HAL Id: hal-00938864
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Submitted on 18 Apr 2014
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Genetic algorithms for Air Traffic Control systems
Daniel Delahaye, Nicolas Durand, Jean-Marc Alliot, Marc Schoenauer
To cite this version:
Daniel Delahaye, Nicolas Durand, Jean-Marc Alliot, Marc Schoenauer. Genetic algorithms for Air Traffic Control systems. IFORS 1996, 14th Triennal Conference of the International Federation of Operational Research Sociaties, Jul 1996, Vancouver, Canada. �hal-00938864�
✕ ✖✗ ✘✙✚ ✕ ✙✚✖✛ ✖✜✙ ✢ ✘✣✤✚✖✥ ✕ ✦ ✧✖✗ ★ ✩✙✖✗ ✪✫ ✖✧✣ ✬ ✚✚✘✤✭ ✫ ✖✧✣ ✮✣✛ ✤✙✗ ✖✦ ✙✧
✯ ✰ ✢ ✬ ✱ ✯ ✰ ✢ ✬ ✲ ✰ ✢ ✬ ✯ ✳ ✯ ✫ ✬ ✴ ✵ ✶
✷ ✸ ✹✺✻✼✽✺
✾✿❀ ❁ ❂❃ ✾❃❄❅ ❆ ❇❈❉❊❃❈❋ ●❍●❊❀■ ❈❏ ❄ ❆❈❑❉ ❊❃❍ ■ ❄❉▲
❄▼❀● ❄❋❋ ❊✿❀ ❄❂❃❆❃❄❏❊ ❊✿❄❊ ◆ ❍ ❂❉ ❂❊● ❄❂❃●❖❄❆❀P ◗❀●❂▼❉●
❆❈❉ ❊❃❈❋ ●❀❆❊❈❃●P ■ ❄❉❄▼❀● ❊✿❀ ◆ ❈❘ ● ❙❀❊❘ ❀❀❉ ❊✿ ❀ ◗❂❚ ❀❃▲
❀❉❊ ❄❂❃❖❈❃❊● ❄❉◗ ❙❀❄❆❈❉●P ❀❉●❑❃❀● ●❀❖❄❃❄❊❂❈❉ ❙❀❊❘ ❀❀❉
❄❂❃❆❃❄❏❊ ◗❑❃❂❉▼ ❊✿❀❂❃ ◆ ❂▼✿ ❊P ❊❄❯❀ ❈❚ ❄❉◗ ❋❄❉◗❂❉▼❱ ✾✿❑●P
❂❊ ❈❖❀❃❄❊❀● ❄❊ ◗❂❚ ❀❃❀❉ ❊ ❋❀❲❀❋●P ❀❄❆✿ ❈❉❀ ❈❏ ❊✿❀■ ◗❀▲
●❂▼❉ ❀◗ ❊❈ ❖ ❃❈❲❂◗❀ ❆❈❉❊❃❈❋P ❀❉●❑❃❀ ●❄❏❀❊❍P ❄❉ ◗ ❋❂■ ❂❊ ❊✿❀
❊❃❄❅ ❆ ❖❄●●❀◗ ❊❈ ❊✿❀ ❏❈❋❋❈❘ ❂❉▼ ❋❀❲❀❋❱ ❳❉ ❊✿❂● ❖❄❖ ❀❃ ❘ ❀
