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2U-01｡｡ｵｭｲｱｵ｡ｹｽ､靉ﾑ､ｷ､ｿﾌﾈｱﾖ･｢･�ｴ･�ｺ･爨ﾋ､隍�nTSP､ﾎｲ｡､ﾋｴﾘ､ｹ､�｡ﾆ､

IA for nTSP with memory mechanism

眛ｴﾖｰｦｹｸ｡｡ｱ｣ﾁ�ﾖ｡｡ｻｳﾅﾄｹｧｼ｣

Naruaki Toma(E-mail:tnal@eva.ie.u-ryukyu.ac.jp), Satoshi Endo, Koji Yamada

ﾎｰｵ蠶邉ﾘｹｩｳﾘﾉ�

Faculty of Engineering, University of the Ryukyus

｡｡｡耄ﾜｼ｡｡�

｣ｱ｡･､ﾏ､ｸ､皃ﾋ

｣ｲ｡･ﾌﾈｱﾖ･｢･�ｴ･�ｺ･�

｣ｳ｡･nTSP､ﾋﾂﾐ､ｹ､�IA､ﾎﾀﾟｷﾗ

｣ｴ｡･､ﾀ､ﾞ､ｷﾌ萃�

｣ｵ｡･ｵｭｲｱ､ﾎﾍﾑ

｣ｶ｡･ｼﾂｸｳ

｣ｶ｡･｣ｱ｡｡ﾌ萃�ﾟﾄ�

｣ｶ｡･｣ｲ｡｡ｼﾂｸｳｷ�ﾌ

｣ｷ｡･､ｪ､�熙ﾋ

ｻｲｹﾍﾊｸｸ･

｣ｱ｡･､ﾏ､ｸ､皃ﾋ

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ﾀｸﾂﾎｷﾏ､ﾋﾆ篌ﾟ､ｹ､�､･ﾆ･�ｸ･ｧ･ﾈ･ｷ･ｹ･ﾆ･爨ﾇ､｢､�ﾈｱﾖｷﾏ､ﾋ､ﾄ､､､ﾆ｡､ｹｩｳﾘﾅｪｱ�ﾍﾑ､ﾋｴﾘ､ｹ､�ﾄﾇｽﾀｭｵﾚ､ﾓ､ｽ､ﾎﾍｭｸ惕ｭ､ｬｵﾄﾏﾀ､ｵ､�ﾏ､皃ﾆ､､､�･

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ﾋﾜｹﾆ､ﾇ､ﾏ｡､･ﾞ･�ﾁ･ｨ｡ｼ･ｸ･ｧ･ﾈ･ｷ･ｹ･ﾆ･爨ﾋﾂﾐ､ｹ､�ﾇﾅｬｲｽﾌ萃熙ﾎｰ�网ﾇ､｢､�ｬｶﾈｽ茣ｻ｡ｼ･�ｹ･ﾞ･萃�(n-Traveling Salesman Problem; nTSP)､ﾋ､ｪ､ｱ､�ﾀ､ﾞ､ｷﾌ萃熙隍�螟ｲ｡､ﾌﾈｱﾖ･｢･�ｴ･�ｺ･�(Immune Algorithms; IA)､ﾎﾆﾃ､ﾋｵｭｲｱｵ｡ｹｽ､ﾅｻ�ｷ､ｿｸ嵂ﾌﾅｪ､ﾊﾃｵｺﾋ､ﾄ､､､ﾆ､ﾎｹﾍｻ｡､ﾔ､ﾊ､ｦ｡･

==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｲ｡･ﾌﾈｱﾖ･｢･�ｴ･�ｺ･�

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ﾌﾈｱﾖ･ｷ･ｹ･ﾆ･爨ﾈ､ﾏ, ﾀｸﾂﾎﾆ筅ﾋｿｯﾆ�､ｹ､�ｿｼ�ｿﾍﾍ､ﾊﾌ､ﾃﾎ､ﾎｹｳｸｶ､ﾋﾂﾐｱ�､ｹ､�ｿ､皃ﾋ, ｺﾙﾋｦｰ菁ﾁｻﾒ､ﾎｺﾆｹｽﾃﾛ､ﾔ､ﾊ､ﾃ､ﾆｹｳｸｶ､ﾋﾂﾐｱ�､ｹ､�ｳﾂﾎ､ｺﾀｸ､ｷ, ｹｳｸｶ､ﾓｽ�ｹ､�ｸﾂﾎｴﾆｻ�ﾉｱﾒｵ｡ｹｽ､ﾇ､｢､�.ｹｩｳﾘﾅｪｱ�ﾍﾑ､ﾎｰ�网ﾋｿｹ､鬢ﾋ､隍ﾃ､ﾆ･筵ﾇ･�ｽ､ｵ､�ｿﾌﾈｱﾖ･｢･�ｴ･�ｺ･�[2]､ｬ､｢､�｣

