経験に基づく知識を活用したGAの消込処理問題への適用

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(1)情報処理学会研究報告 IPSJ SIG Technical Report. Vol.2014-MPS-100 No.16 2014/9/25. ⤒㦂࡟ᇶ࡙ࡃ▱㆑ࢆά⏝ࡋࡓ GA ࡢᾘ㎸ฎ⌮ၥ㢟࡬ࡢ㐺⏝ ዟ⏤㍜†1 ᓊ⏣㝯ど†2 బ⸨⿱஧†1 ᾘ㎸ฎ⌮࡜ࡣࠊ኎᥃㔠࡞࡝ࡀධ㔠ࡉࢀࡓ㝿࡟᫂⣽᭩࡜↷ྜࡋࠊධ㔠ࡢ㐜ᘏࡸ኎᥃㔠ࡀㄳồ㢠㏻ࡾ࡛࠶ࡿ࠿ࢆ☜ㄆࡍࡿ సᴗࢆ♧ࡍࠋ௻ᴗ㛫ࡢྲྀᘬ࡛ࡣࠊㄳồࡢྜィ㢠࡜ධ㔠㢠ࡀ୍⮴ࡋ࡞࠸ሙྜࡀ࠶ࡿࡓࡵධ㔠㢠ࢆᇶ࡟ᑐᛂࡍࡿㄳồࡢෆ ヂࢆồࡵࡿᚲせࡀ࠶ࡿࠋᮏ✏࡛ࡣࠊ㑇ఏⓗ࢔ࣝࢦࣜࢬ࣒(Genetic Algorithm, GA)ࢆ⏝࠸ࡓゎἲࢆᥦ᱌ࡋࠊ᥈⣴⬟ຊྥୖ ࡢࡓࡵ௻ᴗࡀᣢࡘ㢳ᐈࡢ᣺ࡾ㎸ࡳ≧ἣ࡞࡝ࡢࠊ⤒㦂࡟ᇶ࡙ࡃ▱㆑ࢆ GA ࡢึᮇ್࡟ᛂ⏝ࡍࡿᡭἲࢆ᳨ウࡍࡿࠋ. 1. ࡲ࠼ࡀࡁ ᾘ㎸ฎ⌮࡜ࡣ㸪኎᥃㔠࡞࡝ࡀධ㔠ࡉࢀࡓ㝿࡟᫂⣽᭩࡜↷ ྜࡋ㸪ධ㔠ࡢ㐜ᘏࡸ኎᥃㔠ࡀㄳồ㏻ࡾ࡟ᅇ཰ฟ᮶࡚࠸ࡿ࠿ ࢆ☜ㄆࡍࡿసᴗࢆ♧ࡍ㸬௻ᴗ㛫ࡢྲྀᘬ࡛ࡣ㸪᣺㎸ᡭᩘᩱࢆ. ᅗ 1 ᰁⰍయࡢᐃ⩏౛ 2.2 ホ౯㛵ᩘ. ᢚ࠼ࡿࡓࡵ࡟ 100 ௳ࢆ㉸࠼ࡿㄳồࢆ⧳ࡵ࡚ධ㔠ࡍࡿࡇ࡜ࡀ. 㑇ఏⓗ᧯స࡟࠾ࡅࡿホ౯್ࡣ㸪ᰁⰍయ࡟ᑐᛂࡋࡓㄳồ㔠. ୍⯡ⓗ࡛࠶ࡾ㸪㒊⨫ࡸᢸᙜ⪅࡟ࡼࡿྲྀࡾ⧳ࡵࡢ᫬ᮇ࡟ᕪࡀ. 