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主専攻実験(春) 巡回セールスマン問題
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TAKAMASA Saichi
October 16, 2016
Technology
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主専攻実験(春) 巡回セールスマン問題
大学における専攻毎に行われる実験の発表資料です。
計測あたりはあまり良い方法をとっていないので、参考程度に。
実験における詳細記事:
TAKAMASA Saichi
October 16, 2016
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Transcript
ओઐ߈࣮ݧ य़ ϝλώϡʔϦεςΟΫεͱ८ճηʔϧεϚϯ ᜊਸେ
࣮ݧܭը w ݄ w ࣮ݧςΩετͷಡΈࠐΈɺ֤छख๏ΛௐΔͳͲ w ݄ w ࣮ݧͰ༻͍ΔΞϧΰϦζϜͷܾఆͱϨϙʔτͷਐḿ w
ɾ݄ w தؒൃදͷ४උɺΞϧΰϦζϜͷ࣮ɺ࠷ऴൃදͷܭଌ
ࢀߟ w ߨٛࢿྉ QEG w ߹ͤ࠷దԽୈ൛ ཧͱΞϧΰϦζϜ
w l5IF5SBWFMJOHTBMFTNBOQSPCMFNBOENJOJNVNTQBNNJOHUSFFTz w .JDIBFM)FME 3JDIBSE.,BSQ
࣮ͨ͠ख๏ w ݫີղ๏ w ྻڍ๏ w ಈతܭը๏ w ࢬݶఆ๏ ະ
ޙड़ w ώϡʔϦεςΟΫε w ࠷ۙྡ๏ɾ࠷ۙՃ๏ w ম͖ͳ·͠๏
ݫີղ๏ w ྻڍ๏ w ॱྻͷྻڍͱίετͷܭࢉ0 OO w ಈతܭը๏ w
ݱ࣌ͷ֗ͱ౸ୡ͍ͯ͠Δ֗ͷঢ়ଶͰܭࢉ0 O??O ͲͪΒݱ࣮తͰͳ͍
࠷ۙՃ๏ w ࠷ۙྡ๏ w దͳ͔Βग़ൃ͠ɺ·ͩ౸ୡ͍ͯ͠ͳ͍ͷݱࡏͷ͔Β͏ͪ ࠷͍ۙͷΛՃ͍ͯ͘͠ɻશͯͷ౸ୡޙ։࢝Δɻ ߨٛࢿྉΑΓ w ܭࢉྔ͕૿͍͍͑ͯͷͰվྑͯ͠ΈΔ
ྫ վྑແ͠ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ ࢝Λͱͯ͠ߟ͑Δ
ྫ վྑແ͠ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ
࠷ۙྡ๏ͷվྑ w શ͔Β։࢝ ֤Ͱಉ༷ͷૢ࡞Λߦ͏ w ๚Ε͍ͯΔͷू߹ʹଐ͞ͳ͍ͷ͏ͪɺ ๚Ε͍ͯΔͷ͍ͣΕ͔࠷͍ۙΛબͿ w ্هΛ༻͍ͯͭͳ͗ม͑Λߦ͍८ճ࿏Λߋ৽
w ৗʹ८ճ࿏Λߏஙͯ͠࠷ॳͷΔίετΛݮ͢Δ
ྫ վྑ༗Γ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ ࢝ҙͷ ࠓճ
ྫ վྑ༗Γ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ ࠷ۙͷͱͰ८ճ࿏Λੜ
ྫ վྑ༗Γ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ ࠷ۙͷͱͰ८ճ࿏Λੜ
ྫ վྑ༗Γ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ ࠷ۙͷͱͰ८ճ࿏Λੜ
ྫ վྑ༗Γ ͕࠷ͩͱԾఆʢϢʔΫϦουڑʣ ࠷ۙͷͱͰ८ճ࿏Λੜ
ম͖ಷ͠๏ w Թ5ͱPQUͷࢬுସ͑ૢ࡞ΛऔΓೖΕͯԹ͕ऩଋ͢Δ·Ͱ Ұఆͷ֬ͱลͷ૯ͷൺֱͰுସ͑ૢ࡞Λߦ͏ w ࠓճͷύϥϝʔλ5@45"35 5@&/% 5@'"$503 w ลͷுସ͑ૢ࡞ʹؔͯ͠ߨٛࢿྉதͷख๏Λࢀর
