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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 64897, 1427]*) (*NotebookOutlinePosition[ 65655, 1454]*) (* CellTagsIndexPosition[ 65611, 1450]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Optimisation", "Title"], Cell[CellGroupData[{ Cell["\<\ \[CapitalEAcute]tapes de la d\[EAcute]marche d'optimisation par \ algorithme g\[EAcute]n\[EAcute]tique\ \>", "Subsubsection"], Cell["\<\ 1. Commencer avec une population d'individus (chromosomes) g\ \[EAcute]n\[EAcute]r\[EAcute]s al\[EAcute]atoirement. 2. D\[EAcute]terminer l'adaptation de chaque individu dans la population 3. S\[EAcute]lectionner l'individu le mieux adapt\[EAcute] 4. Utiliser cet individu pour produire la nouvelle g\[EAcute]n\[EAcute]ration 5. 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ool000000oooool01Ol0003ooooooooooooooooo000000Gooooo00?o0000ooooooooool0?oooool0 0ol0I_ooooooooooo`0nooooo`03o`3oI_oooooo0?mV097ooooo0002ooooo`03o`000?oooooooooo 00;ooooo00Go0000ooooooooooooooooo`000003ooooo`05o`000?ooooooooooooooool000000ooo ool01Ol0003ooooooooooooooooo000000Gooooo00?o0000ooooooooool0?oooool00ol0I_oooooo ooooo`0oooooo`;o0?mVTOooool000;ooooo00?o0000ooooooooool00_ooool01Ol@413ooooooooo oooooooo410@00?ooooo00Go410@oooooooooooooooooa0@4003ooooo`05oa0@4?oooooooooooooo ool@41001Oooool00ol0003oooooooooo`0oooooo`03o`1Voooooooooooo043ooooo00?o0?mVoooo ooooool0Soooool000;ooooo00?o0000ooooooooool00_ooool01OmgMgOoV9RHoooooonHV9SoMgMg 00?ooooo00GoMgMgoiRHV?ooooooV9RHogMgM`03ooooo`05ogMgMonHV9SooooooiRHV?mgMgL01Ooo ool00ol0003oooooooooo`22ooooo`03o`3oI_oooooooooo08oooooo00000omEEEGoIVIVo`000004 ooooo`05onk^k_lb<S;o0000oc8b<_o^k^h00oooool01Oo^k^ko<S8bo`000?lb<S;ok^k^00?ooooo 00Gok^k^oc8b<_l0003o<S8bonk^kP05ooooo`03o`000?oooooooooo0?oooooo5Oooool0027ooooo 00?o0000ooooooooool0oooooolEooooo`008Oooool00ol0003oooooooooo`3ooooooaGooooo000Q ooooo`03o`000?oooooooooo0?oooooo5Oooool00?oooooo>Oooool00?oooooo>Oooool00?oooooo >Oooool00?oooooo>Oooool00001\ \>"], ImageRangeCache->{{{0, 311.5}, {192.125, 0}} -> {-50.2384, -117.566, \ 1.87444, 7.75585}}] }, Open ]], Cell["1. Composer un \[LeftGuillemet]chromosome\[RightGuillemet]", \ "Subsubsection"], Cell[TextData[{ "Les valeurs ", Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["x", FontSlant->"Italic"], "i"], TextForm]]], " prises par chaque composante peuvent \[EHat]tre \ consid\[EAcute]r\[EAcute]es comme les \[LeftGuillemet]all\[EGrave]les\ \[RightGuillemet] ou valeurs des \[LeftGuillemet]g\[EGrave]nes\ \[RightGuillemet] d'un \[LeftGuillemet]chromosome\[RightGuillemet]. Tirons au \ hasard ces valeurs dans les domaines de d\[EAcute]finition des composantes de \ la fonction :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(dom = {{100, 300}, {80, 150}, {80, 200}, {20, 100}, {100, 300}};\)\), "\[IndentingNewLine]", \(\(but = 765;\)\), "\[IndentingNewLine]", \(init = Table[Random[Real, dom[\([i]\)]], {i, Length[yi]}]\)}], "Input"], Cell[BoxData[ \({265.0346583510013`, 132.5538700084016`, 100.986192629243`, 58.22089185545753`, 201.05604014346574`}\)], "Output"] }, Open ]], Cell["2. D\[EAcute]terminer l'\[LeftGuillemet]adaptation\[RightGuillemet] du \ \[LeftGuillemet]chromosome\[RightGuillemet] ", "Subsubsection"], Cell["\<\ Calculons l'\[EAcute]cart entre la