㢠ࡢྜィ㢠࡜ධ㔠㢠ࡢᕪ㢠ࡢ⤯ᑐ್ࡢ㏫ᩘࢆホ౯್࡜ࡋ࡚. ⏕ࡌࡿ࡜㸪ㄳồ㔠㢠ࡢྜィ㢠࡜ධ㔠㢠ࡀ୍⮴ࡋ࡞࠸ሙྜࡀ. タᐃࡍࡿࡢࡀጇᙜ࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪ࡇࡢタᐃ࡛ࡣ᥈⣴✵㛫. ࠶ࡿ㸬ᚑࡗ࡚㸪ᾘ㎸ฎ⌮࡛ࡣ㸪ධ㔠㢠ࢆᇶ࡟ᑐᛂࡍࡿㄳồ. ࡢᙧ≧ࡀ」㞧࡟࡞ࡗ࡚ࡋࡲ࠺ሙྜࡀ࠶ࡿ㸬ࡑࡇ࡛ࠊ0 ࠿ࡽ 1. 㔠㢠ࡢෆヂࢆồࡵࡿᚲせࡀ࠶ࡿࠋ. ࡢ㛫ࡢ್࡟ṇつ໬ࡋࡓᘧ(1)࡟♧ࡍホ౯㛵ᩘࢆᐃ⩏ࡍࡿ㸬. ⌧ᅾ࡛ࡣ㸪඲ᩘ᥈⣴ࣉࣟࢢ࣒ࣛࡸ」ᩘࡢ⤒⌮㛵ಀ⪅࡟ࡼ ࡿேᾏᡓ⾡࡛ㄳồ㔠㢠ࡢෆヂࢆ᥈ࡋฟࡍᚲせࡀ⏕ࡌ࡚࠸ࡿ㸬 ࡇࡢሙྜ㸪඲ᩘ᥈⣴ࣉࣟࢢ࣒࡛ࣛࡣ㸪ㄳồ௳ᩘࡀ 50 ࡢሙྜ. ݂௘ =. ௙೛ ௙೛ ା௙ೞ. (1). ࡇࡇ࡛㸪fp ࡣᰁⰍయ࡟ᑐᛂࡋࡓㄳồ㔠㢠ࡢྜィ㢠࡛࠶ࡾ㸪. ࡛ࡶ㸪୍⯡ⓗ࡞ PC ࡛ồゎࡲ࡛⣙ 1 ࣨ᭶ࢆせࡍࡿሙྜࡀ࠶. fs ࡣ fp ࡜ධ㔠㢠࡜ࡢᕪࡢ⤯ᑐ್ࢆ♧ࡋ࡚࠸ࡿ㸬݂௘ 㸻1 ࡜࡞ࡗ. ࡾ㸪ேᾏᡓ⾡࡛ࡣᮇᮎ࡞࡝ࡢ≉ᐃࡢ᫬ᮇࡢࡳ࡟㸪⭾኱࡞ᡭ. ࡓಶయࡀධ㔠㢠࡟ᑐᛂࡍࡿಶయ࡛࠶ࡾ㸪᭱㐺ゎ࡜࡞ࡿ㸬. సᴗ࡟ࡼࡿேⓗ㈇Ⲵࡀ㞟୰ࡍࡿ࡞࡝ࡢၥ㢟ࡀ⏕ࡌ࡚࠸ࡿ㸬. 2.3 㑅ᢥ࡜஺ᕪ᪉ἲ. ୖグၥ㢟ࡣ㸪㒊ศ࿴ၥ㢟[1]ࡢ఍ィ㢠ࡀ኱ࡁ࠸≉ู࡞౛࡜. ணഛᐇ㦂ࡢ⤖ᯝ㸪࣮ࣝࣞࢵࢺ㑅ᢥ࡜୍ᵝ஺ཫࡢ⤌ྜࡏࡢ. ࡋ࡚ᐃ⩏࡛ࡁࡿ㸬㒊ศ࿴ၥ㢟ࡣ NP ᏶඲ၥ㢟[2]࡛࠶ࡾ㸪୍. ᫬࡟㸪ㄳồ௳ᩘ N ࡟౫Ꮡࡏࡎྠ୍ࡢ஺ཫ⋡㸪✺↛ኚ␗⋡࡛. ⯡ⓗ࡞㒊ศ࿴ၥ㢟ࡣືⓗィ⏬ἲ㸦Dynamic Programming, DP㸧. Ᏻᐃࡋࡓ཰᮰ᛶࢆᚓࡽࢀࡓࡓࡵ㸪ホ౯ᐇ㦂࡛ࡣ࣮ࣝࣞࢵࢺ. [3]࡛ゎࡅࡿࡇ࡜ࡀ♧ࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪DP ࡣධ㔠㢠ࡢ. 㑅ᢥ࡜୍ᵝ஺ཫࡢ⤌ྜࡏ࡛ᐇ㦂ࢆ⾜࠺㸬. ኱ࡁࡉ࡟ẚ౛ࡋࡓ኱㔞ࡢ࣓ࣔࣜࢆせࡍࡿࡓࡵ㸪௻ᴗ㛫ࡢྲྀ ᘬ࡛ᢅ࠺ࡼ࠺࡞㧗㢠࡞ධ㔠㢠ࡢሙྜࡣ㐺⏝࡛ࡁ࡞࠸㸬ᚑࡗ. 3. ⤒㦂࡟ᇶ࡙ࡃ▱㆑ࡢᛂ⏝᪉ἲ. ࡚㸪DP ࡜ẚ࡭࣓ࣔࣜࢧ࢖ࢬࢆᢚ࠼ࡿࡇ࡜ࡀ࡛ࡁࡿ㑇ఏⓗ. ௻ᴗࡀᣢࡘ㢳ᐈࡢ᣺㎸᝟ሗ࡞࡝ࡢ⤒㦂࡟ᇶ࡙ࡃ▱㆑ࢆ. ࢔ࣝࢦࣜࢬ࣒㸦Genetic Algorithm, GA㸧ࢆ⏝࠸ࡓᾘ㎸ฎ⌮ၥ. ฼⏝ࡋ࡚㸪ᾘ㎸ฎ⌮ࡢ௳ᩘࢆ⤠ࡾ㎸ࡴࡇ࡜ࢆ㸪▱㆑ࢹ࣮ࢱ. 㢟ࡢゎἲࢆᥦ᱌ࡋ[4]㸪ࡉࡽ࡟᥈⣴⬟ຊྥୖࡢࡓࡵ௻ᴗࡀᣢ. ࢆ⏝࠸ࡓฎ⌮࡜ࡇࡇ࡛ࡣᐃ⩏ࡍࡿ㸬౛࠼ࡤ㸪 ࠕA ♫࠿ࡽࡢ᣺. ࡘ㢳ᐈࡢ᣺ࡾ㎸ࡳ≧ἣ࡞࡝ࡢ㸪⤒㦂࡟ᇶ࡙ࡃ▱㆑ࢆ✚ᮌ[5]. ㎸㔠㢠ࡣ X ෇࡛࠶ࡿࡀ㸪ࡑࡢ࠺ࡕ B ௳࠿ࡽ࡞ࡿ Y ෇ศࡢ. ࡜ᤊ࠼࡚ GA ࡢึᮇ್࡟ᛂ⏝ࡍࡿᡭἲࢆ᳨ウࡍࡿ㸬. ᣺㎸ࡣᐃᮇⓗ࡟⾜ࢃࢀࡿࠖ࡜࠸࠺ሙྜ࡟ࡘ࠸࡚⪃࠼ࡿ㸬ࡇ. 2. ᾘ㎸ฎ⌮ࡢࡓࡵࡢ GA ࣉࣟࢢ࣒ࣛࡢタィ. ࡢሙྜ㸪୍⯡࡟᪤▱࡛࠶ࡿ㒊ศࢆษࡾศࡅ࡚ࠕA ௳࠿ࡽ X ෇࡜࡞ࡿ⤌ྜࡏࢆồࡵࡿၥ㢟ࠖ࠿ࡽࠕ(A㸫B)௳࠿ࡽ(X㸫Y). 