NSGA

参考: https://web.njit.edu/~horacio/Math451H/download/SrinivasDeb_GA.pdf

Transcript

1. /4("
2. ଟ໨త࠷దԽ໰୊ ↟Y
   1ᮈ΀ᕓຌแᨷม਺
   ↟OPOEPNJOBOU
   TVQFSJPS
   ᓓᙚ΀਺ֶ᧣ͼḑᶡḿ Min/Max fi (x) … i = 1,2, … , N gi (x) … j = 1,2, … , N hk (x) … k = 1,2, … , N
3. ࠷খԽ໰୊ʹ͍ͭͯ ↟ͥ΀ᙉfY΁YΤᬧ፺ EPNJOBUFT ͩ͸͖Ν
   ↟ΐͱ΁Y΁Yͽରͩ͸ᅿ͵͸͖ Ν CF
   JOGFSJPS
   UP ͺ͖͘
   ↟ᝂͽ᷁ͽΔᬧ፺ͧΞ͸͖ͼ͖f Δͩ͡΁ᅿ͵͸͖ͼ͖ᦉᷯ΁ OPOEPNJOBOUOPOJOGFSJPSͺ ͖͘
   ↟ᱠ᧱ặዧ᩼΀ḑ΁OPOEPNJOBOU ͼḑ΀ͥͺΤ͖͘           Y Y Y
   JT
   TUSJDUSZ
   HSFBUFS
   UIBO
   Y
4. ݹయతͳղ๏ ↟኷᧣΀ᬍΑ᏶ͣ
   ↟ᬍΑΤᑿᠭ
   ↟ฌሜؔ਺
   ↟᤼ጽ᧣ͽϫ⑲δϯψώฌሜΤᠭ͖Ν
   ↟ᱠႝfᱠᖀ໋ᙚ
   ↟ᄑ͖ͩᠸᔬႷ΀኷ᶝᱠ᧱ặ
5. ໨తͷॏΈ෇͚ ↟኷᧣΀ᬍ᠓ᕥͽԠͪ͸ᬍΑϞδύϰΤᕅ୒
   ↟ᓓᙚΚΜfᬍ᠓ႷΤວᅝͩͱϖϱ⑲ύḑΤᄌΝͥͺ͞͹͟Ν Z = N ∑ i=1 wi fi (x) where x ∈ X 0 ≤ wi ≤ 1, N ∑ i=1 wi = 1
6. ڑ཭ؔ਺ ↟኷᧣ؔ਺΁ᤎ᷀ͺͼΝfᴢᓝSďϫ⑲δϯψώฌሜĐ
   ↟Z΁኷ᶝͽରͫΝ෪ମ΀ᱠີᲩ Z = [ N ∑ i=1 | fi (x) − yi |r ] 1/r , 1 ≤ r ≤ ∞
7. NJONBY ↟ᄑ͖ͩᠸᔬႷ΀኷ᶝΤᱠ᧱ặ minimize Fi (x) = max[Zi (x)] Zi (x) = fi − fi fi , i = 1,2, … , N
8. ͜ΕΒͷܽ఺ ↟͖ͬΞΔ୯኷᧣Τᓡᨷͩ͸͜Μḿ࣮ͺ༏ሜ
   ↟ሜᒺม਺ͽରԠ͹͟ͼ͖
   ↟ᬍΑͺ᠓ཏϱϞϰďแᨷม਺Đͽରͩ͸ᑤᓝͽπϸμϋΨϛ
   ↟ͥΞ͞Ჺ኎᧣͹fჯͪዧ᩼Τ᷁ႷΔ᪞Μጿͩḑ͡ᡊ኷ͽͼΝ
9. ୯७໨త ↟ͥ΀ᦉᷯ΀ϖϱ⑲ύḑ΁ͻͥͽ͔Ν ͝Ħ
   ↟
   Y
   
   ΀᎘ғ಺ͽ͔Ν
   ↟ᬍΑΤͯΞͰΞ΀኷᧣ͽରͩ͸ X 
     
     
    ͺม͚Ν
   ↟ͫΝͺϖϱ⑲ύḑΔY
   Y
   Yͺ Y΀᎘ғ಺͹ḑ͖͞͝Κ͘ͽΔ ხ͖͸ͩΐ͘
   ↟ͶΐΜfᑤแᨷ᧣͹͔ΝͺΔᜡ͚Ν Minimize f11 = x2 Minimize f12 = (x − 2)2
10. (FOFUJD
    "MHPSJUIN ↟
    
    3PTFOCFSH
    ၞ኷᧣Τጩ͘୯ᕺᶈᓺዲ΀᭽ᷯ͞ပͥͫặֶ มặᄑ΀μϤϪϱ⑲μϬϸ᳼ᓷͽରͫΝᩮᚳ
    ↟
    4DIBGGFS
    ࣮ᠭ᧣ͼΧϰιϯοϥ 7FDUPS
    &WBMVBUFE
    (FOFUJD
    "MHPSJUIN
    ↟
    (PMECFSH
    7&("΀ᛰᨨΤᏎ͘ͱΓ΀OPOEPNJOBOU
    TPSUJOH Ϝϲμ⑲νϨΤᩮᚳ
    ↟/4("΁ͥΞͽ࿥ͷ͖͸͖Ν
11. /4(" ↟᳔ᩮᚳͺ΁fᕅ୒ίϟϱ⑲τ⑲΀ხᥭͽ͖͜͸΀ΑᤘͼΝ
    ↟༜ͧfมᤘ΁᳔("ͺჯͪ
    ↟ᗌᘡ
    ↟'JSTU
    3BOLΤᨷᤅf᧱ᷯႷ΀υϤ⑲ᲩΤ'΀᭽ஂͽ༩͚ΝfͯΞͰΞͽ ରͩ͸ᅿᲩGJBΤຌᒿf'΀᭽ஂΤ͖᩹ͱ࢒Μ΀෪ମͽରͩ͸ჯ༷΀ ॲሑΤ᪞ΜጿͫfG
    G
    
    j
    
    GJ
12. /4(" ↟ᔬ΍ͻ΀ॲሑΤᕴႚ͹᪞Μጿͩ͸ḝ͘ͽ͔ͱ͵͸f᭽ஂ΁ᦪᓺᒽ ͧΞΝ
    ↟උϚϲϸύΤͻ΀ᷡᷯ͹ᦪᓺᒽͫΝ͝΁᧱ᷯႷͽै͘
    ↟'Ϯϸδ΀෪ମ΁᳔΀Δ΀ΚΜΔ᧱ᷯႷ͞ີ͖ͱΓၞ͡΀θϙ⑲ΤᥭΝ ͥͺ͞͹͟Ν
    ↟ͥΞͽΚΜϖϱ⑲ύḑΊ΀ऩᖣΤ᱉ͫͥͺ͞൱ၙ
    ↟ϚϲϸύϮϸδΤ๕ͽ᭽ஂ΀۠Ꭽ͞൱ၙ
13. /4("
14. /4("ͷϑϩʔνϟʔτ ↟μάΧϯϸε
    ↟ၞ༷ᕥệᏂ΀ͱΓ΀ᬥᶝ
    ↟෪ମJ
    Kණ΀ฌሜͺȀ΀ϖϮϦ⑲τͽΚ͵͸ᶡḿ ͧΞΝ
    ↟ͻͳΛΔQIFOPUZQJD
    ↟ͯΔͯΔͥ΀Κ͘ͼ᪣ᨿ൱ၙͼϖϮϦ⑲τ Τᐾ͚͸ͩΐ͵͸͖Νͥͺ΁ዧ᩼