/'"aDE*,b*Gc
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0
0.2
0.4
x_1
0.6
0.8
1
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1.0*G'b)Ytvunwx5DE?FC"&1DE"KNcWrY5DEK#G"C%oc6E/'"yFC5'167 6E*GKjIz6E/'"DEK#1'.H64IJDEK?6*G.DE"
1.0"$I[1{'&|5DE h*J&"C.}~1'.0"$Dyk*6E/|6E/'"*,I[DE-6E*GKf#m16yDEK#1'.H6p.0G16E*GK.&*DE"CF$6E?NBW_6
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1.0"&€6E\F$K5'16E"36E/'"n"C#‚r"CF$6E*GhO"jhG1'"C. DE"Y*G5mD067?6-5c D7"$6E"$DE.-*Gƒ#67*G*,b
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.0G16E*GK.+I`6r5m"W0W‰"DEG*G"$D4c&3&*G.0FC1'.0.*6*G)6E/'"T"$Š6{.0"CF$6E*G=N
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I;DT©¬ ­ '&36E/'"ta1'FCG*,&"j'DEMI;D®{¯®TK5m"iD76EDN A /'"y,*G*6E*G'b5'D7"i6E"$D4°)*G.4FC'.0*,&V
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2.5
0.35
η=0.4
0.3
η=0.5
2
η=0.7
η=0.5
0.2
Type I robust
front
1
g()
f_2
1.5
η=0.4
0.25
η=0.6
η=0.6
0.15
η=0.7
0.1
0.05
Original front
0.5
0
0
0
0.2
0.4
f_1
0.6
0.8
−0.05
1
ûü;ý=þÿcþ ½¼K¾'¿ÀHÁ‡»;µE¼¹ÁEÀ`»;¼µ‰Ï¸ò³$µE³$¹ÁaδÇG¿³CÀ
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ÇG³CÆ ÈÖ
Type I (theory)
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
f_1
1
ûüJýBþÿcÿþ‡ñ ¿'¹¶$ÁE¸G¼K¹
ø¼»vÁE·³yµE¼¾'¿'ÀHÁÀ0¼KÇG¿Ã
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2
0.25
Type I robust
front
1.5
0.2
1
g()
f_2
0.15
η=0.4
η=0.6
0.1
0.05
0.5
Original front
η=0.4
η=0.6
0
Type I robust front
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
f_1
1
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−0.05
0
0.1
0.2
f_1
0.3
0.4
0.5
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