==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｳ｡･nTSP､ﾋﾂﾐ､ｹ､�IA､ﾎﾀﾟｷﾗ

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[･ｳ｡ｼ･ﾇ･｣･ｰ､ﾈ･ｪ･ﾚ･�ｼ･ｿ]

･ｳ｡ｼ･ﾇ･｣･ｰ､ﾏ･ﾑ･ｹﾉｽｸｽ､ﾑ､､､�･GA･ｪ･ﾚ･�ｼ･ｿ､ﾏ｡､ｸｵ､ﾋ･ｵ･ﾖ･ﾄ･｢｡ｼｸｹｸｵ[3]､ﾑ､､｡､ﾇ､ｰﾕ､ﾎ2ﾅﾔｻﾔ､ｹ､ｹ､�ﾍﾁｳﾊﾑｰﾛ､ﾂﾁｷ､ﾆ､､､�･

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[ｳﾆﾉｾｲﾁｼﾜﾅﾙ､ﾎｷﾗｻｻ]

ﾌﾈｱﾖ･｢･�ｴ･�ｺ･爨ﾋ､ｪ､､､ﾆ､ﾏ｡｢ﾅｬｱ�ﾅﾙ｡｢ﾎ狃ﾙ｡｢ﾇｻﾅﾙ｡｢ｴ�ﾔﾃﾍ､ﾎ4､ﾄ､ﾎｷﾗｻｻｼﾜﾅﾙ､皃皃�ｬﾍﾗ､ｬ､｢､�｣

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• ﾅｬｱ�ﾅﾙ
  • fitness_i = max_path - (work+penalty)｡｡｡ﾊ｣ｱ｡ﾋ
    • max_path=fitness_i､ｬﾉ鬢ﾋ､ﾊ､鬢ﾊ､､､隍ｦ､ﾊﾄ��
    • work = ｦｲ f_d (P_Si})
    • penalty = ﾊｿﾅﾋﾊｬｶﾈ､ｹ､�ｿ､皃ﾎ･ﾚ･ﾊ･�ﾆ･｣
• ﾎ狃ﾙ
  • ay_v,w = (2､ﾄ､ﾎｹｳﾂﾎ､ﾋｶｦﾄﾌ､ｹ､�醯ｩ､ﾎﾅﾔｻﾔｿ�)/m｡｡｡｡｡ﾊ｣ｲ｡ﾋ
• ﾇｻﾅﾙ
  • c_v = (ﾎ狃ﾙ､ｬ�ﾃﾍTac1､ﾛ､ｨ､ｿｿ�)/pop_size｡｡｡ﾊ｣ｳ｡ﾋ
• ｴ�ﾔﾃﾍ
  • e_v = fitness_i ｡ﾟ (1-ay_v,s) ｡ﾟ (1-c_v)｡｡｡｡｡ﾊ｣ｴ｡ﾋ
    • ay_v,s = ｹｳﾂﾎv､ﾈ･ｵ･ﾗ･�ﾃ･ｵ｡ｼｺﾙﾋｦ､ﾈ､ﾎﾎ狃ﾙ

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nTSP､ﾋﾂﾐ､ｹ､�IA､ﾞ｣ｱ､ﾋｼｨ､ｹ｡･

==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｴ｡･､ﾀ､ﾞ､ｷﾌ萃�

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nTSP､ﾋ､ｪ､ｱ､�ﾀ､ﾞ､ｷﾌ萃熙ﾏ2ｽﾅ､ﾎﾆｱｿｴｱﾟｾ螟ﾋﾆｱｿﾎﾅﾔｻﾔ､ｬｶﾑﾅﾋﾊﾂ､ﾀﾅﾔｻﾔﾇﾛﾃﾖ､ﾇ､｢､�･､ｽ､ﾎﾆ箋ｰｱﾟ､ﾎﾈｾｷﾂﾈ讀ﾋ､隍ﾃ､ﾆ2ﾄﾌ､熙ﾎｰﾛ､ﾊ､�ﾇﾅｬｲ､ｶﾉｽ��､ﾄ｡･

