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エルボおよびベンドを考慮した配管設計アルゴリズム
࢚ࣝ࣎࠾ࡼࡧ࣋ࣥࢻࢆ⪃៖ࡋࡓ㓄⟶タィ࢔ࣝࢦࣜࢬ࣒
学正会員

安藤悠人＊

正会員

木村*

元＊*

Ꮫṇ఍ဨ Ᏻ ⸨ ᝆ ே    ṇ఍ဨ ᮌ ᮧ  ඖAn Automatic Piping Algorithm including Elbows and Bendsby  Yuto Andoࠊ Student Member  Hajime Kimuraࠊ Member  

SummaryNowadays, the pipe arrangement has been enabled to be more efficient and economical by development and spread ofCAD(Computer-Aided Design). However, it is difficult to design a piping layout automatically because there are many regulations
and functional design rules which must be satisfied. We propose an automatic routing method for simple pipes including elbows andbends. In a practical design of a piping layout, there are many bends connecting straight eccentric pipes which have gaps within thepipes’ diameter. However, no precedence automatic piping algorithm has been taken into account pipelines with such bends. The
proposed method finds piping routes making use of not only elbows but the bends in order to minimize costs of the path connecting
start point to goal point, while avoiding obstacles such as structures, equipments and the other circuits. In our approach, we regard
the piping route design problem as a routing problem in a directed and weighted graph. Note that the nodes in the proposed graphhave state variables not only locations but directions of the pipes. This graph can easily express the bends as simple edges, and thenthe routing algorithm can easily handle the bends. In addition, the presented method has specifications that the sizes of each cell,which is generated by decomposing of a free space, are not restricted within the diameter of the pipe. The routing algorithm uses
Dijkstra’s method to provide candidate paths. The efficiency of the proposed method is demonstrated through several experimentsᩓ໬ࡋ࡚᥈⣴ࡍࡿᡭἲࡀᏑᅾࡍࡿ㸬ࡇࡇ࡛㸪✵㛫ࢆ㞳ᩓ໬ࡍ
1. ⥴  ゝࡿᡭἲ࡜ࡣ㸪タィᑐ㇟࡜࡞ࡿ✵㛫ࢆࣃ࢖ࣉ┤ᚄ௨ୖࡢᖜࢆ᭷ࡍࡿ࣓ࢵࢩ࡛ࣗศ๭ࡍࡿ࢔ࣉ࣮ࣟࢳࢆព࿡ࡍࡿ㸬ࡲࡎ㸪✵㛫㏆ᖺ㐀⯪ᴗ⏺࡛ࡣ㸪᝟ሗฎ⌮ᢏ⾡ࡢⓎ㐩࡟క࠸㸪ࡇࢀࢆ฼ࢆ㞳ᩓ໬ࡋ࡞࠸࢔ࣉ࣮ࣟࢳࢆ㐺⏝ࡋ࡚࠸ࡿ◊✲౛࡜ࡋ࡚ࡣ⏝ࡍࡿࡇ࡜࡛సᴗࡢ┬ຊ໬ࢆᅗࡗ࡚ࡁࡓ㸬ࡋ࠿ࡋ㓄⟶タィస㬇࣭ᒣཱྀࡽ 1)㸪ụᖹࡽ 2)ࡢ◊✲ࡀᣲࡆࡽࢀࡿ㸬ࡇࢀࡽࡢ࢔ࣉᴗࡣᮍࡔ⇍⦎ᢏ⾡⪅ࡢ⤒㦂࡟㢗ࡿ㒊ศࡀከࡃ㸪タィసᴗࡢ⮬࣮ࣟࢳ࡛ࡣ⤒㊰᥈⣴ࡢ㝿ࡢィ⟬㔞ࢆᢚ࠼ࡿࡇ࡜ࡀ࡛ࡁࡿࡀ㸪ື໬࡟ࡣ⮳ࡗ࡚࠸࡞࠸㸬ࡇࡢཎᅉ࡜ࡋ࡚㸪ඛ⾜◊✲ࡸ᪤Ꮡࡢ」㞧࡞⤒㊰࡟ᑐᛂ࡛ࡁ࡞࠸࡜࠸ࡗࡓၥ㢟ࡀ⏕ࡌࡿ㸬୍᪉࡛㸪⮬ື㓄⟶ࢩࢫࢸ࣒ࡢ⤒㊰᥈⣴ᛶ⬟ࡀ୙༑ศ࡛࠶ࡿࡇ࡜ࡀᣲ✵㛫ࡢ㞳ᩓ໬ࢆ⾜࠺࢔ࣉ࣮ࣟࢳࢆ㐺⏝ࡋ࡚࠸ࡿ◊✲࡜ࡋ࡚㸪ࡆࡽࢀࡿ㸬ࡑࡇ࡛ᮏ◊✲࡛ࡣ㸪㓄⟶タィసᴗࡢ⮬ື໬࡬ྥࡅ

Asmara ࡽ 3), Paulo ࡽ 4)㸪Park ࡽ 5)㸪ఀ⸨ࡽ 6)ࡢ◊✲ࡀᣲ࡚㸪㓄⟶タィၥ㢟ࢆࢢࣛࣇୖࡢ⤒㊰᥈⣴ၥ㢟࡬ᖐ╔ࡍࡿࡇ࡜ࡆࡽࢀࡿ㸬ࡇࢀࡽࡢ࢔ࣉ࣮ࣟࢳࡣ㸪ྛ࣓ࢵࢩࣗ࡟␗࡞ࡿࢥࢫ࡟ࡼࡾ᭱㐺࡞⤒㊰ࢆぢࡘࡅฟࡍ᪂ࡋ࠸ᡭἲࡢᥦ᱌ࢆ⾜࠺㸬ࡉࢺࢆタᐃࡍࡿࡇ࡜࡟ࡼࡾ㸪సᴗဨ⏝ࡢ⤒㊰ࢆ㑊ࡅࡘࡘቨ㝿࡟ࡽ࡟㸪ᮏㄽᩥ࡛ࡣ✵㛫ࢆᒁᡤⓗ࡟ᩳࡵ࡟㏻ࡿ S Ꮠᆺࡢࣃ࢖ࣃ࢖ࣉࢆ㓄⨨ࡍࡿࡇ࡜ࡀྍ⬟࡟࡞ࡿ࡞࡝ࡢඃࢀࡓ≉ᚩࢆ᭷ࣉࣆ࣮ࢫࢆ࣋ࣥࢻ࡜࿧⛠ࡋ㸪ᥦ᱌ᡭἲ࡛ࡣ✵㛫ࢆ┤ゅ࡟᭤ࡀࡋ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪ඛ⾜◊✲࡛ࡢᡭἲࡣ㸪✵㛫ࢆศ๭ࡍࡿ࣓ࡿ࢚ࣝ࣎ࡔࡅ࡛࡞ࡃ㸪࣋ࣥࢻࡶྵࡵࡓ⤒㊰᥈⣴ࢆ⾜࠺ࡇ࡜ࡀࢵࢩࣗࡢᖜࡀࣃ࢖ࣉࡢᚄ࡟౫Ꮡࡋ࡚࠸ࡿࡢ࡛㸪ᐇ㝿ࡢ㓄⟶タྍ⬟࡜࡞ࡿ㸬ィၥ㢟ࢆྲྀࡾᢅ࠺㝿࡟㸪ጞⅬ࣭⤊Ⅼࡸ㞀ᐖ≀࡞࡝ࡀࣃ࢖ࣉࡢ㓄⟶タィၥ㢟࡟࠾ࡅࡿඛ⾜◊✲࡛ࡢ࢔ࣉ࣮ࣟࢳ࡜ࡋ࡚㸪✵ᚄ࡟౫Ꮡࡋࡓ఩⨨࡟Ꮡᅾࡍࡿ࡜ࡣ㝈ࡽ࡞࠸࡞࡝ࡢ⌮⏤࠿ࡽ㸪㛫ࢆ㞳ᩓ໬ࡏࡎ࡟ࣃ࢖ࣉࡢ⤒㊰ࢆ᥈⣴ࡍࡿᡭἲ࡜㸪✵㛫ࢆ㞳⤒㊰ࡢ⮬ື⏕ᡂࡀ୙ྍ⬟࡜࡞ࡿሙྜࡀ⪃࠼ࡽࢀࡿ㸬ࡑࡇ࡛ᮏ◊✲࡛ࡣ㸪✵㛫ࢆศ๭ࡍࡿ࣓ࢵࢩࣗࡢᖜࡀࣃ࢖ࣉࡢᚄ࡟౫Ꮡ㸨஑ᕞ኱Ꮫ኱Ꮫ㝔ᕤᏛ◊✲㝔ᾏὒࢩࢫࢸ࣒ᕤᏛ㒊㛛

原稿受理
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7月
29 
日 ᪥ཎ✏ཷ⌮ᖹᡂ᭶ࡋ࡞࠸㸪ࡼࡾᐇ⏝ⓗ࡞ᡭἲࢆᥦ᱌ࡍࡿ㸬ࡉࡽ࡟ᮏ◊✲ࡢ⊂⮬ࡢ࢔ࣉ࣮ࣟࢳ࡜ࡋ࡚㸪⤒㊰୰࡟✵㛫ࢆ日本船舶海洋工学会論文集 第 15 号