●✿❈❘ ✿❈❘ ❨ ❀❉❀❊❂❆ ❁ ❋▼❈❃❂❊✿■ ● ❆❄❉ ❂■ ❖ ❃❈❲❀ ●❈■ ❀ ❈❏ ❊✿❀
❊❄●❯● ■ ❄❉❑❄❋❋❍ ◗❈❉ ❀ ❙❍ ❊✿❀ ❁ ✾❇ ●❍●❊❀■ ❱ ❁ ❏❊❀❃ ❄ ❙❃❂❀❏
◗❀●❆❃❂❖ ❊❂❈❉ ❈❏ ❨❁ ●P ●❈■ ❀ ❈❏ ❊✿❀ ❂■ ❖ ❃❈❲❀■ ❀❉❊● ❑●❀◗
❩
●❂■ ❑❋❄❊❀◗ ❄❉❉❀❄❋❂❉▼P ●✿❄❃❂❉▼❬P ❘ ❀ ●❊❑◗❍ ❊✿ ❃❀❀ ❄❖❖ ❋❂▲
❆❄❊❂❈❉● ❈❏ ❨❁ ● ❊❈ ❁ ✾❇❱ ❭ ❀ ❪ ❃●❊ ●✿❈❘ ❄❉ ❄❖❖ ❋❂❆❄❊❂❈❉
❈❏ ❨❁ ● ❊❈ ❀❉▲❃❈❑❊❀ ❆❈❉◆ ❂❆❊ ❃❀●❈❋❑❊❂❈❉❱ ✾✿❀❉ ❘ ❀ ▼❂❲❀
❄❉ ❀❫❄■❖ ❋❀ ❈❉ ❨❁ ● ❑●❀◗ ❊❈ ❈❖❊❂■ ❂❴❀ ❄❂❃ ●❖❄❆❀ ●❀❆▲
❊❈❃❂❉▼❱ ✾✿ ❀ ❋❄●❊ ❖❄❃❊ ▼❂❲❀● ❄❉ ❄❖❖❋❂❆❄❊❂❈❉ ❈❏ ❨❁ ● ❊❈
❊❃❄❅ ❆ ❄●●❂▼❉■ ❀❉❊❱
❵ ❛❜❝❞ ❡ ❢ ❣ ❤❝ ✐❡ ❜
❥ ❦❧ ♠ ♥♦ ❥♦♣q r s t✉✈♦t✇ ①♠❥ s ② ③④③✈❧⑤ t⑥ ♣ rt⑦ ✉✈♦④
t⑧ ❧♦♣✈❧③ ♣✈ ⑨ ⑩❧ ❶♥❷❧♦❧✉✈ ✇❧⑩❧✇③ ❸
❹❺ ♠ ♥♦③⑧♣r❧ ❶❧③♥❻✉ ①♣♥♦❼ ♣④③❽ rt✉✈♦t✇ ③❧r✈t♦③❽ ❺❺❺②❺
❾ ❦❧✉ ❿t♥✉ ♥✉❻ ✈❼t ♣♥♦⑧t♦✈③❽♣✉ ♣♥♦r♦♣⑥✈ ⑤ ⑦③✈ ⑥t✇✇t❼
♦t⑦✈❧③ ♣✉❶ ➀ ❧♣rt✉③➁ ✈❦ ❧③❧ ➀ ❧♣rt✉③ ♣♦❧ ✉❧r❧③③♣♦④
⑥t♦ ⑧♥✇t✈③ ✈t ➂✉ t❼ ✈❦❧♥♦ ⑧ t③♥✈♥t✉ ❶⑦♦♥✉❻ ✉♣⑩♥❻♣➃
✈♥t✉ ♣✉ ❶ ❦❧✇⑧ rt✉✈♦t✇✇❧♦③ ✈t ⑩♥③⑦ ♣✇♥③❧ ✈❦❧ ✈♦♣q r❺
♠ ③ ✈❦ ❧♦❧ ♣♦❧ ⑤ ♣✉④ ♣♥♦r♦♣⑥✈ ③♥⑤ ⑦ ✇✈♣✉ ❧t⑦③✇④ ⑧♦❧③❧✉✈
♥✉ ✈❦❧ ③➂④❽ ♣ ③♥✉ ❻✇❧ rt✉✈♦t✇✇❧♦ ♥③ ✉t✈ ♣➀ ✇❧ ✈t ⑤ ♣✉➃
♣❻❧ ♣✇✇ t⑥ ✈❦❧⑤ ❺ ➄t❽ ♣♥♦③⑧ ♣r❧ ♥③ ⑧ ♣♦✈♥✈♥t✉❧❶ ♥✉✈t
❶♥❷❧♦❧✉✈ ③❧r✈t♦③❽ ❧♣r❦ t⑥ ✈❦❧⑤ ➀ ❧♥✉ ❻ ♣③③♥❻✉❧❶ ✈t
♣ rt✉✈♦t✇✇❧♦❺ ❥ ❦♥③ ✈♣③➂ ♣♥⑤ ③ ♣✈ ❶❧③♥❻✉ ♥✉❻ ✈❦❧ ♣♥♦
✉❧✈❼t♦➂ ♣✉❶ ✈❦ ❧ ♣③③tr♥♣✈❧❶ ③❧r✈t♦♥✉❻ ❺
➅➆➇➈➉➊➇ ➋➌➍➉➎➋➇➏ ➋➇ ➐➑ ➒➑➓➔→➑➉➔➣➈ ↔➇↕➊➔➇➈➈➇
➙
➍➛➣➐➇ ➒➑➉➔➣➈➑➐➇ ➜➎➝➇↕➊➔➇➎➊➇ ➋➌➍➐➇➛➉➊➣➈➔➞➎➇➟ ➋➌➍➐➇➛➉➊➣➠
➉➇➛➡➈➔➞➎➇➟➋➌➢➈➤➣➊➥ ➑➉➔➞➎➇ ➇➉ ➋➌➦➧➋➊➑➎➐➔➞➎➇ ➋➇ ➨➣➎➐➣➎➏➇
➩
➢➈➏➉➔➉➎➉ ➋➇ ➫➇➛➡➇➊➛➡➇ ➇➈ ➢➈➤➣➊➥ ➑➉➔➞➎➇ ➋➇ ➨➣➎➐➣➎➏➇
➭
➳❺ ♠ ♥♦ ❥♦♣q r ➵✇t❼ ➸ ♣✉♣❻❧⑤ ❧✉✈ ①♠❥ ➵ ➸ ② ①③✈♦♣✈❧❻♥r
⑧✇♣✉✉ ♥✉❻ ❽ ♣ ⑥❧❼ ❦ t⑦ ♦③ ♣❦ ❧♣❶②❺ ❾ ♥✈❦ ✈❦❧ ♥✉ r♦❧♣③➃
♥✉❻ ✈♦♣q r❽ ⑤ ♣✉④ ⑧♥✇t✈③ r❦tt③❧ ✈❦❧ ③♣⑤ ❧ ♦t⑦✈❧③❽
❻❧✉❧♦♣✈♥✉❻ ⑤ ♣✉④ rt✉➺ ♥r✈③ t✉ ✈❦❧ ➀❧♣rt✉ ③ ♥✉❶⑦ r➃
♥✉❻ t⑩❧♦✇t♣❶❧❶ ③❧r✈t♦③❺ ❥♦♣q r ♣③③♥❻✉⑤ ❧✉✈ ♣♥⑤ ③
♣✈ r❦♣✉❻♥✉❻ ♣♥♦r♦♣⑥✈ ♦t⑦✈❧③ ✈t ♦❧❶ ⑦r❧ ③❧r✈t♦ rt✉➃
❻❧③✈♥t✉ ③❽ rt✉➺♥r✈③ ♣✉❶ rtt♦❶♥✉ ♣✈♥t✉③❺
➻❺ s tt♦❶♥✉ ♣✈♥t✉ ⑧ ✇♣✉✉♥✉❻ ①♣ ⑥❧❼ ✈❧✉ ⑤ ♥✉⑦ ✈❧③ ♣❦ ❧♣❶②❺
❥ ❦♥③ ✈♣③➂ ❻⑦♣♦♣✉✈❧❧③ ✈❦ ♣✈ ✉ ❧❼ ♣♥♦r♦♣⑥✈ ❧✉✈❧♦♥✉❻
③❧r✈t♦③ ❶t ✉t✈ t⑩❧♦✇t♣❶ ✈❦ ❧ ③❧r✈t♦❺
➼❺ s ✇♣③③♥r♣✇ rt✉✈♦t✇ ♥✉ ♠❥ s r❧✉✈❧♦③ ①⑦ ⑧ ✈t ➳➽ ⑤ ✉
♣❦ ❧♣❶②❺ ♠ ✈ ✈❦ ♥③ ✇❧⑩❧✇❽ rt✉✈♦t✇✇❧♦③ ③t✇⑩❧ rt✉➺♥r✈③
➀❧✈❼ ❧❧✉ ♣♥♦r♦♣⑥✈❺
➾❺ s t✇✇♥③♥t✉ ♣⑩t♥❶♣✉ r❧ ③④③✈❧⑤ ③ ①♣ ⑥❧❼ ⑤ ♥✉⑦ ✈❧③
♣❦ ❧♣❶②❺ ❥ ❦♥③ ✇❧⑩❧✇ ♥③ ♣r✈♥⑩♣✈❧❶ t✉✇④ ❼ ❦❧✉ ✈❦❧ ⑧ ♦❧➃
⑩♥t⑦③ t✉❧ ❦♣③ ⑥♣♥✇❧❶ ❺
➚ ♣r❦ ✇❧⑩❧✇ ❦♣③ ✈t ✇♥⑤ ♥✈ ♣✉ ❶ t♦❻♣✉ ♥➪❧ ✈❦❧ ✈♦♣q r ♥✈
⑧♣③③❧③ ✈t ✈❦❧ ✉❧➶✈ ✇❧⑩❧✇❽ ③t ✈❦♣✈ ✈❦♥③ t✉❧ ❼ ♥✇✇ ✉❧⑩❧♦ ➀❧
t⑩❧♦✇t♣❶ ❧❶ ❺
➹ t❼ ❧⑩❧♦❽ ✈❦❧ ♠❥ s ③④③✈❧⑤ ③ ♥✉ ➚⑦ ♦t⑧ ❧ ♣✉❶ ♥✉ ✈❦❧
