Avancées des métaheuristiques pour l'optimisation combinatoire multi-objectif
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Metaheuristics for Multiobjective Combinatorial Optimization Problems: Review and recent issues Matthieu Basseur — El-Ghazali Talbi — Antonio Nebro — Enrique Alba. N° 5978 Septembre 2006. ISSN 0249-6399. apport de recherche. ISRN INRIA/RR--5978--FR+ENG. Thème NUM.
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(44) B . 2b67 2A@P0. #. ¸°o°< A¼}{ }¥O¯¥o``q(¥Io¯µ<}q(¯pÆl8=moµ Ácq-{· q8mo}¯qBm moo( Ip%ooq-{Aq%qB O}`AmoqÀ`q²°¸`i¯}`Amo{qt(|OqB{}{°¸¯oALp}`O A¶ q({ <}`mAI}`D´²q )o¯¥OzkI|Ooq¶ o|· ~qB¯q-}`|²O¥Oqq Xg`}qmo}q- Lt{oq-o`OmOµkmoq-l8{-mAÈ=q¨l8omo`q-|z%q-`{`q {AO°t{{qBq-qBOÀ}`O| `q-° }¯}zmAq A{¥O¯oq(¥)oq-}`moq3}q-( A{(q(¯||}/}`O°eA<{{q(Z}){q-o }¯OpL } mo}~zq OAq-|}3°o|±Ä|Op¤¯AAqOµ r3I|O}`~)|qB±G¾X}`{²Ooq-q({ ¥O}t{q(q(±GAOA|)`~q-o}}q(o¯¯²z±¿qiµ{`(A¯Oo=q-o4p AeI}momoqBq {(ÈeOl8Imo}q-{q/`zÁBo}omo`q-OzOAmo{qq-{cO|Ztq-`o}}O`}{}A^{}°¸`q-`p }}}`mAmoqq/²u ¯,^A { fi. F. . Multiobjective optimization methods Preferences. A priori. Interactive. A posteriori. Resolution algorithms Heuristics. Exact algorithms. Branch. Dynamic. and bound. programming. A*. Specific heuristics. Simulated annealing. Genetic algorithms. Metaheuristics. Tabu search. Scatter search. Genetic programming. .... Resolution approaches. Scalar approaches. Aggregation. E−constraint. non−scalar non−Pareto approaches. Pareto approaches. Goal programming. ¯¥o`q_SAÈ {`{¹Z-}¯ °po}±GO|~q-}¯²qOpo¯A}`e|}`pL¯³-}¯ p¤q(}mo|o{-µ g. Parallel selection. Lexicographic selection. QLR i$Q'S.
(45)
(46) . ##. ¯|°¸OÃÄ p}mA}`qÆO °¸¯ZO· |¯}8o¥ }mo{qB{3(}¯¯O{Z{{(¼Á¹N(·/qÆ}`Oo`¯Á[q oA¯z q-A{q)qB{q(q-°¸Oq(}L8}`}`$moqÆ' O}Jmo)=`q(Oq´' (¢¯¡*O)¿{µ {q-{¤°)pLq}`mo|o{(Á/°¸L°¸A}`moq( .