220

2012 年 6 月

ᒁᡤⓗ࡟ᩳࡵ࡟㏻ࡿ S Ꮠࡢ⤒㊰ࢆ᥈⣴ࡢ⪃៖࡟ධࢀࡿ㸬ࡇ࠙ࣃ࢖ࣉࡢ㓄⨨ྍ⬟࡞᪉ྥࠚࣃ࢖ࣉࡣ㸪ᒁᡤⓗ࡟౑⏝ࡉࢀࡿࡢࡼ࠺࡞⤒㊰ࢆᮏㄽᩥ࡛ࡣ࣋ࣥࢻ࡜࿧⛠ࡍࡿ㸬ࡇࡢࡼ࠺࡞ࣃ࣋ࣥࢻ㒊ศࢆ㝖࠸࡚㸪タィᑐ㇟࡛࠶ࡿ┤᪉యࡢྛ㎶࡟ᖹ⾜࡞࢖ࣉࣆ࣮ࢫࡣᐇ㝿ࡢ㓄⟶⤒㊰࡟࠾࠸࡚㸪࢚ࣝ࣎ࡢࡳ࡛ࡣ⌧ᐇ᪉ྥ࡬㓄⨨ࡉࢀࡿࡶࡢ࡜ࡍࡿ㸬ࡲࡓ㸪㐍⾜᪉ྥࢆኚ࠼ࡿ㝿ࡣⓗ࡞ᑐᛂࡀ࡜ࢀ࡞࠸ಶᡤ࡟౑⏝ࡉࢀ࡚࠸ࡿ㸬JIS つ᱁࡟ᑐᛂࡋࡓ 90 ᗘࡢ࢚ࣝ࣎ࢆ౑⏝ࡍࡿࡶࡢ࡜ࡍࡿ㸬㓄⮬ືタィ࡟࠾࠸࡚㸪࣋ࣥࢻࡢ⪃៖ࢆ⾜ࢃ࡞࠸ሙྜ㸪Fig.1⟶タィ࡟࠾࠸࡚ࡣ㸪ಖᏲ⟶⌮ࡸᕤసࡢᐜ᫆ࡉ㸪࠾ࡼࡧࣃ࢖ࣉࡀ♧ࡋ࡚࠸ࡿࡼ࠺࡞㎽ᅇ⤒㊰ࢆ⏕ᡂࡍࡿྍ⬟ᛶࡀ࠶ࡿ㸬ᨭᣢࡸᶵჾ㓄⨨ࡢ㒔ྜୖ㸪ୖグࡢタᐃࡀᇶᮏ࡜࡞ࡗ࡚࠸ࡿ㸬

Fig.1 ࡢ⤒㊰ࡣ㸪ࣃ࢖ࣉ┤ᚄࡀࣃ࢖ࣉࡢጞⅬ࣭⤊Ⅼࡢ⦪᪉ྥ࠙ࣃ࢖ࣉࡢጞⅬ࣭⤊Ⅼ࣭┤ᚄࠚᑐ㇟࡜ࡍࡿࣃ࢖ࣉࡢጞⅬࡢ఩ࡢࢠࣕࢵࣉࡼࡾࡶ኱ࡁ࠸ሙྜ࡟⋓ᚓࡉࢀࡿゎࢆ♧ࡋ࡚࠸ࡿ㸬⨨ᗙᶆ࡜ࡑࡇ࠿ࡽࣃ࢖ࣉࡀఙࡧ࡚࠸ࡿ᪉ྥ࣋ࢡࢺࣝ㸪࠾ࡼࡧࡇࡢࡼ࠺࡞᮲௳ࡢሙྜ㸪⤒㊰୰ࡢ┤ᚄࢆᆒ୍࡟ಖࡘᙧ≧ไ⣙⤊Ⅼࡢ఩⨨ᗙᶆ࡜ࡑࡇ࠿ࡽࣃ࢖ࣉࡀఙࡧ࡚࠸ࡿ᪉ྥ࣋ࢡࢺࢆᏲࡿࡓࡵ㸪⋓ᚓࡉࢀࡿゎࡣ㎽ᅇࡋࡓ⤒㊰࡜࡞ࡗ࡚࠸ࡿ㸬ࡑࣝࡀ୚࠼ࡽࢀ࡚࠸ࡿࡶࡢ࡜ࡍࡿ㸬ࡲࡓࣃ࢖ࣉࡢ┤ᚄࡶணࡵ୚ࡇ࡛ᥦ᱌ᡭἲ࡛ࡣ㸪Fig.1 ࡢࡼ࠺࡞࢚ࣝ࣎ࡔࡅ࡛ࡣᑐᛂࡀ⌧࠼ࡽࢀ࡚࠸ࡿ㸬ᐇⓗ࡛࡞࠸ゎࢆ㑊ࡅ㸪Fig.2 ࡢࡼ࠺࡞࣋ࣥࢻࢆ౑⏝ࡋࡓ⌧ᐇ࠙㞀ᐖ≀ࡢᗄఱ᝟ሗࠚタィᑐ㇟✵㛫ෆ࡟Ꮡᅾࡍࡿᵓ㐀㒊ᮦࡸⓗ࡞ゎࡢ⮬ື⏕ᡂࢆヨࡳࡿ㸬ᮏㄽᩥ࡛ࡣ㸪࠸ࡃࡘ࠿ࡢࢩ࣑ࣗᶵჾ࡞࡝ࡢ఩⨨᝟ሗࡀ୚࠼ࡽࢀ࡚࠸ࡿࡶࡢ࡜ࡍࡿ㸬タィᑐ㇟࣮ࣞࢩࣙࣥࢆ㏻ࡌ࡚ᮏᡭἲࡢ᭷⏝ᛶࢆ᳨ドࡍࡿ㸬ࡢࣃ࢖ࣉࡣ㸪ࡇࢀࡽ࡜ࡢᖸ΅ࢆチࡉࢀ࡞࠸㸬
࠙㏻㊰✵㛫ࠚ஌⤌ဨ⏝㏻㊰࡜ࡋ࡚౑⏝ࡍࡿ࡜ண᝿ࡉࢀࡿタィᑐ㇟✵㛫ෆ࡛ࡢ㡿ᇦࡀணࡵ୚࠼ࡽࢀ࡚࠸ࡿࡶࡢ࡜ࡍࡿ㸬ࡇࡢ㡿ᇦෆ࡬ࣃ࢖ࣉࢆ㏻ࡍࡇ࡜ࡣ㸪ᴟᗘ࡞㎽ᅇ⤒㊰࡜࡞ࡿሙྜࢆ㝖࠸࡚㸪ᴟຊᅇ㑊ࡋ࡞ࡅࢀࡤ࡞ࡽ࡞࠸㸬㏻㊰✵㛫࡟㛵ࡋ࡚ࡣ㸪ᮏㄽᩥ࡛ࡢᐇ㦂࡛ࡣྲྀࡾᢅࡗ࡚࠸࡞࠸ࡀ㸪㏻㊰✵㛫࡟ࢥࢫࢺࢆタᐃࡍࡿࡇ࡜࡛㸪≉ᐃࡢ✵㛫࡬ࡢࣃ࢖ࣉࡢ㏻㐣ࢆ㜵ࡄᡭἲࡣ㸪Paulo ࡽ 4)㸪ఀ⸨ࡽ 6)࡟ࡼࡾ᪤࡟♧ࡉࢀ࡚࠸ࡿ㸬
Fig.1 An example of a pipe route with only elbows

࠙ࣃ࢖ࣉࣛࢵࢡ✵㛫ࡢᨭᣢࠚணࡵࣃ࢖ࣉࢆ㏻ࡍࡇ࡜ࢆ๓ᥦ࡜
ࡋ࡚⏝ពࡉࢀࡓ✵㛫ࡸ㸪ࣃ࢖ࣉࣛࢵࢡࡀタ⨨ࡋࡸࡍ࠸ኳ஭௜
㏆ࡸቨ௜㏆ࡢ✵㛫ࡀᨭᣢࡉࢀ࡚࠸ࡿࡶࡢ࡜ࡍࡿ㸬ࡇࡢࡼ࠺࡞
✵㛫ࢆᮏ◊✲࡛ࡣࠕࣃ࢖ࣉࣛࢵࢡ✵㛫ࠖ࡜࿧ࡪ㸬タィᑐ㇟✵㛫ෆ࡟ࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆタ⨨ࡍࡿࡇ࡜࡛㸪ࣃ࢖ࣉࢆቨ㝿࡟タ⨨ࡍࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ㸬タィᑐ㇟ࡢࣃ࢖ࣉࡣ㸪ࡇࡢࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆ㏻ࡿࡇ࡜ࡀᮃࡲࡋ࠸㸬