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ｿﾞ｣ｲ(a)､ﾏ､ﾉ､ﾁ､鬢ｫｰ��､ﾎｱﾟ､茣ｷ､ﾆ､ｫ､鯆ｾﾊ�､茣ｹ､�ﾗ･鬣�(c-type)､ｬｺﾇﾅｬｲﾈ､ﾊ､�网ﾇ｡､ｿﾞ｣ｲ(b)､ﾏｳｰｱﾟ､ﾈﾆ箜ﾟ､ﾟ､ﾋｽ茣ｹ､�ﾗ･鬣�(o-type)､ｬｺﾇﾅｬｲﾈ､ﾊ､�网ﾇ､｢､�･､ｳ､ﾎ､隍ｦ､ﾋｰﾛ､ﾊ､�ﾇﾅｬｲ､ｶﾉｽ�ｬﾂｸｺﾟ､ｹ､�ﾀ､ﾞ､ｷﾌ萃熙ﾋ､ｪ､､､ﾆ､ﾏIA､ﾎｵｭｲｱｺﾙﾋｦ､ﾆﾍﾑ､ｹ､�ｳ､ﾈ､ﾋ､隍�ｵｺｬﾍﾆｰﾗ､ﾋ､ﾊ､�ﾈｹﾍ､ｨ､鬢��･

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==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｵ｡･ｵｭｲｱ､ﾎﾍﾑ

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ﾎ狃ﾎﾌ萃熙ｫ､�ﾖ､ｷｲｯﾉｬﾍﾗ､ﾎ､｢､��遉ﾋ｡､ｲ盞釥ﾎｵｭｲｱ､ﾑ､ｹ､�ｳ､ﾈ､ﾇｸ昀ｨﾎﾉ､ｯﾃｵｺﾔ､ﾊ､ｦ､ｳ､ﾈ､ｬｲﾄﾇｽ､ﾇ､｢､�･

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､ｳ､ﾎ､隍ｦ､ﾊﾎ狃萃熙ﾞ｣ｳ､ﾋｼｨ､ｹ｡･ﾆｱｿﾞ､ﾏ｡､IA､ﾋ､隍�ｵｺﾇ､ﾏ｡､ﾌ萃�1､ﾋ､ｪ､､､ﾆｶﾉｽ�ﾇ､｢､�ｬﾌ萃�2､ﾇ､ﾏｺﾇﾅｬｲﾈ､ﾊ､�､ﾎ狃萃熙ﾎﾅｵｷｿﾅｪ､ﾊﾎ网ﾇ､｢､�･ﾌ萃�1､ｵｺ讀ﾋｶﾉｽ�-type､ﾋｼ�ﾂｫ､ｷｻﾏ､皃�ﾈ､ｽ､�鬢ｵ･ﾗ･�ﾃ･ｵ｡ｼｺﾙﾋｦ､ﾋｵｭｲｱ､ｹ､�ｳ､ﾈ､ﾋ､隍遙､ﾅｬｱ�ﾅﾙ､ﾎﾄｴﾀｰ､ﾔ､ﾊ､､ﾊﾌ､ﾎﾃｵｺﾀ､ﾘ､ﾈｰﾜｹﾔ､ｹ､�(ｰ�｡ﾌﾈｱﾖｱ�ﾅ�)｡･､ﾞ､ｿ｡､ﾌ萃�1､ﾎﾃｵｺ讀ﾋｶﾉｽ�ﾈ､ﾊ､ﾃ､ﾆ､､､�o-type､ｭｲｱｺﾙﾋｦ､ﾋｵｭｲｱ､ｹ､�ｳ､ﾈ､ﾋ､隍遙､ﾌ萃�2､ﾋ､ｪ､ｱ､�ｵｺｬｸ昀ｨﾅｪ､ﾋｹﾔ､ﾊ､ｨ､�ﾈｹﾍ､ｨ､鬢��(ﾆ｡ﾌﾈｱﾖｱ�ﾅ�)｡･

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==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｶ｡･ｼﾂｸｳ

｣ｶ｡･｣ｱ｡｡ﾌ萃�ﾟﾄ�

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ﾎ狃萃熙ﾈ､ｷ､ﾆ､ﾀ､ﾞ､ｷﾌ萃熙ﾟﾄ熙ｷ｡､ｵｭｲｱ､ﾎｺﾆﾍﾑ､ﾋ､隍�ｵｺｬﾍﾆｰﾗ､ﾋ､ﾊ､�ｳ､ﾈ､ﾎ､ｫ､皃�･ﾌ萃熙ﾏﾉｽ｣ｱ､ﾎ､隍ｦ､ﾋﾀﾟﾄ熙ｷ｡､ﾅﾔｻﾔﾇﾛﾃﾖ､ﾏｽﾐﾈｯﾅﾔｻﾔ､ﾟ､ﾎﾃ豼ｴ､ﾋﾃﾖ､ｭ｡､ｳｰｱﾟ､ﾈﾆ箜ﾟｾ螟ﾋ､ﾏ6ﾅﾔｻﾔ､ｺ､ﾄ､ﾈ､ｷ､ｿ｡･IA､ﾎ･ﾑ･鬣癸ｼ･ｿ､ﾏﾉｽ~\ref{IA-parameter}､ﾎ､隍ｦ､ﾋﾀﾟﾄ熙ｷ､ｿ｡･