w ղۭؒͷੑ࣭͕ʹґଘ͢ΔͨΊ͝ͱʹύϥϝʔλΛ༻ҙ
ܭଌʹ͋ͨͬͯ w MBOHVBHF$ w NBDIJOF.BD#PPL1SP 3FUJOB JODIɺ&BSMZ w
DPNQJMFSHDDWFSTJPO Y@BQQMFEBSXJO w DQV$PSFJ6 ()[ w DPNQJMFPQUJPOH 0TUED
541-*#Λ༻͍ͯܭଌ ॲཧ࣌ؒ NT ճ ճ ճ TUUTQ ࢢ
QSUTQ ࢢ UTQUTQ ࢢ MJOUTQ ࢢ ࠷ۙՃ๏ ݁Ռ ࠷దղ ࣮ߦղ TUUTQ ࢢ QSUTQ ࢢ UTQUTQ ࢢ MJOUTQ ࢢ ֓ͶഒҎ ࢢఔ·ͰͰ͋ΕTFD΄Ͳ
࠷ۙՃ๏ͷܭଌ w ۤखͳέʔεɾஔ͕͋Δ w શ͔Β։࢝ͯ͠ղͷ্ݶܾ·ͬͯ͠·͏ w ΞϧΰϦζϜࣗମͷվྑͰ্͔͠͠ͳ͍ w վળͷݟࠐΈ͕ബ͍ w
ͨͩ ᩦཉʹՃ͍ͯ͘͠ͷͰಘΒΕΔղۭؒΛ શ୳ࡧͯ͋͠Δఔͷ࣌ؒͰऴྃ͢ΔͨΊ ͦ͏͍͏Ͱ༏ल
541-*#Λ༻͍ͯܭଌ ম͖ಷ͠๏ ෮ճ 5@45"35 5@&/% 5@'"$503 ॲཧ࣌ؒ NT ճ ճ
ճ TUUTQ ࢢ QSUTQ ࢢ UTQUTQ ࢢ MJOUTQ ࢢ ࣌ؒͷ૬ؔ΄΅ແ͠ ॳظϧʔτੜͳͲͷ࣌ؒ
541-*#Λ༻͍ͯܭଌ ম͖ಷ͠๏ ෮ճ 5@45"35 5@&/% 5@'"$503 ݁Ռ ࠷దղ ճฏۉ TUUTQ
ࢢ QSUTQ ࢢ UTQUTQ ࢢ MJOUTQ ࢢ TU΄΅࠷ద ෮ճ͕গͳͯ͘ྑ͍ղ ࢢ͕ଟ͍ͱղ ζϨΔେ͖͘
541-*#Λ༻͍ͯܭଌ ম͖ಷ͠๏ ෮ճ 5@45"35 5@&/% 5@'"$503 ॲཧ࣌ؒ NT ճ ճ
ճ TUUTQ ࢢ QSUTQ ࢢ UTQUTQ ࢢ MJOUTQ ࢢ ઌͱൺͯ࿐ࠎʹ͘ͳΔ
541-*#Λ༻͍ͯܭଌ ম͖ಷ͠๏ ݁Ռ ࠷దղ ύϥϝʔλ มߋલ ճฏۉ TUUTQ ࢢ
QSUTQ ࢢ UTQUTQ ࢢ MJOUTQ ࢢ ෮ճ 5@45"35 5@&/% 5@'"$503 ࢢ͕ଟ͍ํ͕Ըܙ͕ଟ͍ গͳ͍ํͰٯʹਫ਼͕ѱԽ
ম͖ಷ͠๏ͷܭଌ w ෮ճ w ͷࢢঢ়ଶʹΑͬͯมԽͤ͞Δͱ্ͷ༨͕͋Δ w ͨͩ͠ہॴղʹམͪͯ͠·͏߹͋Δ w ہॴղʹରͯ͠ w
্هͷہॴղʹରͯ͠ཚԹΛ্ख͘ௐ͢Δ w ࠷ۙՃ๏ͷΑ͏ʹہॴղʹམͪͯऴྃ͢Δ͜ͱݮΔ w దͳղۭؒΛݟ͚ͭ Կ͔ௐ͢Δͱঘྑ
ݫີղͷߴԽ w ݫີղΛߨٛࢿྉͷଞͷ࣮Λߟ͑Δ w Ҋ w ࢬݶఆ๏ w ࢬΧοτ๏ w
4"5ผʹม w ͳͲͳͲ ߨٛࢿྉʹهࡌ͞Ε͍ͯͨͨΊઓ
ࢬݶఆ๏ w ͷ୳ࡧΛϕʔεʹߟ͑Δ w ݶఆૢ࡞ w ͋Δ݅Λݩʹ෦͕୳ࡧՄೳ͔ͷ݅ذ w ࢬמΓ͕Ͱ͖ΔͷͰຊདྷͷΦʔμʔΑΓগͳ͘ݟੵΕΔ w
ࢬૢ࡞ w Λ͍͔ͭ͘ͷ෦ʹ͚ͯߟ͑Δ w ֤εςοϓʹ͍ͭͯݶఆૢ࡞ͰՄೳͱஅ͞ΕΕ୳ࡧΛߦ͏
541ʹؔ͢ΔΞΠσΞ ྫ ८ճ࿏ ८ճ࿏ ८ճ࿏ ८ճ࿏ ८ճ࿏ ८ճ࿏
541ʹؔ͢ΔΞΠσΞ w .JOVNVN4QBOOJOH5SFF .45 Λ༻͍ͯԼքΛࢉग़ w 1SJN,SVTLBMʹͯ0 O? ఔͰࢉग़Ͱ͖Δ w
શମͱͯ͠0 ?OO? w ݶఆૢ࡞ͰࢬמΓ͕ՄೳʹͳΔ w ࢀߟl5IF5SBWFMJOHTBMFTNBOQSPCMFNBOENJOJNVNTQBNNJOHUSFFTz
541ʹؔ͢ΔΞΠσΞ w USFFͷఆٛ w ͷ͕࣍Ͱ͋Δ w ͔ΒลΛҰͭআ͢Δͱ࠷খશҬʹͳΔ w ಋग़0 O?