(47)
(48) . Ol8|mA~q¤q-Z}¯²{q)¯¤A|qq-µ 2oA[ooq(p`Nz[q(¯o ¥´°{-¥Oq(oq-¾`p¤Nq(pL}moq(|}moo|{o¯{8{¾°¸}`O`¯A· {~°¸O}`mop¯{t}¯ook`OO°ÆmÈ u-, K}·8o{)Æ{¯o¥¯q± X· ¦ mo`Aqm}« Ì NOpL¬||ª } \¯oÐ pI }{3 {OÌ p¯ª | o}Я¯oÑ A¯oÈ{-¥Æµ l8}moÿmo}¨{q¨O²D{A{¯¯o{q}`Z{L{¯°8 I}{~mo}}qL°¸¹AAo{Z{°¸}}`¯p¤pLZq(o{}mo¥¯| }omA{q oA¯zk{q-Oo°¸q|}`¯mo~OqBq}` }`¥q-²O oqLq(°¸oA}`O}`O°ÁÁ ¥q-oq(¯z^{%}` o¯¥OoqBz|q-·8ZDq-zUAL' ¡I/);¤'9#:}`#-mo¢q )GµAl8moqipL`q(q-}{q(o¼{<}{moO|O{}`q(%o°¸qB)i}mo}q mo·qiq(`¯q-¥{mI}X¯|²}`qBO}O °[}µXmoq/rtoq(²`q-o}`¯moq(pq± pLqB{q{-}`ÁZomooq(Aq}{~}`¯-}`{({^Áe{{¯ApLomW¯ ({^¼}~zO¥Áoq-o}mAq¯}`{^¯oo¥O`O`O¼}`mom¨p·8{O'9{ #:#-o`Ác¥q-[z¨ÁcA¡|{qBÁ #-¢Æ¡[Áe}`¡mo q)GÁc¯¼{}`q(p%o}¯A}qqB´¯Wo|oÊNqBq-¯q-AO¥ } 'P# #B[ Á SO|Á #D*¡ )¿ÁAZÀ}o´{q- m ' ¢¢ )Gµ Î Ð ©(ª-«D¬ ª Ì ª Ð Ñ/® ÃĨ}`mo{ oo`OOmÁO}moq)p}}q( {8o}¯p¤¯³(¯o¥°¸oA}`O {o|± ~¸q-O|}t~q-}À}¯(²q A{}!3¯{Io}`o{ ~q-O } }}`mo¨qO}Amo{q-}3¯oO}~q-{8}` ²Oq)}mA°¸qoA}`}mo¯q(3A{-Oµ |~l8q-mI}Z¯{(²ÁNqBÀ{ ¯{{t¯o{¥OOq(²O±Gq-Oc|"µ ~q-!i}¯`²Oq)Ao{8`²o¯¯oq(q-p { x[°<pLqZ{~q}`Ço`pLI}`o{ ¯q-{¨(°¨pLNqq}`¥mo¯²q(Aq(¨{~}}`¤¯-Z{q°¸Oo¯¯qt· }`¤A¥ ¥Oq(mooq q-`±Ä}q¾OA²{~}```OAI{}¨Xooq(}`¤O|m½}`p`q'9{#- I¯I|Á}`O#DA*{()µ ¸¥Oq(oq(}¯¥`}mop{ !3Á ' :¡ S)¸}`AÆ{q-`m !Á|Af '9#- OJ )¸m[z[o`¯ pLq}`moq(A{~}`¯-{ !µ $# Ð ¬ %« Ð Z«¬ È3ÃÄ}mo{pLq}`mo|cÁc}`moqÀ|q-(¯{¯kp ¶ q()p%A{~}|q(¹AoqL}`moqL¥O¯{-Ác q(°i°¸q(}`mo`q(qLAo(q-`{-Á(o}`¯3q(pÆ`q-ÁN}m^°¸A{=°¸q-`pLmAO¥¨|~})q-¯}I¯}² qOµ={l8¯omo¥q-¯q{±¿qX²o~¯q-oq-}`{²Oq`Oµ qXgoIO}`)|q|ÇoA(pLq-o¾¯¯qOÁN}`} mA}qLmAqX(O°¸{}t`p°¸ooZ}}`¯O ·/('P# O#B¤ J ¶ )¯I{)U}{q-A¥p%ooz[¯}q ¯}o¾qB¥Æ ·pLq(o¯q¥}`omIq-}moqBq(¯AooH¥ O{~!}`Áo¯p -{¾Z· Amo{' ¯o*¢ m%¥ )pLÂ}}`mA¯o¯o{pL´{`¯{³(moqBqBq-{Xp¤}qmAm q3!µ |q$q(²['P#B¢A}S|¯Á&¤#B · ¡J)}mLU¥}q-mAoq q}`¥¯OL¯{-¯¥µO^}ÊNmAq-pLq-{O!} Á }`¶ `oA,t· {°¸°/¯q-(o`pL¥oq}{¯qNº}mAo}t¯{¾°}mA {tq¤op(o})A}{k¯±¿oq(|q(`Ç[~q-qBmZÆ}Ao¯²{`q´}¯o²A¯q¤q(OpÆ{ooµt`q-²l8p»q-mAz ¯¯{tI°i}}~z[}ZmA q¤q¤{°¥o¥¥O`oq(q(o¥I±GO`O|}`~oq-¥mÆ}¯pLmA²DqÆq(²O}qmoA|mAq´o{-kµ)qBÀ OÃÄkA¯¥`}^q-q-{(o°q(24{ZNG(ÁN DM}qB5mo{ Dq{ AOoooOqqWo{}`Oq-ºp o}}`¯-{Æ{hµpL¥goZoO¯ ({¼q-}~I²z }q(q-q¤AcX {¼}`¯q(A}·£´}`OoApL}{-¯Á|opL²Do}` ¯}~}`zÅZO{/°8Z}Imo{~q¨}BpLµ,°¸q}`ol8q(Zmo {/qk{OO|q¾|}A¯}`pL{Oq-AƳB{-{Á}%¯o}o mZ}%} A°%}º}mAoq){¯u o¯¥zk¯q,^¹A±¿½Aoo~-{q- }`oZ²O¯zqq {(O¯{²}3qB´{`{{|q-²q-`}`q- }¯(pL q-{-}ÁcA }L|q(Ntq}q Ç|N¹Aq(AA{{²Oq-q²µ q(X`q}¨|}`pX{¯|}¯Z{(µ)l8moqLpLoo}`}`OA M COP. M COPλ. M COPλ. λ. . fk. fk. i. . '&. ()+*,-.