somme des composante et le \ \[LeftGuillemet]but\[RightGuillemet] :\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Abs[Apply[Plus, init] - but]\)], "Input"], Cell[BoxData[ \(7.148347012430804`\)], "Output"] }, Open ]], Cell[TextData[{ "Ainsi que la valeur de la fonction avec avec les valeurs ", Cell[BoxData[ FormBox[ SubscriptBox[ StyleBox["x", FontSlant->"Italic"], "i"], TextForm]]], " obtenues :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Sum[yi[\([i]\)] /. x \[Rule] init[\([i]\)], {i, Length[yi]}]\)], "Input"], Cell[BoxData[ \(2356.0946401402744`\)], "Output"] }, Open ]], Cell["\<\ Le \[LeftGuillemet]chromosome\[RightGuillemet] le mieux adapt\ \[EAcute] sera celui qui minimise une certaine \[LeftGuillemet]distance\ \[RightGuillemet].. Nous utilisons ici l'\[EAcute]cart comme distance pour \ mesurer l'\[LeftGuillemet]adaptation\[RightGuillemet].\ \>", "Text"], Cell["\<\ 3. S\[EAcute]lectionner, parmi une population, un \ \[LeftGuillemet]chromosome\[RightGuillemet] bien adapt\[EAcute]\ \>", \ "Subsubsection"], Cell[TextData[{ "G\[EAcute]n\[EAcute]rons une population de ", StyleBox["n", FontSlant->"Italic"], " \[LeftGuillemet]chromosomes\[RightGuillemet] et trions-la par ordre d\ \[EAcute]croissant des distances :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(n = 3;\)\), "\[IndentingNewLine]", \(pop = Sort[Table[ RotateLeft[{poptemp = Table[Random[Real, dom[\([i]\)]], {i, Length[yi]}], Abs[Apply[Plus, poptemp] - but], Sum[yi[\([i]\)] /. x \[Rule] poptemp[\([i]\)], {i, Length[yi]}]}], {n}]]\)}], "Input"], Cell[BoxData[ \({{39.843671139738035`, 2510.0462102069473`, {155.14088002696928`, 117.30722648827691`, 152.64168641842588`, 67.44244492417602`, 232.62409100241385`}}, {54.339045158386284`, 2397.2501946688053`, {230.08700039413665`, 136.15685351058374`, 195.05745854073152`, 31.98117344994835`, 117.37846894621347`}}, {126.75853097471895`, 3198.906037997335`, {292.620139138437`, 103.13811000585207`, 196.91022619035837`, 76.14571667875026`, 222.9443389613211`}}}\)], "Output"] }, Open ]], Cell["", "Text"], Cell["\<\ S\[EAcute]lectionnons maintenant un \[LeftGuillemet]chromosome\ \[RightGuillemet] parmi les mieux adapt\[EAcute]s (jusqu'\[AGrave] une \ profondeur \[LeftGuillemet]prof\[RightGuillemet]) :\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(prof = 3;\)\), "\[IndentingNewLine]", \(\(pop[\([Random[Integer, {1, prof}]]\)]\)[\([2]\)]\)}], "Input"], Cell[BoxData[ \(2397.2501946688053`\)], "Output"] }, Open ]], Cell["4. G\[EAcute]n\[EAcute]rer une population \[AGrave] partir d'un \ \[LeftGuillemet]chromosome\[RightGuillemet]", "Subsubsection"], Cell[TextData[{ "Pour g\[EAcute]n\[EAcute]rer une nouvelle population \[AGrave] partir du \ chromosome retenu, nous utiliserons la fonction \[LeftGuillemet]boole\ \[RightGuillemet] qui donne \[LeftGuillemet]vrai\[RightGuillemet] lorsque la \ probabilit\[EAcute] ", StyleBox["p", FontSlant->"Italic"], " de muter est sup\[EAcute]rieure ou \[EAcute]gale \[AGrave] un nombre tir\ \[EAcute] au hasard :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(boole[p_] := If[Random[] \[LessEqual] p, \ True, False]\)], "Input"], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(boole\\)\\\" is similar to existing symbol \ \\\"\\!