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kichinosukey
December 12, 2018
Science
0
37
NSGA
参考:
https://web.njit.edu/~horacio/Math451H/download/SrinivasDeb_GA.pdf
kichinosukey
December 12, 2018
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Transcript
/4("
ଟత࠷దԽ ↟Y1ᮈᕓຌแᨷม ↟OPOEPNJOBOU TVQFSJPSᓓᙚֶ᧣ͼḑᶡḿ Min/Max fi (x) … i =
1,2, … , N gi (x) … j = 1,2, … , N hk (x) … k = 1,2, … , N
࠷খԽʹ͍ͭͯ ↟ͥᙉfYYΤᬧ፺ EPNJOBUFT ͖ͩΝ ↟ΐͱYYͽରͩᅿ͵͖ Ν CFJOGFSJPSUP ͺ͖͘ ↟ᝂͽ᷁ͽΔᬧ፺ͧΞ͖ͼ͖f Δͩ͡ᅿ͵͖ͼ͖ᦉᷯ
OPOEPNJOBOUOPOJOGFSJPSͺ ͖͘ ↟ᱠ᧱ặዧ᩼ḑOPOEPNJOBOU ͼḑͥͺΤ͖͘ Y Y YJTTUSJDUSZHSFBUFSUIBOY
ݹయతͳղ๏ ↟᧣ᬍΑͣ ↟ᬍΑΤᑿᠭ ↟ฌሜؔ ↟ጽ᧣ͽϫ⑲δϯψώฌሜΤᠭ͖Ν ↟ᱠႝfᱠᖀ໋ᙚ ↟ᄑ͖ͩᠸᔬႷᶝᱠ᧱ặ
తͷॏΈ͚ ↟᧣ᬍ᠓ᕥͽԠͪᬍΑϞδύϰΤᕅ ↟ᓓᙚΚΜfᬍ᠓ႷΤວᅝͩͱϖϱ⑲ύḑΤᄌΝͥͺ͟͞Ν Z = N ∑ i=1 wi fi
(x) where x ∈ X 0 ≤ wi ≤ 1, N ∑ i=1 wi = 1
ڑؔ ↟᧣ؔᤎ᷀ͺͼΝfᴢᓝSďϫ⑲δϯψώฌሜĐ ↟ZᶝͽରͫΝ෪ମᱠີᲩ Z = [ N ∑ i=1 |
fi (x) − yi |r ] 1/r , 1 ≤ r ≤ ∞
NJONBY ↟ᄑ͖ͩᠸᔬႷᶝΤᱠ᧱ặ minimize Fi (x) = max[Zi (x)] Zi (x)
= fi − fi fi , i = 1,2, … , N
͜ΕΒͷܽ ↟͖ͬΞΔ୯᧣Τᓡᨷͩ͜Μḿ࣮ͺ༏ሜ ↟ሜᒺมͽରԠ͟ͼ͖ ↟ᬍΑͺ᠓ཏϱϞϰďแᨷมĐͽରͩᑤᓝͽπϸμϋΨϛ ↟ͥΞ͞Ჺ᧣fჯͪዧ᩼Τ᷁ႷΔΜጿͩḑ͡ᡊͽͼΝ
୯७త ↟ͥᦉᷯϖϱ⑲ύḑͻͥͽ͔Ν ͝Ħ ↟Y᎘ғͽ͔Ν ↟ᬍΑΤͯΞͰΞ᧣ͽରͩ X
ͺม͚Ν ↟ͫΝͺϖϱ⑲ύḑΔY Y Yͺ Y᎘ғḑ͖͞͝Κ͘ͽΔ ხ͖ͩΐ͘ ↟ͶΐΜfᑤแᨷ᧣͔ΝͺΔᜡ͚Ν Minimize f11 = x2 Minimize f12 = (x − 2)2
(FOFUJD"MHPSJUIN ↟3PTFOCFSHၞ᧣Τጩ͘୯ᕺᶈᓺዲ᭽ᷯ͞ပͥͫặֶ มặᄑμϤϪϱ⑲μϬϸᓷͽରͫΝᩮᚳ ↟4DIBGGFS࣮ᠭ᧣ͼΧϰιϯοϥ 7FDUPS&WBMVBUFE(FOFUJD "MHPSJUIN ↟(PMECFSH7&("ᛰᨨΤᏎ͘ͱΓOPOEPNJOBOUTPSUJOH Ϝϲμ⑲νϨΤᩮᚳ ↟/4("ͥΞͽͷ͖͖Ν
/4(" ↟᳔ᩮᚳͺfᕅίϟϱ⑲τ⑲ხᥭͽ͖͜ΑᤘͼΝ ↟༜ͧfมᤘ᳔("ͺჯͪ ↟ᗌᘡ ↟'JSTU3BOLΤᨷᤅf᧱ᷯႷυϤ⑲ᲩΤ'᭽ஂͽ༩͚ΝfͯΞͰΞͽ ରͩᅿᲩGJBΤຌᒿf'᭽ஂΤ͖᩹ͱΜ෪ମͽରͩჯ༷ ॲሑΤΜጿͫfGGjGJ
/4(" ↟ᔬͻॲሑΤᕴႚΜጿͩḝ͘ͽ͔ͱ͵f᭽ஂᦪᓺᒽ ͧΞΝ ↟උϚϲϸύΤͻᷡᷯᦪᓺᒽͫΝ͝᧱ᷯႷͽै͘ ↟'Ϯϸδ෪ମ᳔ΔΚΜΔ᧱ᷯႷ͞ີ͖ͱΓၞ͡θϙ⑲ΤᥭΝ ͥͺ͟͞Ν ↟ͥΞͽΚΜϖϱ⑲ύḑΊऩᖣΤ᱉ͫͥͺ͞൱ၙ ↟ϚϲϸύϮϸδΤ๕ͽ᭽ஂ۠Ꭽ͞൱ၙ
/4("
/4("ͷϑϩʔνϟʔτ ↟μάΧϯϸε ↟ၞ༷ᕥệᏂͱΓᬥᶝ ↟෪ମJ KණฌሜͺȀϖϮϦ⑲τͽΚ͵ᶡḿ ͧΞΝ ↟ͻͳΛΔQIFOPUZQJD ↟ͯΔͯΔͥΚ͘ͼ᪣ᨿ൱ၙͼϖϮϦ⑲τ Τᐾ͚ͩΐ͵͖Νͥͺዧ᩼