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ｳﾎﾇｧﾊ�ﾋ｡､ﾏｰﾊｲｼ､ﾎ､隍ｦ､ﾋｹﾔ､ﾊ､ｦ｡･

• [Step1]｡｡ｵｭｲｱ､ﾊ､ｷ､ﾎｾﾖ､ﾇc-type､ﾎﾌ萃�1､ｯ｡･
• [Step2]｡｡Step1､ﾎｵｭｲｱ､ﾑ､ｷ､ﾆo-type､ﾎﾌ萃�2､ｯ｡･
• [Step3]｡｡Step2､ﾎｵｭｲｱ､ﾑ､ｷ､ﾆc-type､ﾎﾌ萃�3､ｯ｡･
• [Step4]｡｡Step1､ﾎｵｭｲｱ､ﾑ､ｷ､ﾆc-type､ﾎﾌ萃�3､ｯ｡･｡｡

Step1-4､ﾎﾃｵｺﾎﾍﾍｻﾒ､豕ﾓ､ｹ､�･

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ｰﾊｲｼ､ﾇ､ﾏStep1､_empty｡､Step2､_c｡､Step3､'_oc｡､Step3､'_c､ﾈﾉｽｵｭ､ｹ､�･ｼﾂｸｳ､ﾇ､ﾏｰﾊｲｼ､ﾎ2ﾄﾌ､熙ﾎｵｭｲｱﾍﾑ､ﾋ､隍�ｵｺ昀ｨ､豕ﾓ､ｹ､�･

• Case1 : C_empty => O_c => C'_oc
• Case2 : C_empty => C'_c

==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｶ｡･｣ｲ｡｡ｼﾂｸｳｷ�ﾌ

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ｼﾂｸｳｷ�ﾌ､ﾞ｣ｴ｡､ｿﾞ｣ｵ､ﾋｼｨ､ｹ｡･ｿﾞ｣ｴ､ﾏ､ｽ､�ｾ､�､C_empty(ﾆｱｿﾞｾ�)｡､O_c(ﾆｱｿﾞｺｸﾃ�)｡､C'_oc(ﾆｱｿﾞｺｸｲｼ)｡､C'_c(ﾆｱｿﾞｱｦｲｼ)､ﾎﾃｵｺﾇﾆﾀ､鬢�ｿｺﾇﾎﾉｲﾈ､ｽ､ﾎﾅｬｱ�ﾅﾙ｡､ﾀ､ﾂ蠢ｽ､ｷ､ﾆ､､､�･ｿﾞ｣ｵ､ﾏ3ﾌ萃熙ﾎﾃｵｺ昀ｨ､豕ﾓ､ｷ､ﾆ､ｪ､遙､ｽﾄｼｴ､ﾏｺﾇﾅｬｲ�1､ﾈ､ｷ､ﾆ･ｹ･ｱ｡ｼ･�ｰ､ｷ､ｿﾅｬｱ�ﾅﾙ｡､ｲ｣ｼｴ､ﾏﾀ､ﾂ蠢ｽ､ｷ､ﾆ､､､�･

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ｿﾞ｣ｴ､隍遙､ﾆｱ､ｸc-type､ﾎﾌ萃熙ｳ､ｱ､ﾆｲｯCase1､隍熙簀ﾓﾃ讀ﾇo-type､ﾎﾌ萃熙ｯCase2､ﾎﾊ�､ｬﾅｬｱ�ﾅﾙ｡､ﾀ､ﾂ蠢ｦ､ﾋﾎﾉ､､､ｳ､ﾈ､ｬﾊｬ､ｫ､�･､ｽ､ﾎﾍ�ﾍｳ､ﾈ､ｷ､ﾆ､ﾏﾊﾌ､ﾎﾌ萃熙､､ｿ､ｿ､癸､､筅ｷ､ｯ､ﾏｲ､､ｿﾌ萃�ｬﾂｿ､､､ｿ､皃ﾋｵｭｲｱ､ｬﾀ�､ｵ､�ｿｲﾄﾇｽﾀｭ､ｬ､｢､ｲ､鬢��･