\\(Boole\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::spell1\\\"]\\)\"\>"}]], "Message"] }, Open ]], Cell[TextData[{ "La fonction \[LeftGuillemet]muter\[RightGuillemet] nous permettra ainsi de \ modifier, avec une probabilit\[EAcute] ", StyleBox["p", FontSlant->"Italic"], StyleBox[", la valeur d'un g\[EGrave]ne ", FontVariations->{"CompatibilityType"->0}], StyleBox["g. \n", FontSlant->"Italic", FontVariations->{"CompatibilityType"->0}], StyleBox["En cas de mutation, la nouvelle valeur du g\[EGrave]ne est une de \ celles du chromosome retenu :", FontVariations->{"CompatibilityType"->0}] }], "Text"], Cell[BoxData[ \(muter[p_, g_, parent_] := If[boole[p], \[IndentingNewLine]parent[\([Random[ Integer, {1, Length[parent]}]]\)], g]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(p = 0.2; \ (*\ probabilit\[EAcute]\ de\ mutation\ *) \[IndentingNewLine]Map[ muter[p, #, \(pop[\([1]\)]\)[\([2]\)]] &, \(pop[\([Random[ Integer, {1, prof}]]\)]\)[\([2]\)]]\)], "Input"], Cell[BoxData[ \(3198.906037997335`\)], "Output"] }, Open ]], Cell["\<\ Rassemblons les instructions permettant d'obtenir: \[Bullet] le liste des valeurs initiales \[Bullet] l'\[EAcute]cart au but (pour les valeurs initiales) \[Bullet] la valeur de la fonction (pour les valeurs initiales) \[Bullet] la nouvelle g\[EAcute]n\[EAcute]ration \[Bullet] les valeurs de l'individu le mieux adapt\[EAcute] de cette g\ \[EAcute]n\[EAcute]ration\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(n = 10;\)\ (*\ nombre\ d' individus\ dans\ le\ population\ *) \), "\[IndentingNewLine]", \(\(prof = 3;\)\ (*\ profondeur\ de\ recherche\ d' un\ individu\ adapt\[EAcute]\ *) \), "\[IndentingNewLine]", \(\(p = 0.2;\)\ (*\ probabilit\[EAcute]\ de\ mutation\ *) \), "\[IndentingNewLine]", \(\(dom = {{100, 300}, {80, 150}, {80, 200}, {20, 100}, {100, 300}};\)\), "\[IndentingNewLine]", \(\(but = 756;\)\ \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(\(yi = {0.0015 x^2 + 1.8 x + 40, \[IndentingNewLine]0.003 x^2 + 1.7 x + 60, \[IndentingNewLine]0.0126 x^2 + 2.1 x + 100, \[IndentingNewLine]0.08 x^2 + 2 x + 25, \[IndentingNewLine]0.001 x^2 + 1.9 x + 120};\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(boole[p_] := If[Random[] \[LessEqual] p, \ True, False]\), "\[IndentingNewLine]", \(\(\(muter[pmute_, g_, parent_] := If[boole[ pmute], \[IndentingNewLine]parent[\([Random[ Integer, {1, Length[parent]}]]\)], g];\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(init = Table[Random[Real, dom[\([i]\)]], {i, Length[yi]}]\), "\[IndentingNewLine]", \(Abs[Apply[Plus, init] - but]\), "\[IndentingNewLine]", \(Sum[ yi[\([i]\)] /. x \[Rule] init[\([i]\)], {i, Length[yi]}]\), "\[IndentingNewLine]", \(pop = Sort[Table[ RotateLeft[{poptemp = Table[Random[Real, dom[\([i]\)]], {i, Length[yi]}], Abs[Apply[Plus, poptemp] - but]}], {n}]]\), "\[IndentingNewLine]", \(Map[ muter[p, #, \(pop[\([1]\)]\)[\([2]\)]] &, \(pop[\([Random[ Integer, {1, prof}]]\)]\)[\([2]\)]]\)}], "Input"], Cell[BoxData[ \({261.98387450325896`, 141.6072566013995`, 160.1786549403554`, 32.912906712020344`, 296.9492161522577`}\)], "Output"], Cell[BoxData[ \(137.63190890929195`\)], "Output"], Cell[BoxData[ \(2684.939311045746`\)], "Output"], Cell[BoxData[ \({{5.131229212178823`, {292.0620281710628`, 85.48119592207736`, 186.37223821901114`, 35.240739123101484`, 