2.1 ᰁⰍయࡢᐃ⩏. ෇࡜࡞ࡿ⤌ྜࡏࢆồࡵࡿၥ㢟ࠖ࡟⡆␎໬ࡍࡿࡇ࡜࡛㸪᥈⣴. ᾘ㎸ฎ⌮ၥ㢟ࢆᑐ㇟࡜ࡋࡓᰁⰍయࡢᐃ⩏౛ࢆᅗ 1 ࡟♧ࡍ㸬. ⠊ᅖࢆ⤠ࡾ㎸ࡴࡇ࡜ࡀ࡛ࡁࡿ㸬୍᪉㸪ࡇࡢ᫬⤠ࡾ㎸ࡳࢆ⾜. ྛㄳồ㡯┠࡟ࡑࢀࡒࢀ␗࡞ࡿ㑇ఏᏊᗙࢆᑐᛂࡉࡏ㸪㑇ఏᏊ. ࡗࡓ B ௳ࡢෆ࡟୍௳࡛ࡶㄗࡾࡀ᭷ࡗࡓሙྜ㸪ゎ࡞ࡋၥ㢟࡜. ᗙࡢ್ࡀ 1 ࡛࠶ࡿ㒊ศࡢㄳồ࡟ᑐᛂࡋࡓධ㔠ࡀࡉࢀࡓ࡜⪃. ࡞ࡗ࡚ࡋࡲ࠺㸬ࡇࡢၥ㢟ࡢᑐ⟇࡜ࡋ࡚㸪▱㆑ࢹ࣮ࢱ࡟࢚ࣛ. ࠼ࡿ㸬ᚑࡗ࡚㸪ᰁⰍయࡢᐃ⩏㛗ࡣㄳồ௳ᩘ࡜୍⮴ࡍࡿ㸬ᅗ. ࣮ࡀྵࡲࢀ࡚࠸ࡿሙྜࢆ⪃៖ࡋࡓ GA ࡢタィࢆᥦ᱌ࡍࡿ㸬. ࡛ࡣㄳồ㡯┠ 2㸪3㸪5 ࡟ᑐᛂࡍࡿ㑇ఏᏊᗙࡢ್ࡀ 1 ࡛࠶ࡿ. GA ࡢึᮇಶయ⩌ࡢ୍㒊࡟㸪▱㆑ࢹ࣮ࢱࢆゎࡢᵓᡂせ⣲. ࡓࡵ㸪ࡑࢀࡒࢀᑐᛂࡋࡓ㔠㢠 300 ෇㸪250 ෇㸪620 ෇ࡢ㔠㢠. 㸦Building Block, BB㸧࡜ࡋ࡚㐺⏝ࡍࡿ㸬ࡇࡢሙྜ㸪✚ᮌ௬. ࢆྜィࡋࡓ 1170 ෇ࡀᮏᰁⰍయࡢ♧ࡍධ㔠㢠࡜࡞ࡿ㸬. ㄝ[5]ࡼࡾ᥈⣴⬟ຊࡢྥୖࡀᮇᚅ࡛ࡁ㸪▱㆑ࢹ࣮ࢱ࡟ㄗࡾࡀ. †1 ἲᨻ኱Ꮫ Hosei University †2 (ᰴ)᪥❧࣐ࢿࢪ࣓ࣥࢺࣃ࣮ࢺࢼ࣮ Hitachi Management Partner Ltd. . ⓒ 2014 Information Processing Society of Japan. ᭷ࡗࡓሙྜ࡛ࡶ㸪ၥ㢟↓ࡃゎ᥈⣴ࢆ⾜࠺ࡇ࡜ࡀฟ᮶ࡿ㸬 ㄳồ㔠㢠ࡀ 3000 ෇㸪BB ࡜ࡋ࡚ά⏝ࡋࡓ▱㆑ࢹ࣮ࢱࡀ. 1.