Fig.2 An example of a pipe route with a bend௨ୖࡢ᮲௳ࡢࡶ࡜࡛㸪௨ୗࡢࣃ࣓࣮ࣛࢱࢆ᥈⣴ࡍࡿ㸸࠙ࣃ࢖ࣉ⤒㊰ࠚタィᑐ㇟࡛࠶ࡿ┤ᚄࡀኚ໬ࡏࡎ㸪ศᒱࡢ↓࠸
2. 㓄⟶⤒㊰タィၥ㢟ࡢࣔࢹࣝ໬ ᮏࡢࣃ࢖ࣉࡢጞⅬ࡜⤊Ⅼࢆ⤖ࡪ⤒㊰ࡣ㸪㏵୰ࡢ࢚ࣝ࣎࡜࣋ࣥࢻࡢᗙᶆࣜࢫࢺ࡛⾲ࡉࢀࡿ㸬㓄⟶タィࢆ⾜࠺㝿࡟㸪௨ୗࡢ᮲௳ࢆ௬ᐃࡍࡿ㸸ࣃ࢖ࣉ⤒㊰ࡢタィ┠ᶆࡣ㸪௨ୗࡢ࡜࠾ࡾ࡛࠶ࡿ㸸࠙タィᑐ㇟✵㛫ࠚࣃ࢖ࣉࢆ㓄⨨ྍ⬟࡞✵㛫ࡢ⠊ᅖࡀணࡵ୚࠼1)ࣃ࢖ࣉ㛗ࡀ▷࠸ࡇ࡜ࡽࢀ࡚࠸ࡿࡶࡢ࡜ࡍࡿ㸬ᮏ◊✲࡛ࡣࡇࡢ✵㛫ࢆ┤᪉య࡟㝈ᐃ2)࢚ࣝ࣎࠾ࡼࡧ࣋ࣥࢻࡢᩘࡀᑡ࡞࠸ࡇ࡜ࡋ࡚࠸ࡿ㸬3)㏻㊰✵㛫୰ࢆ㏻ࡿࡇ࡜ࢆᴟຊᅇ㑊ࡍࡿࡇ࡜࠙ᑐ㇟࡜ࡍࡿࣃ࢖ࣉࠚᮏၥ㢟タᐃ࡛ࡣ㸪ศᒱࢆᣢࡓࡎ㸪࠿ࡘ4)㐲ᅇࡾ࡟࡞ࡽ࡞࠸㝈ࡾࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆ㏻ࡿࡇ࡜

ጞⅬ࠿ࡽ⤊Ⅼࡲ࡛┤ᚄࡀኚ໬ࡋ࡞࠸㸯ᮏࡢࣃ࢖ࣉࢆᑐ㇟࡜ࡇࢀࡽࡢ㓄⟶タィၥ㢟ࢆ༢┠ⓗ᭱㐺໬ၥ㢟࡬ᐃᘧ໬ࡍࡿࡍࡿ㸬」ᩘࣃ࢖ࣉࢆタィᑐ㇟࡜ࡍࡿሙྜࡣ㸪㓄⨨ࢆ⤊࠼ࡓ௚ࡓࡵ㸪ࣃ࢖ࣉࡢ㛗ࡉ࡟ẚ౛ࡋࡓࢥࢫࢺ㸪࢚ࣝ࣎࠾ࡼࡧ࣋ࣥࢻࡢࣃ࢖ࣉࢆ㞀ᐖ≀࡜ࡳ࡞ࡋ࡚㸯ᮏࡢࣃ࢖ࣉࡢ⤒㊰タィࢆ⧞ࡢࢥࢫࢺ㸪㏻㊰✵㛫ࡸࣃ࢖ࣉࣛࢵࢡࢆ㏻ࡿሙྜࡢࢥࢫࢺࢆࡑ

ࡾ㏉ࡍࡇ࡜࡛ᑐᛂࡍࡿ㸬ࣃ࢖ࣉࣛࢵࢡࢆ౑⏝ࡍࡿࡇ࡜࡛㸪ኴࢀࡒࢀ୚࠼࡚࠾ࡃࡶࡢ࡜ࡍࡿ㸬ࣃ࢖ࣉ⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒ࡉࡢ␗࡞ࡿ」ᩘᮏࡢࣃ࢖ࣉࡢ㧗ࡉࢆᥞ࠼ࡿ➼࡟ࡘ࠸࡚ࡣ 5.3

ࡣ㸪ୖグࢥࢫࢺࡢྜィࡀ᭱ᑠ࡟࡞ࡿ᭱㐺࡞⤒㊰ࢆ᥈⣴ࡍࡿ㸬⠇࡟࡚㏙࡭ࡿ㸬エルボおよびベンドを考慮した配管設計アルゴリズム

3. 㓄⟶⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒

221ࡢᑍἲศࡔࡅఙࡤࡍࡇ࡜࡟┦ᙜࡍࡿࡢ࡛㸪ࡑࡢ㊥㞳࡟ẚ౛ࡋࡓࢥࢫࢺࡀຍ⟬ࡉࢀࡿ㸬ࡉࡽ࡟ Current node ࠿ࡽ┤㐍ࡋࡓሙ

3. 1 ᑐ㇟✵㛫ࡢ࣓ࢵࢩࣗศ๭࡟ࡼࡿࢢࣛࣇ⾲⌧ྜ࡟㞀ᐖ≀࡜ࡢᖸ΅ุᐃࡀ⾜ࢃࢀࡿ㸬ᖸ΅ุᐃࡣ㸪ࣃ࢖ࣉ࡟ᮏ◊✲࡛ࡣ⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚㸪ඛ⾜◊✲࡛ᥦ᱌ෆ᥋ࡍࡿ᭱ᑠࡢ┤᪉య࡜㞀ᐖ≀࡜ࡢᖸ΅ࢆ㸪ࡑࢀࡒࢀࡢᗙᶆࡋ࡚࠸ࡿࢲ࢖ࢡࢫࢺࣛἲࢆ㐺⏝ࡋࡓ࢔ࣝࢦࣜࢬ࣒ࢆ౑⏝ࡍࢆẚ㍑ࡍࡿࡇ࡜࡛⾜࠺㸬ᖸ΅ࡋ࡞࠸࡜☜ㄆࡉࢀࡓሙྜ㸪᪂ࡓ7)ࡿ 㸬ࡇࡢ࢔ࣝࢦࣜࢬ࣒࡛ࡣ㓄⟶⤒㊰᥈⣴ၥ㢟ࢆ㔜ࡳ௜ࡁࢢ࡞㑄⛣ඛೃ⿵࡜࡞ࡿ㸬ࣛࣇ㸦ࢿࢵࢺ࣮࣡ࢡ㸧ୖࡢ⤒㊰᥈⣴ၥ㢟࡟ᖐ╔ࡉࡏࡿࡇ࡜࡛ḟ࡟㸪࢚ࣝ࣎ࢆ⤒⏤ࡋ࡚ᕥྑ࡟᭤ࡀࡿሙྜ࡛ࡢ㑄⛣ඛࣀ࣮᭱ᑠࢥࢫࢺࡢ⤒㊰ࢆ᥈⣴ࡋ࡚࠸ࡿ㸬ࡲࡓ㸪ࡇࡢ࢔ࣝࢦࣜࢬ࣒

ࢻࡣ Next node2 ࠾ࡼࡧ Next node3 ࡛♧ࡉࢀ࡚࠸ࡿ㸬ࡇࢀࡽࡣ㸪タィᑐ㇟✵㛫ࢆ᱁Ꮚ≧࡟ศ๭ࡍࡿ㝿࡟㸪㔜ࡳ௜ࡁࢢࣛࣇࡢࣀ࣮ࢻࡣ┤⟶࡜࢚ࣝ࣎ࢆ㓄⨨ࡍࡿࡇ࡜࡛㑄⛣ྍ⬟࡞᭱ࡶࡢࣀ࣮ࢻ㸦⠇Ⅼ㸧ࢆ≉ᚩ௜ࡅࡿ≧ែ㔞࡜ࡋ࡚㸪᱁Ꮚศ๭ࡋࡓ

㏆࠸఩⨨࡟Ꮡᅾࡍࡿ㸬࢚ࣝ࣎ࢆ౑⏝ࡍࡿሙྜࡢᖸ΅ุᐃࡣ㸪ྛ᱁Ꮚࡢ఩⨨ᗙᶆ࡟ຍ࠼㸪ࡑࡢ᱁Ꮚࢆ㏻ࡿࣃ࢖ࣉࡢ᪉ྥࢆ⪃࢚ࣝ࣎࡟ෆ᥋ࡍࡿ᭱ᑠࡢ┤᪉య࡜㞀ᐖ≀࡜ࡢᖸ΅ุᐃࢆ⾜៖ࡍࡿࡇ࡜࡟ࡼࡾ㸪᱁Ꮚ㛫㝸ࡀࣃ࢖ࣉࡢ┤ᚄ࡟౫Ꮡࡋ࡞࠸࡜࠺㸬ࡉࡽ࡟㸪ࢥࢫࢺ࡜ࡋ࡚ࣀ࣮ࢻ㛫ࡢ࣐ࣥࣁࢵࢱࣥ㊥㞳࡟࢚࠸ࡗࡓඃࢀࡓ≉ᚩࢆ᭷ࡋ࡚࠸ࡿ㸬ࡉࡽ࡟ᮏ◊✲࡛ࡣඛ⾜◊✲ࣝ࣎࡟ᛂࡌࡓ್ࢆ௜୚ࡍࡿ㸬௨ୖࡢࡼ࠺࡞ฎ⌮ࢆ⾜࠺ࡇ࡜࡛7)࡛ࡢ㓄⟶⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒ࢆ࢚ࣝ࣎ࡔࡅ࡛࡞ࡃ࣋ࣥ