541ʹؔ͢ΔΞΠσΞ w USFFͷಛ w ࠷খશҬ͕ߏ͢Δล શͯͷ͕ܨ͕͍ͬͯΔάϥϑͷ࠷খ w NJO8 w USFFNJO8ΑΓάϥϑΛߏ͢Δίετߴ͍
w POF58 w POF58NJO8͕Γཱͭ
541ʹؔ͢ΔΞΠσΞ w USFFͷಛ w ·ͨ ͋Δάϥϑ͕USFFΛߏ͢Δͱ͖ ͦͷάϥϑ͔Βಋ͚ Δ८ճ࿏ͷղPOF5BOT w POF5BOTPOF58Ͱ͋Δ͜ͱ͕ݴ͑Δ
w ͜ͷ͜ͱUSFF͕८ճ࿏ʹͳΔ߹Λߟྀ͢Δͱ໌Β͔ w ΑͬͯPOF5BOTPOF58NJO8͕ݴ͑Δ
541ʹؔ͢ΔΞΠσΞ w ͋Δ෦͔Βಋ͔ΕΔఆղΛ9ͱ͢Δͱ w 9ΑΓେ͖ͳPOF58ͷΛอͭUSFF 9ΑΓখ͞ͳఆղΛ࣋ͨͳ͍ w POF5BOTPOF58NJO8ΑΓ w
Αͬͯɺ෦தͰUSFFΛߏங͢ΔͱఆղΛݩʹ ݶఆૢ࡞͕ߦ͑ΔΑ͏ʹͳΔ
࣮ w ࢬૢ࡞ʹ͓͍ͯ lઈରʹ༻͠ͳ͍ลzͱzઈରʹ༻͢ΔลzΛ ༻͍ͯ෦Λੜ w ͕࣍Ҏ্ͷࢬૢ࡞͕Ͱ͖Δ આ໌ུ w
લॲཧؚΊͯߦఔͷ࣮ w ͜ͷൃද·Ͱʹਖ਼͘͠ಈ͖·ͤΜͰͨ͠ɻ w খ͍͞έʔε O ఔಈ࡞͢Δ
·ͱΊ w ۙࣅࢉ๏Λߏங͢Δʹ͋ͨͬͯͷͱରͷղۭؒΛٻΊ ͦΕʹԠͯ͡ύϥϝʔλΛௐઅ͢ΔඞཁͳͲ͕͋Δ w ͕ෳࡶʹͳΕύϥϝʔλ૿͑ΔͨΊௐ͘ͳΔ w ݫີղΛٻΊΔͨΊʹάϥϑߏ -1ͷ෦ͳͲΛߟ͑Δඞ ཁ͕͋Δ
w ෦ʹؔͯۙ͠ࣅࢉ๏ͳͲΛద༻͠ Լք͕ܾΊΒΕΕͨͱ ͑࠷ۙՃ๏ͷΑ͏ʹ্͕Ίͳͯ͘׆͔ͤΔ͔͠Εͳ͍
࣮ݧͷײ w ݫີղ๏ʹؔͯ͠ଟ࣌ؒ͘Λׂͭ͘Γ͕ͩͬͨࢬݶఆ๏ʹؔ͠ ͯΞΠσΞΛ࣮͢ΔͷͰ΄ͱΜͲ͕࣌ؒͳ͘ͳͬͯ͠·ͬͨ w ͨͩ ࢬݶఆ๏ʹݶͬͯԼքͷಋग़ํ๏ʹؔͯ͠จݙ͕େྔʹ͋ Δ΄͔ɺ෦ฒྻԽ͢ΔͳͲͷख๏ݟͨͬͨ w ࠷ऴൃදʹ͚ͯͷ੍࣌ؒͰจݙΛࢀߟఔʹ͔͠Ͱ͖ͳ͔ͬ
ͨͷͰޙʑಡΜͰΈ͍ͨ
͜ΕͰൃදऴΘΓͰ͢