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(51) 8. `}ÃÄZqBO}`|mo}`}8q-o{}¥3q mo}qBmo{oqqo²pL`Oq(`O}OmomoA|q-{o{-o{-Á=ÈOpL|±ÄO{}pL¯zÅpLAq(Z{{q-o OA qXZOO|o~oq-}}¯¯²q-Z{{{q(A°3{`¯}|q(}¯¯zµZl8{(Ámoq(qB`qi{qBqÇ|{~m }<¯{%A(z) ``°¸q-qB·g{~O}`|A}|¯[q-z { idikjl mDnbop.
(52) D. 2b67 2A@P0. #. uT¾¬|q( o«,^¬q(} Ì {3{)© ¯Ì¥°¸`Ì `p&}ª mo \x|Ðp /!mAÈÆÁ¾Êe{l8q-q(moXqBqÆ'P}#B¹A{¨ J{~}`)¿}moµ qÅ·l8moA qÀo¶ ²[|q-|²ZAq-{O{~{ Z}`qBA°¸Å¥Op ¯½¥O}Amo`{¼q }`¯omo¥ pÆA¥Á `q-! q(oI%q} }`T ¯ÆN A ¥Oo!X¯qB`}¼}`}`¯mo6p%i{²(}`( A{|O}¯oqB²O¥q }¥Wq-oqBq(m }`OoÁ|~q-}mA}`q²OZqOÁoZo|q(}`NOq( Aoq({3I|}¯¯²[zk¯o}`q-´Æ}mA¯OqÀ}`¨}`Lmoq([o{pNAq(qt¸A°i{`Ao¯Zq(/Oo{q-oqB}`}¯OA{ !µÆ· motomÆ`¯o¯{ ¥WqBq- IOAm }{q-qB}mo}`q q- [op-NOq(`¤|¯o°3¥ O}`| ~q-}mo}¯q²qB{|~qB°¾}`O²O{q }°¸AµA}`l8OmAAq {%! }k%T O| }¯pL¯¥³-Oqµf}mo%p"m O{pLAoZZI{OqBo{Lo}mo}`qkOq( I}¯¯q{ ZA{Oq-o o[zÀ}`O}`moÁAq(3Z |}mooOo`¯{_qB{8'9#:}#Bmo[qÁN¥O*q(o)Gµ q(}¾Nq(}O`_{ \mAo¥OqÁo(I{{²q- !µl8mo{ oAIm¨·8{ Ì Ð Z«1¬ % © Ì Ì ª U Ð ÈÃÄ }mo{Loo`OOmÁ}moqÆ{q(¯q-}`O {¤-`¯q- O|}((|¯o¥ }}ÅmoqÆ{¥OOo`¼|¹Nq-(Z`q(q¨}`¯q(O²Oq(ÁX|° q¹A}`Amoq-q O[|zÅ~q-}}mo¯qƲqB|{(qBµÅl8{¯mo¯ {Lpo o¶ `q(O ' SIm |Á{L: So{~}`Ái¯ /SZ)¿µ{qBl8mA¯g¯{%{q-²|q-q(`¤/|(qO¹Z{oqBq-{({ Á q-{ZqB¯z¨· moq(´L¯q- moq-``m[zLqÇ|{~}{8Zq(}~·/q-q( }mAq|¼Êeq(`q(I} o~q-}`²Oq¾°¸oA}`OA{-µ . i. fi. '. -.
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