Current node ࠿ࡽࡢ㑄⛣ඛࣀ࣮ࢻࢆ⋓ᚓࡋ࡚࠸ࡃ㸬㑄⛣ඛࡢࢻࡶ⪃៖ࡍࡿ௙ᵝ࡟ᣑᙇࡋ࡚࠸ࡿ㸬ࡲࡓ㸪ࣀ࣮ࢻ㛫ࢆ⤖ࡪࣜࣀ࣮ࢻࡲ࡛ࡢ㊥㞳ࢆࡑࡢ㒔ᗘィ⟬ࡋ࡚࠸ࡃࡢ࡛㸪࣓ࢵࢩࣗᖜࣥࢡ㸦࢚ࢵࢪ㸧ࡣ㸪ࣀ࣮ࢻ㛫ࡢ㊥㞳࡟ẚ౛ࡋࡓࢥࢫࢺ࡟ࡼࡾࡀ➼㛫㝸࡛࡞ࡃ࡜ࡶฎ⌮ࡀྍ⬟࡛࠶ࡿ㸬≉ᚩ௜ࡅࡽࢀࡿ㸬ࡉࡽ࡟㸪࢚ࣝ࣎ࡶࡋࡃࡣ࣋ࣥࢻࢆ౑⏝ࡍࡿሙྜࡣ㸪ࡑࢀࡽࡢࣃ࢖ࣉࣆ࣮ࢫࢆ౑⏝ࡋ࡚࠸ࡿࣜࣥࢡ࡟ᮦᩱ㈝ࢆ♧ࡍ㏣ຍࢥࢫࢺࡀຍ⟬ࡉࢀ࡚࠸ࡿ㸬

3. 2 ࣋ࣥࢻࡢࢢࣛࣇ⾲⌧᪉ἲࡢᥦ᱌ᮏᡭἲ࡛ࡣ㸪ඛ⾜◊✲࡛ࡣ⪃៖ࡉࢀ࡚࠸࡞࠿ࡗࡓ࣋ࣥࢻࢆ⤒⏤ࡋࡓሙྜࡢ㑄⛣ඛ౛ࡶ᥈⣴ࡋ࡚࠸ࡿ㸬ᮏㄽᩥ࡛࿧⛠ࡋ࡚࠸ࡿ࣋ࣥࢻࡣ㸪ࣃ࢖ࣉ᭤ࡆຍᕤᶵࢆ౑⏝ࡋ࡚┤⟶ࢆ௵ពࡢゅᗘ࡛᭤ࡆࡿࡇ࡜࡛ᕤసྍ⬟࡞ࣃ࢖ࣉࣆ࣮ࢫ࡛࠶ࡿ㸬ඛࡎ㸪࣋ࣥࢻࢆࢢࣛࣇ⾲⌧ࡍࡿ࡟࠶ࡓࡾ㸪Fig.4 ࡛♧ࡋ࡚࠸ࡿࡼ࠺࡟࣋ࣥࢻࢆୖୗ࡟఩⨨ࡍࡿ᭤⟶㒊ศ࡜㸪ࡑࡢ୰㛫࡟఩⨨ࡍࡿ┤⟶㒊ศࡢ 3 ࡘࡢࣃ࣮ࢶ࡟ศ๭ࡋ࡚⪃࠼ࡿ㸬

Fig.3 A grid partioning network model in case ofstraight and elbows

Fig.3 ࡣ⤒㊰୰࡟࠾࠸࡚㸪┤㐍࠾ࡼࡧ࢚ࣝ࣎ࢆ㓄⨨ࡋ࡚ᕥྑ࡟᪉ྥࢆኚ࠼ࡿሙྜࡢࣀ࣮ࢻ㛫ࡢ㑄⛣ඛ౛ࢆ♧ࡋ࡚࠸ࡿ㸬Fig.3 ࡢ Current node ࡛♧ࡉࢀ࡚࠸ࡿࣀ࣮ࢻࡣ㸪᥈⣴୰ࡢࣃ࢖ࣉࡀୗ᪉࠿ࡽ⌧ᅾࡑࡢࣀ࣮ࢻࡲ࡛ఙࡧ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬ࣃ࢖ࣉࡣ Current node ࡛♧ࡉࢀࡓࣀ࣮ࢻࡢୗ᪉࡟࠶

Fig.4 A bend part composed of three primitivesࡿ㛗᪉ᙧ࡛࠶ࡾ㸪✵㛫ࢆศ๭ࡋࡓ࣓ࢵࢩࣗࡢᖜࡼࡾࡶ኱ࡁ࡞┤ᚄࢆ᭷ࡋ࡚࠸ࡿ㸬ᮏᡭἲ࡛ࡣ Current node ࡟࠾ࡅࡿࣀ࣮ࢻࡇࡇ࡛࣋ࣥࢻࡢᕤసୖࡢไ⣙࠿ࡽỴࡲࡿ᭤ࡆ༙ᚄಀᩘ Į1,ࡢ఩⨨ᗙᶆ࠾ࡼࡧࣃ࢖ࣉࡢ᪉ྥࢆࢲ࢖ࢡࢫࢺࣛἲ࡛ᢅ࠺ 1

Į2 ཬࡧタィୖࡢせồ࠿ࡽỴࡲࡿ d ࢆ୚࠼ࡿࡇ࡜࡛㸪࣋ࣥࢻࡘࡢ≧ែ㔞࡜ࡍࡿ㸬Current node ࠿ࡽ┤㐍ࡍࡿሙྜ࡟⛣ືྍࡢ᭤ࡀࡾゅᗘ ȕ ࢆ௨ୗࡢᘧ࡛ồࡵࡿ㸬⬟࡞ࣀ࣮ࢻࡣ㸪ࣃ࢖ࣉࡢ㐍⾜᪉ྥ࡟ἢࡗ࡚㸪1 ࡘඛ࡟఩⨨ࡋ
࡚࠸ࡿ Next node1 ࡛࠶ࡿ㸬ࡇࡢሙྜࡣ㸪ࣃ࢖ࣉࢆ࣓ࢵࢩࣗE­° d  2 u D 1 u R ½°­°½°
2 u D1arcsin ®
¾  arcsin ®
¾ (1)2222°̄ (2 u D 1)  (D 2) °¿°̄ (2 u D 1)  (D 2) °¿日本船舶海洋工学会論文集 第 15 号

222

2012 年 6 月

4. ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂ࡉࡽ࡟㸪ᘧ(1)࡟ࡼࡾ୚࠼ࡽࢀࡓ ȕ ࢆ⏝࠸࡚㸪࣋ࣥࢻࡢタ⨨࡟ᚲせ࡞᭱ᑠࡢ㊥㞳࡛࠶ࡿ L ࢆ௨ୗࡢᘧࡼࡾồࡵࡿ㸬

4. 1 ᐇ㦂タᐃ

L( 2 u D 1 u R u sin E )  (D 2 u R u cos E )(2)ᮏᡭἲࡢືసࢆ☜ㄆࡍࡿࡓࡵ㸪㞀ᐖ≀࡜ࡋ࡚ 10 ಶࡢ㞀ᐖ≀ࡀ㓄⨨ࡉࢀࡓ㸪x ᗙᶆ 0~16m㸪y ᗙᶆ 0~3m㸪z ᗙᶆ 0~3mࡓࡔࡋ㸪ᮏ◊✲࡛ࡣ Į1 = 5, Į2 = 0, d < R ࡜タᐃࡋࡓ㸬ࡇࡇࡢタィᑐ㇟✵㛫࡛ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⾜࠺㸬ࣃ࢖ࣉࡢጞⅬࡣ࡛㸪d < R ࡜タᐃࡋ࡚࠸ࡿ⌮⏤ࡣ 1 ❶࡟࠾ࡅࡿ Fig.1, 2 ࡛♧ᗙᶆ(0.5, 1.75, 1.5)࡛࠶ࡾ x ㍈ṇ᪉ྥ࡬ఙࡧࡿ㸬ࣃ࢖ࣉࡢ⤊ࡋࡓࡼ࠺࡟㸪d < R ࡢ᮲௳᫬࡛ࡢ࣋ࣥࢻࢆ⪃៖ࡋ࡞࠸ሙྜ࡟

Ⅼࡣᗙᶆ(15.75, 1.5, 1.5)࡛࠶ࡾ x ㍈ṇ᪉ྥ࠿ࡽࣃ࢖ࣉࡀఙ࠾ࡅࡿ㠀⌧ᐇⓗ࡞ゎࡢ⏕ᡂࢆ㑊ࡅࡿࡓࡵ࡛࠶ࡿ㸬ࡲࡓ㸪Į1,ࡧ࡚ࡁ࡚⤊Ⅼࡢᗙᶆ࡟࡚Ṇࡲࡿ㸬ࡇࡢタィᑐ㇟✵㛫ࢆ 0.25m