➘ ➄ ❦♣⑩❧ ✉t❼ ♦❧♣r❦ ❧❶ ✈❦❧♥♦ ✇♥⑤ ♥✈③❽ ♣✇✈❦ t⑦❻❦ ✈❦❧ ♦❧♣➃
③t✉ ③ ♣♦❧ ❶♥❷❧♦❧✉✈ ♥✉ ✈❦❧③❧ ✈❼t ♦❧❻♥t✉ ③❺ ❥ ❦❧♦❧⑥t♦❧❽ t✉ ❧
r♣✉ ♦❧♣③t✉♣➀✇④ ❧➶⑧❧r✈ ✈❦♣✈ t⑧ ✈♥⑤ ♥➪♥✉❻ ✈❦❧ ③④③✈❧⑤ ❼ ♥✇✇
⑧♦t⑩♥❶ ❧ ③⑦➀ ③✈♣✉✈♥♣✇ ➀❧✉❧⑨ ✈③ ♥✉ ✈❧♦⑤ ③ t⑥ ③♣⑥❧✈④❽ r♣⑧♣r➃
♥✈④❽ ♣✉ ❶ ♥✉❶ ⑦r❧❶ rt③✈③❺ ➴✉ ✈❦♥③ ⑧ ♣⑧ ❧♦ ❼ ❧ ③❦t❼ ❦t❼
➷ ❧✉ ❧✈♥r ♠ ✇❻t♦♥✈❦⑤ ③ r♣✉ ➀ ♦♥✉❻ ✉❧❼ ③t✇⑦✈♥t✉ ③ ✈t ♥⑤ ➃
⑧♦t⑩❧ ③t⑤ ❧ t⑥ ✈❦❧ ✈♣③➂③ ⑧♦❧⑩♥t⑦③✇④ ❶ ❧③r♦♥➀❧❶ ❺ ❥ ❦❧ ⑨ ♦③✈
⑧♣♦✈ ③❦ t♦✈✇④ ❶❧③r♦♥➀ ❧③ ❻❧✉❧♦♣✇ ⑧ ♦♥✉r♥⑧✇❧③ t⑥
➷
♠ ♣✉❶
♥✉✈♦t❶⑦r❧③ ③t⑤ ❧ ♥⑤ ⑧♦t⑩❧⑤ ❧✉✈③ ✈❦♣✈ ❼❧ ⑥t⑦ ✉❶ ⑦③❧⑥⑦ ✇❺
➴✉ ✈❦❧ ③❧rt✉❶ ⑧ ♣♦✈❽ ❼ ❧ ❼ ♥✇✇ ❻♥⑩❧ ♣ ❶❧③r♦♥⑧✈♥t✉ t⑥ ✈❦❧
✈❦♦❧❧ ⑧ ♦t➀✇❧⑤ ③ ❼❧ ③t✇⑩❧❽ ✈❦❧ rt❶♥✉❻ ❼❧ r❦tt③❧ ♣✉❶
✈❦❧ ♦❧③⑦✇✈③ t➀ ✈♣♥✉❧❶ ❺ ❥ ❦♥③ ⑧♦t❿❧r✈ ♥③ ⑧❧♦⑥t♦⑤ ❧❶ ➀④
✈❦❧ s❧✉✈♦❧ ❶ ➬➚ ✈⑦❶❧③ ❶❧ ✇♣ ➮ ♣⑩♥❻♣✈♥t✉ ♠ ❧♦♥❧✉✉❧ ①♥✉➃
③✈♥✈⑦✈❧ ♥✉ r❦ ♣♦❻❧ t⑥ ③✈⑦ ❶♥❧③ ♣✉❶ ♦❧③❧♣♦r❦ ⑥t♦ ♥⑤ ⑧♦t⑩➃
♥✉ ❻ ✈❦❧ ⑥♦❧✉r❦ ♠❥ s ③④③✈❧⑤ ③② ♣✉❶ ✈❦❧ ➚ rt✇❧ ➮ ♣✈♥t✉♣✇❧
❶❧ ✇➬♠ ⑩♥♣✈♥t✉ s♥⑩♥✇❧❺ ❥ ❦❧ ➚rt✇❧ ➮ ♣✈♥t✉ ♣✇❧ ➄⑦⑧ ❧♦♥❧⑦♦❧
❶ ➬➚ ✇❧r✈♦t✉♥➱⑦❧❽ ❶ ➬➚ ✇❧r✈♦t✈❧r❦✉ ♥➱⑦❧❽ ❶ ➬➴✉⑥t♦⑤ ♣✈♥➱⑦ ❧ ❧✈
❶ ➬➹ ④❶♦♣⑦ ✇♥➱⑦❧ ❶❧ ❥t⑦ ✇t⑦ ③❧ ♣✉❶ ✈❦❧ s ❧✉✈♦❧ ❶❧ ➸ ♣✈❦ ❧➃
⑤ ♣✈♥➱⑦ ❧③ ♠ ⑧⑧✇♥➱⑦❧❧③ ❶ ❧ ✇➬➚ rt✇❧ ✃ t✇④✈❧r❦✉ ♥➱⑦❧ rt✇✇♣➀➃
t♦♣✈❧❶ ✈t ✈❦♥③ ⑧♦t❿❧r✈❺