(2) 情報処理学会研究報告 IPSJ SIG Technical Report. Vol.2014-MPS-100 No.16 2014/9/25. ⾲ 1 ホ౯ᐇ㦂ࡢ⎔ቃ. 1000 ෇ศ࡛࠶ࡗࡓሙྜࡢ▱㆑ࢹ࣮ࢱࡢ㐺⏝౛ࢆᅗ 2 ࡟♧ࡍ㸬 GA ࡢึᮇಶయ⩌୰ࡢ▱㆑ࢹ࣮ࢱࢆ㐺⏝ࡍࡿಶయ࡟࠾࠸࡚㸪 1000 ෇ศࡢ▱㆑ࢹ࣮ࢱ࡟ᑐᛂࡋࡓ㑇ఏᏊࢆ඲࡚ 1 ࡜ࡋ㸪ࡑ ࢀ௨እࡢ 2000 ෇ศࡢ㑇ఏᏊࢆࣛࣥࢲ࣒⏕ᡂࡍࡿ㸬ࡓࡔࡋ㸪 ▱㆑ࢹ࣮ࢱ࡟࢚࣮ࣛࡀྵࡲࢀ࡚࠸ࡿሙྜࢆ⪃៖ࡍࡿࡓࡵ㸪 1000 ෇ศࡢ㑇ఏᏊ࡟ࡣ㸪ṇゎࡀ 0 ࡛࠶ࡿ㑇ఏᏊᗙࢆྵࡵࡿ㸬. OS ࣉࣟࢭࢵࢧ ࣓ࣔࣜ(RAM) ࢩࢫࢸ࣒ࡢ✀㢮 ࢶ࣮ࣝ ࣉࣟࢢ࣒ࣛゝㄒ. Windows7 Intel(R) Core™ i5 CPU 2.50GHz 6.00 GB 64 ࣅࢵࢺ࣮࢜࣌ࣞࢸ࢕ࣥࢢࢩࢫࢸ࣒ Visual Studio 2010 C ゝㄒ. ⾲ 2 GA ࡢᐇ⾜ࣃ࣓࣮ࣛࢱ 200. ಶయᩘ 㑇ఏᏊ㛗 ஺ཫ⋡ ✺↛ኚ␗⋡ 㑅ᢥ᪉ᘧ ஺ཫ᪉ᘧ ✺↛ኚ␗᪉ᘧ. ᅗ 2 GA ࡢึᮇಶయ⩌࡬ࡢ▱㆑ࢹ࣮ࢱࡢ㐺⏝. 4. ホ౯ᐇ㦂 4.1 ホ౯᪉ἲ ホ౯ᐇ㦂ࡢ⎔ቃࢆ⾲ 1 ࡟㸪GA ࡢᐇ⾜ࣃ࣓࣮ࣛࢱࢆ⾲ 2. DP ࡣධ㔠㢠 S ࡢไ㝈ࡀ࠶ࡾ௻ᴗ࡛ࡢᾘ㎸ฎ⌮࡟ᐇ⏝ୖ 㐺⏝࡛ࡁ࡞࠸ࡓࡵ㸪ࡇࡇ࡛ࡣ඲ᩘ᥈⣴㸦Exhaustive Search,. ࣮ࣝࣞࢵࢺ㑅ᢥ ୍ᵝ஺ཫ ༢⣧✺↛ኚ␗. ⾲ 3 ES ࡜ GA ࡢᐇ⾜᫬㛫 (N, k) (10, 7) (20, 14) (30, 23) (40, 17) (50, 18). ࡟♧ࡍ㸬GA ࡢᐇ⾜ࣃ࣓࣮ࣛࢱࡣ㸪㑅ᢥ࡜஺ཫ᪉ἲࢆỴᐃ ࡍࡿ㝿ࡢணഛᐇ㦂ࢆ㏻ࡋ࡚Ỵᐃࡋ࡚࠸ࡿ㸬. ඲ㄳồ௳ᩘ㸦N㸧 0.6 0.03. ES 0.001s 1.116s 20m43s 350h 360,000h. GA (Average) 0.001s 0.574s 1m 2m18s 6m58s. GA (Worst) 0.020s 1.860s 4m22s 6m43s 12m50s. ⾲ 4 ▱㆑ࢹ࣮ࢱ㐺⏝ಶయᩘ Population of Knowledge Data 0. Execution Time (sec.) 35,307. Worst Execution Time (sec.) 165,063 101,066. ES㸧࡜ GA ࡢồゎࡲ࡛ࡢᐇ⾜᫬㛫ࢆẚ㍑ࡍࡿ㸬ࡲࡓ㸪᭱㐺. 50. 20,582. 100. 17,895. 78,410. ࡞▱㆑ࢹ࣮ࢱ㐺⏝ಶయᩘࢆồࡵࡿࡓࡵ㸪▱㆑ࢹ࣮ࢱ㐺⏝ಶ. 150. 19,427. 110,212. యᩘࢆࣃ࣓࣮ࣛࢱ࡟ྲྀࡾ㸪ồゎࡲ࡛ࡢᐇ⾜᫬㛫ࢆẚ㍑ࡍࡿ㸬. 200. 23,684. 112,071. ES ࡜ GA ࡢẚ㍑࡛ࡣ㸪ྛㄳồ㔠㢠ࡢ᱆ᩘࡀ 8 ᱆㹼13 ᱆. 5. ࠾ࢃࡾ࡟. ࡲ࡛ࡢᩘ್ࢆṇつ஘ᩘ࡛⏕ᡂࡋࡓࢸࢫࢺࢹ࣮ࢱࢆ⏝࠸࡚㸪 ㄳồ௳ᩘ N ࢆ 10 ࠿ࡽ 50 ࡲ࡛ኚ໬ࡉࡏ࡚ᐇ㦂ࢆ⾜࠺㸬ධ㔠 ௳ᩘ k ࡣ஘ᩘ࡛タᐃࡍࡿ㸬 ▱㆑ࢹ࣮ࢱࡢ᭱㐺࡞㐺⏝ಶయᩘࢆồࡵࡿᐇ㦂࡛ࡣ㸪ྛㄳ ồ㔠㢠ࡢ᱆ᩘࡀ 8 ᱆㹼12 ᱆ࡲ࡛ࡢᩘ್ࢆṇつ஘ᩘ࡛⏕ᡂ ࡋࡓࢸࢫࢺࢹ࣮ࢱࢆ⏝࠸࡚㸪ㄳồ௳ᩘ N ࢆ 30㸪ධ㔠௳ᩘ k ࢆ 20㸪▱㆑ࢹ࣮ࢱ㐺⏝㑇ఏᏊ㛗ࢆ 15㸪▱㆑ࢹ࣮ࢱࡢ࢚࣮ࣛ ᩘࢆ 1 ࡜ࡋ࡚ᐇ㦂ࢆ⾜࠺㸬 4.2 ᐇ㦂⤖ᯝ ㄳồ௳ᩘ N ࢆኚ࠼࡚ ES ࡜ GA ࡢồゎࡲ࡛ࡢᐇ⾜᫬㛫ࢆ ẚ㍑ࡋࡓ⤖ᯝࢆ⾲ 3 ࡟♧ࡍ㸬ES ࡟࠾࠸࡚ N=30 ࡲ࡛ࡣᐇ ್㸪N=40 ௨ୖࡣ⌮ㄽୖࡢ᭱ᝏ್ࢆグ㘓ࡋ㸪GA ࡢᐇ⾜ᅇᩘ ࡣ 20 ࡜ࡋࡓ㸬N=20 ௨ୗ࡛ࡣ ES㸪GA ඹ࡟ᐇ⏝ୖၥ㢟࡞࠸ ್࡛࠶ࡿ㸬N=30 ࢆ㉺࠼ࡿ࡜ ES ࡣᛴ⃭࡟ቑຍࡍࡿࡢ࡟ᑐࡋ ࡚ GA ࡣ⦆ࡸ࠿࡞ቑຍࢆ♧ࡋ㸪ES ࡜ẚ࡭࡚ N=40 ࡛ࡣ⣙ 3,000 ಸ㸪N=50 ࡛ࡣ⣙ 168 ୓ಸ㧗㏿࡟᭱㐺ゎࢆᚓࡓ㸬 ▱㆑ࢹ࣮ࢱࢆ㐺⏝ࡍࡿಶయᩘࢆኚ࠼࡚㸪ồゎࡲ࡛ࡢᐇ⾜ ᫬㛫ࢆẚ㍑ࡋࡓ⤖ᯝࢆ⾲ 4 ࡟♧ࡍ㸬ᐇ⾜ᅇᩘࡣ 50 ࡜ࡋࡓ㸬 ᖹᆒ࣭᭱ᝏᐇ⾜᫬㛫ඹ࡟▱㆑ࢹ࣮ࢱࡣಶయᩘ 200 ࡟ᑐࡋ㸪 100 ಶయ㐺⏝ࡍࡿሙྜࡀ᭱㐺࡛࠶ࡾ㸪▱㆑ࢹ࣮ࢱࢆ㐺⏝ࡋ. ᮏ✏࡛ࡣ㸪ᾘ㎸ฎ⌮ၥ㢟ࢆ㒊ศ࿴ၥ㢟࡜ᐃ⩏ࡋ㸪GA