Į2 ࡢタᐃ࡟㛵ࡋ࡚ࡣ࣋ࣥࢻࡢຍᕤ࡟⏝࠸ࡿᶵᲔࡢไ⣙࡟ᛂ㛫㝸࡛᱁Ꮚศ๭ࡋ㸪ጞⅬ࣭⤊Ⅼ࠾ࡼࡧ㞀ᐖ≀ࡢ఩⨨ࢆኚ໬ࡉࡌ࡚タᐃࡍࢀࡤࡼ࠸㸬ࡼࡗ࡚㸪ᮏᐇ㦂࡛ࡢタᐃࡣ 1 ࡘࡢ඾ᆺࡏࡎ࡟㸪ࣃ࢖ࣉࡢ┤ᚄࡢࡳࢆኚ໬ࡉࡏࡓሙྜ࡟࡝ࡢࡼ࠺࡞⤒౛ࢆ♧ࡋ࡚࠸ࡿ㸬㊰ࡀ⋓ᚓࡉࢀࡿࡢ࠿࡟ࡘ࠸࡚☜ㄆࡍࡿ㸬ࣃ࢖ࣉࡢ┤ᚄࡣ᱁Ꮚᮏᡭἲࡣ㸪ᘧ(2)࡟ࡼࡾồࡵࡓ L ௨ୖࡢ㊥㞳࡟Ꮡᅾࡋ㸪࠿㛫㝸௨ୗࡢ 0.2m ࡢ࡯࠿᱁Ꮚ㛫㝸௨ୖ࡛࠶ࡿ 0.3, 0.4, 0.5,

ࡘ᭱ࡶ㏆࠸ሙᡤ࡟఩⨨ࡍࡿࣀ࣮ࢻ࡟ᑐࡋ࡚࣋ࣥࢻࡢ㐺⏝ࡶ

0.6, 0.7, 0.8, 0.9m ࡢィ 8 ✀㢮࡟ࡘ࠸࡚㸪⤒㊰୰࡟࠾ࡅࡿ࣋

⪃៖ࡋ࡞ࡀࡽጞⅬ࣭⤊Ⅼ㛫ࢆ⤖ࡪ⤒㊰ࡢ᥈⣴ࢆ⾜࠺㸬ࣥࢻࡢฟ⌧ࢆ⪃៖ࡋ࡚࠸ࡿሙྜ࡜ࡋ࡚࠸࡞࠸ሙྜࡢࡑࢀࡒ
ࢀ 2 ࣃࢱ࣮ࣥࡎࡘ㸪ྜィ 16 ࣃࢱ࣮ࣥࡢࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⾜࠺㸬ࡲࡓ㸪ࢥࢫࢺタᐃ࡜ࡋ࡚ࡣ㸪┤⟶ࡢ༢఩㛗(1m)ࢆࢥ
ࢫࢺ  ࡜ࡋ㸪࢚ࣝ࣎ࡢࢥࢫࢺ࡜ࡋ࡚ࡣࣃ࢖ࣉ㛗࡟┦ᙜࡍࡿࢥࢫࢺ࡟ຍ࠼㸪࢚ࣝ࣎ 1 ࡘ࠶ࡓࡾ࡟ࢥࢫࢺ 0.1 ࢆຍ⟬ࡋࡓ㸬ࡲࡓ࣋ࣥࢻࡢࢥࢫࢺ࡟㛵ࡋ࡚ࡶࣃ࢖ࣉ㛗࡟┦ᙜࡍࡿࢥࢫࢺ࡟
ຍ࠼㸪࣋ࣥࢻ 1 ࡘ࠶ࡓࡾ࡟ࢥࢫࢺ 0.3 ࢆຍ⟬ࡋࡓ㸬ࡇࢀࡽࡢࢥࢫࢺタᐃࡣᐇ㦂࡟࠾ࡅࡿ୍౛࡛࠶ࡾ㸪ᐇၥ㢟࡟ᑐᛂࡍࡿ
ሙྜࡣࡑࢀࡒࢀࡢࣃ࢖ࣉࣆ࣮ࢫࡢ್ẁࢆタᐃ࡛ࡁࡿ㸬࡞࠾㸪ヲࡋ࠸㞀ᐖ≀ࡢ㓄⨨࡟ࡘ࠸࡚ࡣ Appendix ࡟グ㍕ࡍࡿ㸬

4. 2 ᐇ㦂⤖ᯝ

Fig.5 A grid partitioning network model in case of bends ィ⟬⎔ቃࡣ㸪OS ࡟ Windows7 ࢆ౑⏝ࡋ㸪CPU ࡣ Intel Core2Duo 2.8Ghz㸪࣓࣮ࣔࣜࡣ 2.00GB㸪ࣉࣟࢢ࣒ࣛゝㄒࡣ Javaversion 1.6 ࢆ⏝࠸ࡓ㸬

Fig.5 ࡣ 2 ḟඖ✵㛫࡟࠾ࡅࡿ࣋ࣥࢻࢆ⤒⏤ࡋࡓሙྜ࡟࠾ࡅ

⤒㊰୰࡟࠾ࡅࡿ࣋ࣥࢻࡢฟ⌧ࢆ⪃៖ࡋ࡚࠸ࡿሙྜ࡟࠾ࡅࡿࣀ࣮ࢻࡢ≧ែ㑄⛣౛࡛࠶ࡿ㸬Fig.5 ࡟࠾࠸࡚ Current nodeࡿ㸪ᮏᡭἲ࡛⋓ᚓࡉࢀࡓ⤒㊰ࢆ Fig.6 ~ Fig.13 ࡟♧ࡍ㸬ࡲࡓ㸪࡛♧ࡉࢀࡓࣀ࣮ࢻࡣ㸪᥈⣴୰ࡢࣃ࢖ࣉ⤒㊰ࡀୗ᪉࠿ࡽୖ᪉࡬ྲྀࡾᢅࡗࡓࢢࣛࣇ࡟࠾ࡅࡿࣀ࣮ࢻࡢᩘ㸪⤒㊰୰ࡢ࢚ࣝ࣎ࡢᩘ㸪ఙࡧ㸪⌧ᅾࡑࡢࣀ࣮ࢻࡲ࡛ఙࡧ࡚࠸ࡿࡇ࡜ࢆ♧ࡋ࡚࠾ࡾ㸪ࣃ࣋ࣥࢻࡢᩘ㸪ጞⅬ࠿ࡽ⤊Ⅼࡲ࡛ࡢࢥࢫࢺྜィ㸪⤒㊰᥈⣴࡟せ࢖ࣉࡣ✵㛫ࢆศ๭ࡋࡓ࣓ࢵࢩࣗࡢᖜࡼࡾ኱ࡁ࡞ᚄࢆ᭷ࡋ࡚ࡋࡓ᫬㛫࡟ࡘ࠸࡚ࣃ࢖ࣉࡢ┤ᚄࡈ࡜࡟ Table 1 ࡟ࡲ࡜ࡵࡓ㸬࠸ࡿ㸬ࡇࡢ Current node ࠿ࡽྑ࡟ࡎࢀࡿ࣋ࣥࢻࢆ⤒⏤ࡍࡿࡇ⤒㊰୰࡟࣋ࣥࢻࡢฟ⌧ࡀ☜ㄆࡉࢀࡓࡢࡣ㸪┤ᚄࡀࡑࢀࡒࢀ

࡜࡛฿㐩ྍ⬟࡜࡞ࡿࣀ࣮ࢻࡀᅗ୰ࡢ Next node ࡛࠶ࡿ㸬Next0.3, 0.4, 0.5, 0.6, 0.9m ࡢሙྜ࡛࠶ࡾ㸪ࡇࢀࡽࡢゎࡣᮏᡭἲnode ࢆ᥈⣴ࡍࡿ㝿࡟ࡣ㸪࣋ࣥࢻࢆ㓄⨨ࡍࡿࡓࡵࡢ✵㛫୰࡟࡟ࡼࡗ࡚ึࡵ࡚ᚓࡽࢀࡓࡶࡢ࡛࠶ࡿ㸬ࡲࡓࣃ࢖ࣉ┤ᚄࡀ᱁Ꮚ㞀ᐖ≀ࡀ࠶ࡿ࠿࡝࠺࠿ࡢᖸ΅ุᐃࢆ⾜࠺㸬ࡇࡢሙྜࡢᖸ΅ุ㛫㝸௨ୗ࡛࠶ࡿ 0.2m ࡢሙྜࡣ㸪ࡑࡢ௚ࡢሙྜ࡜ẚ㍑ࡋ࡚ᩘᐃࡣ㸪࣋ࣥࢻࢆୖ༙㒊࡟ෆ᥋ࡍࡿ᭱ᑠࡢ┤᪉య࡜ୗ༙㒊࡟ෆಸࡢ᥈⣴᫬㛫ࡀᚲせ࡛࠶ࡿࡇ࡜ࡀ☜ㄆࡉࢀࡓ㸬ࡉࡽ࡟㸪ࡍ࡭᥋ࡍࡿ᭱ᑠࡢ┤᪉య࡟⨨ࡁ᥮࠼࡚⾜࠺㸬ࡑࡋ࡚≀⌮ⓗ࡟㓄⨨࡚ࡢ┤ᚄ࡟࠾࠸࡚࣋ࣥࢻࢆ⪃៖ࡋࡓሙྜࡢ᪉ࡀ㸪⪃៖ࡋ࡞࠸ྍ⬟࡞ሙྜࡢࡳ㸪ࡇࢀࡽࡢࣀ࣮ࢻࢆ᪂ࡋ࠸ࣜࣥࢡ࡛⤖ࡧࢿࢵሙྜࡼࡾࡶ᥈⣴᫬㛫ࡀ㛗࠿ࡗࡓࡀ㸪ᇶᮏⓗ࡟ᩘ⛊⛬ᗘࡢᕪ࡛ࢺ࣮࣡ࢡࢆᵓᡂࡋ࡚࠸ࡃ㸬ࡇࡢ᪂ࡋ࠸ࣜࣥࢡ࡟ࡣ㸪࢚ࣝ࣎ࢆ࠶ࡾ㸪࣋ࣥࢻࢆ⪃៖ࡍࡿࡇ࡜࡛᥈⣴᫬㛫ࡀ኱ᖜ࡟ቑຍࡍࡿࡇ㓄⨨ࡍࡿሙྜ࡜ྠᵝ࡟㸪ࣀ࣮ࢻ㛫ࢆ᥋⥆ࡋࡓࣃ࢖ࣉࡢ㛗ࡉ࠾࡜ࡣ࡞࠸࡜⪃࠼ࡽࢀࡿ㸬ࡼࡧ࣋ࣥࢻ࡟ᛂࡌࡓࢥࢫࢺࢆᐤ୚ࡍࡿ㸬エルボおよびベンドを考慮した配管設計アルゴリズム