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ｰﾊｾ螟ﾎｷ�ﾌ､ｫ､鬘､ﾎ狃萃熙ﾎﾃｵｺﾋ､ｪ､､､ﾆｲ盞釥ﾎｵｭｲｱ､ﾑ､ｹ､�ｳ､ﾈ､ﾇﾍﾆｰﾗ､ﾋ､ﾇ､ｭ､�ﾈｹﾍ､ｨ､鬢��･

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==> ｺﾇｽ鬢ﾋﾌ皃�

｣ｷ｡･､ｪ､�熙ﾋ

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ﾅｬｱ�･｢･�ｴ･�ｺ･爨ﾎｰ��｡､ﾇ､｢､�ﾈｱﾖ･｢･�ｴ･�ｺ･爨TSP､ﾘﾅｬﾍﾑ､ｷ｡､､ｽ､ﾎｹｩｳﾘﾅｪｱ�ﾍﾑ､ﾋﾂﾐ､ｹ､�ﾄﾇｽﾀｭ､ﾋ､ﾄ､､､ﾆｸ｡ﾆ､､ｷ､ｿ｡･ﾎ狃萃熙ﾈ､ｷ､ﾆ､ﾀ､ﾞ､ｷﾌ萃熙隍�螟ｲ｡､ﾃｵｺﾆｰﾗ､ﾋ､ﾇ､ｭ､�ﾄﾇｽﾀｭ､ｬ､｢､�ｳ､ﾈ､ｨ､ｷ､ｿ｡･ﾆﾃ､ﾋ｡､ｵｭｲｱｵ｡ｹｽ､靉ﾑ､ｹ､�ｳ､ﾈ､ﾇ｡､ﾆｰﾅｪｴﾄｶｭ､ﾋ､ｪ､ｱ､�狃萃熙ﾎｷｫ､�ﾖ､ｷｲ隍ｬﾍﾗ､ﾈ､ｹ､�ﾝﾂ熙ﾋﾂﾐ､ｷ､ﾆﾍｭｸ妤ﾋｵ｡ﾇｽ､ｹ､�ﾈｹﾍ､ｨ､鬢��･ﾊ｣ｿﾎﾌ萃�雍�ﾜ､ﾈ､ｹ､�ﾞ･�ﾁ･ｨ｡ｼ･ｸ･ｧ･ﾈｷﾏ､ﾎﾍｭｸ妤ﾊ･｢･�ｴ･�ｺ･爨ﾈ､ｷ､ﾆ､ﾎIA､ﾎﾍﾑ､ｬｴ�ﾔ､ｵ､��･

==> ｺﾇｽ鬢ﾋﾌ皃�

ｻｲｹﾍﾊｸｸ･

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1. ｿｹ ｰ�ｷ,ﾃﾛｻｳ ﾀｿ,ﾊ｡ﾅﾄ ﾋｭﾀｸ, ﾌﾈｱﾖ･｢･�ｴ･�ｺ･爨ﾋ､隍�ｿﾊｭｴﾘｿﾇﾅｬｲｽ,T.IEE Japan, Vol.117-C, No.5, 1997.
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2. ﾏﾂﾅﾄ ｷｷｲ�,ﾏﾂﾅﾄ ｲﾂｻﾒ, ｻｳﾅﾐ､�ﾓﾃ釥ﾎｿﾊｲｽ､ﾈﾌﾈｱﾖ･ｷ･ｹ･ﾆ･猾ﾀ､ﾋ､ﾄ､､､ﾆ,ｿ�ｲﾊｳﾘ, NO.353, NOVEMBER, 1992
3. ｻｳﾂｼ ｲ晥ｬ｡､ｾｮﾌ� ｵｮｵﾗ｡､ｾｮﾎﾓ ｽﾅｿｮ｡､ ｷﾁｼﾁ､ﾎｰ菁ﾁ､ﾅｻ�ｷ､ｿｰ菁ﾁﾅｪ･｢･�ｴ･�ｺ･爨ﾋｴﾅ､ｯｽ茣ｻ｡ｼ･�ｹ･ﾞ･萃熙ﾎｲ｡｡､ｿﾍｹｩﾃﾎﾇｽｳﾘｲ�､Vol.7, No.6, Nov. 1992
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==> ｺﾇｽ鬢ﾋﾌ皃�

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ｰ�ﾄﾁｰ､ﾎ･ﾚ｡ｼ･ｸ(ｸｶｹﾆｽｸ)､ﾋﾌ皃�

･ﾛ｡ｼ･爭ﾚ｡ｼ･ｸ ､ﾘﾌ皃