ࢆ ⏝࠸ࡓゎἲ࡟ࡘ࠸࡚඲ᩘ᥈⣴࡜ GA ࡢ㏿ᗘẚ㍑ࢆ⾜࠸㸪ࡑ ࡢ᭷⏝ᛶࢆ♧ࡋࡓ㸬ࡉࡽ࡟㸪GA ࡟⤒㦂࡟ᇶ࡙ࡃ▱㆑ࢆά ⏝ࡍࡿᡭἲࢆᥦ᱌ࡋ㸪㏿ᗘホ౯ࢆ⾜ࡗࡓ㸬ࡑࡢ⤖ᯝ㸪ㄗࡗ ࡓㄳồ㔠㢠ࢆ⤠ࡾ㎸ࢇࡔሙྜ࡛ࡶ GA ࡛ࡣ᭱㐺ゎࢆồࡵࡿ ࡇ࡜ࡀ࡛ࡁ㸪▱㆑ࢹ࣮ࢱࢆ㐺⏝ࡍࡿࡇ࡜࡛㏿ᗘྥୖ࡟ࡶຠ ᯝࡀ࠶ࡿࡇ࡜ࢆ♧ࡋࡓ㸬. ཧ⪃ᩥ⊩ 1) 㒊ศ࿴ၥ㢟 http://ja.wikipedia.org/wiki/%E9%83%A8%E5%88%86%E5%92%8C %E5%95%8F%E9%A1%8C (cited Mar.24, 2013). 2) ⚟⏣࿴┿㸪ⴗཎᩧ㸪୰᳃┾⌮㸬ࢼࢵࣉࢨࢵࢡၥ㢟ࡢ☜⋡࢔ࣝ ࢦࣜࢬ࣒ࡢゎᯒ㸬ᩘ⌮ゎᯒ◊✲ᡤㅮ✲㘓 947 ᕳ, pp. 162-171 (1996). 3) 㛗ᑿᬛᬕⴭ, ͇᭱㐺໬࢔ࣝࢦࣜࢬ࣒͇, ᫛᫭ᇽ (2006). 4) Ṋ⏣⏤⨾㸪ዟ⏤㍜㸪ᓊ⏣㝯ど㸪బ⸨⿱஧㸬ᾘ㎸ฎ⌮ၥ㢟࡬ࡢ GA ࡢ㐺⏝࡜ࣁ࣑ࣥࢢ㊥㞳ࢆ⪃៖ࡋࡓᒁᡤ᥈⣴⬟ຊࡢྥୖ࡟ࡘ࠸ ࡚㸬㐍໬ィ⟬ࢩ࣏ࣥࢪ࣒࢘ 2013. 5) D.E.Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning", Addison-Wasley Publishing Company (1989). 6) Yuji Sato, Yusuke Oku, Masanori Fukuda. Applying GA with Local Search by Taking Hamming Distances into Consideration to Credit Erasure Processing Problems. pp.1183-1190 GECCO-2014.. ࡞࠸ሙྜ࡜ẚ࡭㸪2 ಸ⛬ᗘࡢฎ⌮㏿ᗘྥୖࢆ♧ࡋࡓ㸬. ⓒ 2014 Information Processing Society of Japan. 2.

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