223

Table 1 Features of obtained solutions with 0.25(m) meshes of x, y, and z direction

㻌㻌Without
Considerationof Bends

WithConsiderationof Bends

Diameter[m]

Num. ofNodes

Num. ofElbows

Num. ofBends

Total Costs

Time0.2

㻌 43070

9

㻌

17.9

1260

0.3

㻌 37766

919.4

306

0.4

㻌 35441919.9

2980.5

㻌 35441919.9

2880.6

㻌 19007822.3

680.7㻌 17237

922.4

530.8

㻌 17010

922.4

500.9

㻌 154461527.5440.2

㻌 430709017.91285

0.3

㻌 3787871194470.4

㻌 35467

7

119.5

387

0.5

㻌 35408

8

119.6

373

0.6

㻌 18997

7

121.5

800.7

㻌 173979022.4680.8

㻌 171929022.4630.9

㻌 1517114126.7

45[s]

Fig.6 An obtained route with 0.2(m) diameter of the pipe

Fig.8 An obtained route with 0.4(m) diameter of the pipe

Fig.7 An obtained route with 0.3(m) diameter of the pipe

Fig.9 An obtained route with 0.5(m) diameter of the pipe

日本船舶海洋工学会論文集 第 15 号

224

2012 年 6 月

5. ⪃ᐹ

5. 1 ᐇ㦂⤖ᯝ࡟ࡘ࠸࡚
Fig.7 ~ Fig.13 ࡛♧ࡉࢀ࡚࠸ࡿ⤒㊰ࡣ㸪ࣃ࢖ࣉ┤ᚄࡀ࣓ࢵࢩ
ࣗᖜࡼࡾࡶ኱ࡁ࠸࡜࠸࠺ほⅬ࠿ࡽᮏᡭἲ࡟ࡼࡗ࡚ึࡵ࡚ᚓࡽࢀࡓゎ࡛࠶ࡿ㸬ࡲࡓ㸪⤒㊰୰࡟࣋ࣥࢻࡀ☜ㄆࡉࢀࡓࡢࡣ㸪┤ᚄࡀࡑࢀࡒࢀ 0.3, 0.4, 0.5, 0.6, 0.9m ࡢሙྜ࡛࠶ࡗࡓ㸬Fig.7 ~ Fig.10 ࠾ࡼࡧ Fig.13 ࡢ㓄⟶⤒㊰୰࡟࠾࠸࡚㸪▮༳࡛♧ࡉࢀ࡚࠸ࡿ㒊ศࡀ࣋ࣥࢻ࡛࠶ࡾ㸪࣋ࣥࢻࢆ⪃៖ࡋ࡚࠸࡞
Fig.10 An obtained route with 0.6(m) diameter of the pipe࠸ᚑ᮶ᡭἲ࡛ࡣᚓࡽࢀ࡞࠿ࡗࡓゎ࡛࠶ࡿ㸬Fig.6 ࡛♧ࡉࢀ࡚࠸ࡿࢣ࣮ࢫ࡛ࡣ㸪ࣃ࢖ࣉࡢᚄࡀ✵㛫ࢆศ๭ࡋ࡚࠸ࡿ࣓ࢵࢩࣗᖜࡼࡾࡶᑠࡉࡃ㸪⤒㊰ࡢࢥࢫࢺࡶ඲⤒㊰ࡢ୰࡛᭱ᑠ࡛࠶ࡿࡇ࡜ࡀ☜ㄆࡉࢀࡿ㸬ࡇࢀ࡟ᑐࡋ࡚㸪ࣃ࢖ࣉࡢᚄࡀ኱ࡁࡃ࡞ࡿ࡟ࡘࢀ࡚㸪ࢥࢫࢺࡀ኱ࡁࡃ࡞ࡗ࡚࠸ࡿ㸬ࡼࡗ࡚㸪ࡇࡢᐇ㦂࡟ࡼࡾ㸪ᮏ᮶ࡣ኱ࡁࡃ㎽ᅇࡋ࡚࠸ࡓ⤒㊰࡟ᑐࡋ࡚㸪࣋ࣥࢻࢆ㐺⏝ࡍࡿࡇ࡜࡛ྛࣃ࢖ࣉ┤ᚄ࡟ᛂࡌࡓไ⣙᮲௳ࢆ‶ࡓࡍ᭱㐺࡞⤒㊰ࢆ⋓ᚓࡍࡿࡇ࡜ࡀ㸪Table 1 ࡼࡾ☜ㄆ࡛ࡁࡿ㸬ࡲࡓ㸪Fig.7 ~ Fig.10 ࠾ࡼࡧ Fig.13 ࡟࠾࠸࡚ࡢ࣋ࣥࢻࡢฟ⌧ಶᡤࡣ࠸ࡎࢀࡶጞⅬ௜㏆࡛࠶ࡿࡇ࡜ࡀ☜ㄆࡉࢀࡿ㸬ࡇࢀࡣ⤒㊰ࡢ⮬⏤ᗘࡀጞⅬ௜㏆࡛㝈ࡽࢀࡿࡓࡵ࡛࠶ࡿ࡜⪃࠼ࡽࢀ

Fig.11 An obtained route with 0.7(m) diameter of the pipeࡿ㸬ࡼࡗ࡚㸪ᮏᡭἲ࡛ࡣ⤒㊰ࡢጞⅬ࣭⤊Ⅼ௜㏆ࡢ࡯࠺ࡀ㸪⤒㊰ࡢ୰┙ࡼࡾࡶ࣋ࣥࢻࡀ⌧ࢀࡿྍ⬟ᛶࡀ㧗࠸࡜⪃࠼ࡽࢀࡿ㸬᭱ᚋ࡟ࣃ࢖ࣉࡢ┤ᚄࡀᑠࡉࡃ࡞ࡿ࡟ࡘࢀ࡚⤒㊰᥈⣴᫬㛫ࡀቑຍࡋ࡚࠸ࡿࡇ࡜ࡀ Table 1 ࡼࡾ☜ㄆ࡛ࡁࡿ㸬⤒㊰୰࡟࠾ࡅࡿࣀ࣮ࢻࡢᩘࡀቑຍࡋ࡚࠸ࡿࡇ࡜࠿ࡽ⪃࠼࡚㸪ࡇࢀࡣࣃ࢖ࣉࡢ┤ᚄࡀᑠࡉࡃ࡞ࡿࡇ࡜࡛㸪タィᑐ㇟✵㛫ෆ࡛ࡢ⤒㊰᥈⣴ࢆ⾜࠺㡿ᇦࡀቑຍࡋࡓࡓࡵ࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡼࡗ࡚ࣃ࢖ࣉࡢ┤ᚄࡀᑠࡉ࠸ሙྜࡢฎ⌮᫬㛫▷⦰ࢆ┠ⓗ࡜ࡋࡓ㓄⟶⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒ࡢᨵⰋࢆィ⏬ࡋ࡚࠸ࡿ㸬ᮏᡭἲ࡟࠾࠸࡚
⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚ά⏝ࡋ࡚࠸ࡿࢲ࢖ࢡࢫࢺࣛἲࡣ㸪ࢢࣛࣇၥ㢟ࡢ᥈⣴࡟࠾࠸࡚㞄᥋ࡋࡓ඲࡚ࡢࣀ࣮ࢻ࡟ࡘ࠸

Fig.12 An obtained route with 0.8(m) diameter of the pipe࡚᥈⣴ࢆ⾜࠺ᶓᆺ᥈⣴࡟ศ㢮ࡉࢀࡿࡀ㸪ࡇࡢᶓᆺ᥈⣴ࢆ㐺⏝ࡋࡓሙྜ㸪ゎࡢ⏕ᡂ࡟ከࡃࡢ࣓࣮ࣔࣜ࡜᫬㛫ࢆせࡍࡿ㸬ࡼࡗ࡚㸪௒ᚋࡢ᪉㔪࡜ࡋ࡚㸪ࢲ࢖ࢡࢫࢺࣛἲࢆࡉࡽ࡟ᨵⰋࡋࡓA*࢔ࣝࢦࣜࢬ࣒ࡢ㐺⏝ࢆ᳨ウࡋ࡚࠸ࡿ㸬
5. 2 ࣓ࢵࢩࣗ㛫㝸࡟࠾ࡅࡿၥ㢟࡟ࡘ࠸࡚ᮏᐇ㦂࡜ࡣィ⟬⎔ቃ㸪タィ✵㛫ࡢࢧ࢖ࢬ㸪㞀ᐖ≀࠾ࡼࡧጞ
Ⅼ࣭⤊Ⅼࡢ఩⨨ࡣኚ࠼ࡎ࡟㸪x ㍈᪉ྥ࡟࠾ࡅࡿ᱁Ꮚศ๭ᖜࢆ
0.5m ࡜ࡋࡓሙྜࡢᐇ㦂⤖ᯝࢆ Table 2 ࡟♧ࡍ㸬ࡇࡢᐇ㦂࡛⋓ᚓࡉࢀࡓ⤒㊰ࡣ㸪᱁Ꮚᖜ 0.25m ࡢሙྜ࡜ẚ࡭㸪඲ࡃྠᵝࡢ⤒㊰࡛࠶ࡗࡓ㸬ࡋ࠿ࡋ㸪᥈⣴࡟せࡋࡓ᫬㛫ࡀ㸪≉

Fig.13 An obtained route with 0.9(m) diameter of the pipe࡟ࣃ࢖ࣉࡢᚄࡀ࣓ࢵࢩࣗᖜࡼࡾࡶᑠࡉ࠸ሙྜ࡟኱ᖜ࡟▷⦰ࡉࢀࡓࡇ࡜ࡀ Table 1 ࡜ Table 2 ࢆẚ㍑ࡍࡿࡇ࡜࠿ࡽ☜ㄆࡉエルボおよびベンドを考慮した配管設計アルゴリズム

225ࢀࡿ㸬ࡇࡢ⤖ᯝࡼࡾ㸪タィ✵㛫࡟࠾ࡅࡿྛ᪉ྥ࡟ࡘ࠸࡚㐺ษ࡞࣓ࢵࢩࣗ㛫㝸ࢆタᐃࡍࡿࡇ࡜࡛㸪⤒㊰᥈⣴࡟せࡍࡿ᫬㛫ࢆ▷⦰ࡍࡿࡇ࡜ࡀྍ⬟࡛࠶ࡿ࡜⪃࠼ࡽࢀࡿ㸬ࡼࡗ࡚㸪ᵝࠎ࡞タィᑐ㇟✵㛫࡟ᑐࡋ࡚㸪࡝ࡢ⛬ᗘࡢ࣓ࢵࢩࣗ㛫㝸ࢆタᐃࡍࢀࡤጇᙜ࡛࠶ࡿ࠿࡟㛵ࡋ࡚㸪௒ᚋࡢ◊✲ࡀᚲせ࡛࠶ࡿࠋ

Table 2 Features of obtained solutions with 0.5(m) meshes
ofx axis, 0.25(m)meshes of y and z direction

Diameter[m]

Num. ofElbows

Num. ofBends

Total
Costs

Time[s]

0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9

97787
99
14011
1
100
1

17.9
19.0
19.5
19.6
21.5
22.4
22.4
26.7

213
146
126
126
24
23
22
12

Fig.14 An obtained pipeline without pipe-rack area

5. 3 ࣃ࢖ࣉࣛࢵࢡࢆྵࢇࡔ⤒㊰᥈⣴ࣃ࢖ࣉࣛࢵࢡࢆྵࢇࡔタィᑐ㇟✵㛫࡛ࡢືస☜ㄆࢆ⾜࠺ࡓࡵࡢ༢⣧࡞㏣ຍᐇ㦂ࢆ⾜ࡗࡓ㸬 x ᗙᶆ 0~3m㸪y ᗙᶆ0~2.5m㸪z ᗙᶆ 0~2m ࡢタィᑐ㇟✵㛫ෆ࡟㸪ጞⅬ (0.5, 2.00.5)࠾ࡼࡧ⤊Ⅼ (2.75, 2.0, 0.5)ࢆ㓄⨨ࡋ㸪ࡇࢀࡽࢆ⤖ࡪ┤ᚄ

Fig.15 An obtained pipeline with pipe-rack area

0.6m ࡢ㓄⟶⤒㊰ࢆ᥈⣴ࡍࡿ㸬x ᗙᶆ 1.3~1.7m㸪y ᗙᶆFig.15 ࡟࠾࠸࡚▮༳࡛♧ࡉࢀ࡚࠸ࡿ✵㛫ࡀࣃ࢖ࣉࣛࢵࢡ

0.75~2m㸪z ᗙᶆ 0~0.75m ࡢ⠊ᅖࢆ㞀ᐖ≀࡜ࡋ࡚タᐃࡋ㸪x✵㛫࡛࠶ࡿ㸬Table 3 ෆࡢẚ㍑ࡼࡾ㸪ࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆタ

ᗙᶆ 0~3m㸪y ᗙᶆ 0~0.75m㸪z ᗙᶆ 0~2m ࡢ⠊ᅖࢆࣃ࢖ࣉ

ᐃࡋ㸪㏻㐣ࡋࡓሙྜࡢ᪉ࡀ㸪ࣃ࢖ࣉࡢ⥲㛗ࡀ㛗ࡃ࡜ࡶࢥࢫࢺ

ࣛࢵࢡ✵㛫࡜ࡍࡿ㸬ࡇࡢᐇ㦂࡛ࡣ㸪ࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆ⪃៖࡜ࡋ࡚ࡣప࠸್ࢆ♧ࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬௒ᚋࡢㄢ㢟࡜ࡋࡍࡿሙྜ࡜㸪⪃៖ࡋ࡞࠸ሙྜࡢ 2 ㏻ࡾࡢᐇ㦂ࢆ⾜࠺㸬࡚㸪⌧ẁ㝵࡛ࡣࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆ࡜ࣃ࢖ࣉ⤒㊰ࡀᑡࡋ࡛ࡶࢥࢫࢺタᐃ࡜ࡋ࡚ࡣ㸪࢚ࣝ࣎ࡢࢥࢫࢺࢆ 1 ࡘ࠶ࡓࡾ 0.1㸪ᖸ΅ࡋࡓሙྜ㸪⤒㊰ࡀࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆ㏻ࡗࡓ࡜ࡳ࡞ࡋ࡚

࣋ࣥࢻࡢࢥࢫࢺࢆ 1 ࡘ࠶ࡓࡾ 0.3㸪┤⟶ࡢࢥࢫࢺࢆ༢఩㛗ࡉ࠸ࡿࡀ㸪ࣃ࢖ࣉࣛࢵࢡ࡜⤒㊰ࡢᖸ΅ࡢᗘྜ࠸ࢆ

(1m)࠶ࡓࡾ 1.0 ࡟タᐃࡋࡓ㸬ࡲࡓ㸪ࣃ࢖ࣉࣛࢵࢡࢆ㏻㐣ࡍࡿ᭦ࡍࡿࡇ࡜ࢆ᳨ウࡋ࡚࠸ࡿ㸬ࡉࡽ࡟㸪௒ᅇࡢᐇ㦂࡛ࡣࣃ࢖ࣉ㒊ศࡢ㓄⟶ࡢࢥࢫࢺࡣ 10 ศࡢ 1 ࡟㍍ῶࡉࢀࡿࡼ࠺タᐃࡋࡓ㸬ࣛࢵࢡ✵㛫࡛ࡢ๭ᘬ⋡ࢆ 0.1 ࡟タᐃࡋ࡚࠸ࡿࡀ㸪᭱㐺࡞๭ᘬࡇࡢࣃ࢖ࣉࣛࢵࢡ✵㛫࡛ࡢ๭ᘬ⋡࡟㛵ࡋ࡚ࡣ࣮ࣘࢨ࣮ࡀタ⋡࡟㛵ࡋ࡚ࡶࡉࡽ࡞ࡿ᳨ウࡀᚲせ࡛࠶ࡿ㸬ࡿ௙ᵝ࡟ኚᐃ࡛ࡁࡿ௙ᵝ࡜࡞ࡗ࡚࠸ࡿ㸬Table 3 ࡟⤒㊰ࡢヲ⣽ࢆ♧ࡍ㸬ࡇࡢࡼ࠺࡞ࣃ࢖ࣉࣛࢵࢡ✵㛫ࢆ᪤࡟タᐃࡉࢀࡓ⤒㊰ࡢᶓࡲࡓ㸪ࣃ࢖ࣉࣛࢵࢡࢆタᐃࡋ࡞࠸ሙྜࡢ⋓ᚓ⤒㊰ࢆ Fig.14㸪࡟㓄⨨ࡍࡿࡇ࡜࡛㸪ᐇ㝿ࡢ㓄⟶⤒㊰ࡢࡼ࠺࡟」ᩘᮏࡢࣃ࢖ࣉタᐃࡍࡿሙྜࡢ⋓ᚓ⤒㊰ࢆ Fig.15 ࡟ࡑࢀࡒࢀ♧ࡍ㸬ィ⟬⎔ࢆ᮰࡟ࡍࡿࡇ࡜ࡸ㸪ࣃ࢖ࣉࣛࢵࢡ✵㛫ࡢ࣓ࢵࢩࣗᖜࢆኚ໬ࡉ

ቃࡣ 4 ❶࡛ࡢࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂࡜ྠᵝ࡛࠶ࡿ㸬ࡏࡿࡇ࡜࡛ࣃ࢖ࣉࡢ㧗ࡉࢆᥞ࠼ࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ㸬Table 3 Features of obtained solutions with and withoutᮏᐇ㦂࡜ࡣ␗࡞ࡗࡓᐇ㦂᮲௳ୗ࡛㸪Fig.16 ࡢࡼ࠺࡞ࣃ࢖ࣉ

pipe-rack area

Without
pipe-rackWith
pipe-rack

5. 4 ⤒㊰᥈⣴࡟࠾ࡅࡿၥ㢟࡟ࡘ࠸࡚

Diameter[m]

Num. ofElbows

Total
Length [m]

Total
Costs

ࡀ⮬㌟࡜ᖸ΅ࡋࡓゎࡀᚓࡽࢀࡿࢣ࣮ࢫࡀ☜ㄆࡉࢀࡓ㸬ᥦ᱌ᡭ

0.6

43.25

7.25

ᗙᶆ࠾ࡼࡧ᪉ྥࢆ⏝࠸࠾ࡾ㸪Fig.16 ࡀ♧ࡋ࡚࠸ࡿࡼ࠺࡞⮬㌟

ἲ࡛ࡣࢲ࢖ࢡࢫࢺࣛἲ࡛ᢅ࠺ 1 ࡘࡢࣀ࣮ࢻ࡜ࡋ࡚㸪ࣃ࢖ࣉࡢ࡜ᖸ΅ࡋ࡚࠸ࡿࢣ࣮ࢫ࡛ࡣ᥈⣴ࡢ᭱୰࡟ᗙᶆࡣྠࡌࡔࡀ᪉
0.645.25

5.2ྥࡣ㐪࠺ 2 ࡘࡢࣀ࣮ࢻࡀ⋓ᚓࡉࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋࢲ࢖ࢡࢫࢺ日本船舶海洋工学会論文集 第 15 号

226

vol.27, pp.327-330 (2004 ᖺ 12 ᭶)ࣛἲࡣࡑࡢᵓ㐀ୖ㸪᥈⣴ࡀ⤊ࢃࡿࡲ࡛࡝ࡢࣀ࣮ࢻࡀ౑⏝ࡉࢀࡿ࠿ศ࠿ࡽ࡞࠸ࡢ࡛㸪ᗙᶆࡀྠࡌࡔ࠿ࡽ࡜࠸ࡗ࡚ࡑࡇ࠿ࡽඛ2)ụᖹ ᛭ྐ: ⯪⯧ศ㔝࡟࠾ࡅࡿ㓄⟶タィࡢ⮬ື໬ᡭἲ࡟
㛵ࡍࡿ◊✲, ஑ᕞ኱Ꮫ, ༤ኈㄽᩥ (2010 ᖺ)ࡢ᥈⣴ࢆᡴࡕษࡿࡇ࡜ࡀ୙ྍ⬟࡛࠶ࡿ㸬ࡼࡗ࡚ࣃ࢖ࣉࡀ⮬㌟࡜ᖸ΅ࡋ࡚࠸ࡿゎࡀᚓࡽࢀࡓᚋ࡛㸪ࡑࡢゎࢆ⮬ືⓗ࡟㝖ཤࡍ

2012 年 6 月3)

Asmara, A. and U. Nienhuis: Automatic piping system inship, proceedings of the 5th International Conference. onࡿࡼ࠺࡞࢔ࣝࢦࣜࢬ࣒ࡢᨵⰋࡀᚲせ࡛࠶ࡿ㸬Computer and IT Application(COMPIT), Mar. Ind. 2006.
Leiden.
4)

T. M. Paulo, and V. J. A. S Lobo: A Tool for AutomaticRouting of Auxiliary Circuits in Ships, Proceedings of 14thPortuguese Conference on Artificial Intelligence (EPIA2009), Aveiro ( Oct. 2009)5)

J. H. Park, and R. L. Storch: Pipe-routing Algorithm
Development: Case Study of A Ship Engine Room Design,
Journal of Expert Systems with Applications, Vol,23, No.1,pp.299-309 (2002)

Fig.16 An obtained self interfered route6)ఀ⸨ ↷᫂, ⚟⏣ ཰୍: 㑇ఏⓗ࢔ࣝࢦࣜࢬ࣒ࢆ⏝࠸ࡓ㓄⟶⤒㊰᥈⣴ἲࡢ᳨ウ, ேᕤ▱⬟Ꮫ఍ㄅ, Vol.13, No.5,pp.791-802 (1998 ᖺ)

6. ⤖ゝ7)ᮌᮧ ඖ㸸ࢲ࢖ࢡࢫࢺࣛἲࢆ⏝࠸ࡓ㓄⟶タィ࢔ࣝࢦࣜࢬ࣒㸪᪥ᮏ⯪⯧ᾏὒᕤᏛ఍ㅮ₇ㄽᩥ㞟㸪Vol.11㸪pp.121-124 ᮏㄽᩥ࡛ࡣ㸪㓄⟶タィసᴗࡢ⮬ື໬࡟ྥࡅ࡚㸪㞀ᐖ≀ࡀከ

2010 ᖺ 11 ᭶ᩘᏑᅾࡍࡿ」㞧࡞✵㛫ෆ࡛ศᒱࡢ࡞࠸ 1 ᮏࡢࣃ࢖ࣉࡢ᭱㐺࡞⤒㊰ࢆぢฟࡍࡓࡵ㸪S Ꮠᆺࡢࣃ࢖ࣉࣆ࣮ࢫࢆ⤒㊰୰࡟⪃៖Appendixࡍࡿᡭἲࢆᥦ᱌ࡋࡓ㸬ࡲࡓ㸪ᮏ◊✲࡛౑⏝ࡋ࡚࠸ࡿ⤒㊰᥈⣴࢔ࣝࢦࣜࢬ࣒ࡣ㸪✵㛫ࢆ᱁Ꮚศ๭ࡍࡿ㝿ࡢ࣓ࢵࢩࣗࡢᖜࡀࣃ ❶ࡢᐇ㦂࡟࠾ࡅࡿ㞀ᐖ≀ࡢᗙᶆࣜࢫࢺ࢖ࣉࡢᚄ࡟౫Ꮡࡋ࡞࠸࢔ࣉ࣮ࣟࢳࢆ᥇⏝ࡍࡿࡇ࡜࡛㸪ࡼࡾᐇၥ㢟࡟ᑐᛂࡋࡓ⤒㊰᱌ࢆ⋓ᚓ࡛ࡁࡿ௙ᵝ࡜࡞ࡗ࡚࠸ࡿ㸬ࡉࡽ࡟㸪⤒㊰᥈⣴ࡢ㝿࡟ࢲ࢖ࢡࢫࢺࣛἲࢆ㐺⏝ࡋ࡚࠸ࡿࡢ࡛㸪⋓ᚓࡉࢀࡿ⤒㊰᱌ࡣ᭱ᑠࢥࢫࢺࡀಖドࡉࢀ࡚࠸ࡿ㸬ࡇࢀࡽࡢᡭἲࢆ Java ࣉࣟࢢ࣒ࣛ࡟ᐇ⿦ࡋ㸪タィᑐ㇟㸪ጞⅬ࣭⤊Ⅼ㸪㞀ᐖ≀ࡢ㓄⨨ࡣኚ໬ࡉࡏࡎ࡟㸪ࣃ࢖ࣉࡢᚄࡢࡳࢆኚ໬ࡉࡏࡓሙྜ࡟࠾ࡅࡿ౛㢟࡬㐺⏝ࡍࡿࡇ࡜࡛㸪ࡑࢀࡽࡢ⋓ᚓࡉࢀࡓ⤒㊰ࡀࣃ࢖ࣉࡢྛ┤ᚄ࡟ᛂࡌࡓ᭱㐺ゎ࡜࡞ࡗ࡚࠸ࡿࡇ࡜ࢆ᳨ドࡋࡓ㸬ㅰ㎡

 ᮏ◊✲ࡣ㸪᪥ᮏᏛ⾡᣺⯆఍⛉Ꮫ◊✲㈝⿵ຓ㔠ᇶ┙◊఍ (B)ㄢ㢟␒ྕ 23360388 ࡼࡾ୍㒊⿵ຓࢆཷࡅࡓ㸬ཧ ⪃ ᩥ ⊩1)㬇 ᩄ࿴, ᒣཱྀ ኴ㑻: ᶵჾ㓄⨨࣭㓄⟶ࡢ⮬ື໬࡜ 3 ḟඖ⾲♧, ᝟ሗ࣭ࢩࢫࢸ࣒࣭฼⏝࣭ᢏ⾡ࢩ࣏ࣥࢪ࣒࢘ㄽᩥ㞟,