161.97502777692617`}}, {23.90063944501958`, {219.41574706612676`, 84.65448801963328`, 142.53936028030225`, 75.85917151608943`, 257.4318725628678`}}, {24.483013316185747`, {125.86681883713686`, 114.52893634814889`, 162.0380222848442`, 58.357270403516765`, 270.7259388101676`}}, {41.65764951580172`, {281.1357472152033`, 104.17841643076488`, 138.51347699579105`, 29.972065710935645`, 243.8579431631068`}}, {81.99250539604782`, {254.9750650914018`, 110.55584584621322`, 81.54991915822302`, 27.164006306694056`, 199.76265820142004`}}, {92.78487546689553`, {198.4800142356073`, 146.55487987731766`, 118.66850472003739`, 72.97878317925885`, 126.53294252088321`}}, {95.04805063305855`, {201.77778390633364`, 148.05199954495444`, 183.98807416161347`, 34.86815617995014`, 282.3620368402069`}}, {109.41770923453896`, {171.9470717147241`, 139.72246870406798`, 118.75368824109093`, 36.27401856191683`, 179.8850435436613`}}, {138.98833951429378`, {137.2778040520965`, 139.71041144830232`, 144.41939720610364`, 84.19306256424404`, 111.41098521495965`}}, {170.53373183746237`, {155.21240688998176`, 144.93362147899643`, 84.8893485097297`, 37.83862353228507`, 162.59226775154468`}}}\)], "Output"], Cell[BoxData[ \({292.0620281710628`, 85.48119592207736`, 186.37223821901114`, 35.240739123101484`, 161.97502777692617`}\)], "Output"], Cell[" 5. Faire \[EAcute]voluer la population", "Subsubsection"], Cell["\<\ Pour faire \[EAcute]voluer la population, nous retenons les valeurs \ de l'individu le mieux adapt\[EAcute] et nous recommen\[CCedilla]ons le cycle \ (\[EAcute]tapes 2 \[AGrave] 4) :\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{\(ecart = pop[\([1, 1]\)]\), "\[IndentingNewLine]", \(parent = pop[\([1, 2]\)]\), "\[IndentingNewLine]", \(somme = Apply[Plus, parent]\), "\[IndentingNewLine]", \(valeur = Sum[yi[\([i]\)] /. x \[Rule] init[\([i]\)], {i, Length[yi]}]\), "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{ "\"\<G\[EAcute]n\[EAcute]ration \>\"", ",", "j", ",", "\"\<: \>\"", ",", "parent", ",", "\"\< Ecart=\>\"", ",", "ecart", ",", " ", "\"\< \!\(\(TextForm\`\[Sum]\)\)\!\(TextForm\`x\_i\)=\>\"", ",", RowBox[{"somme", "\"\< \!\(TextForm\`Y\_i\)=\>\""}], ",", "valeur"}], "]"}]}], "Input"], Cell[BoxData[ \(5.131229212178823`\)], "Output"], Cell[BoxData[ \({292.0620281710628`, 85.48119592207736`, 186.37223821901114`, 35.240739123101484`, 161.97502777692617`}\)], "Output"], Cell[BoxData[ \(761.1312292121788`\)], "Output"], Cell[BoxData[ \(2684.939311045746`\)], "Output"], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"G\[EAcute]n\[EAcute]ration \"\>", "\[InvisibleSpace]", "j", "\[InvisibleSpace]", "\<\": \"\>", "\[InvisibleSpace]", \({292.0620281710628`, 85.48119592207736`, 186.37223821901114`, 35.240739123101484`, 161.97502777692617`}\), "\[InvisibleSpace]", "\<\" Ecart=\"\>", "\[InvisibleSpace]", "5.131229212178823`", "\[InvisibleSpace]", "\<\" \ \\!\\(\\(TextForm\\`\[Sum]\\)\\)\\!\\(TextForm\\`x\\_i\\)=\"\>", "\[InvisibleSpace]", RowBox[{ "761.1312292121788`", " ", "\<\" \\!\\(TextForm\\`Y\\_i\\)=\"\>"}], "\[InvisibleSpace]", "2684.939311045746`"}], SequenceForm[ "G\[EAcute]n\[EAcute]ration ", j, ": ", {292.06202817106282, 85.481195922077362, 186.37223821901114, 35.240739123101484, 161.97502777692617}, " Ecart=", 5.1312292121788232, " \!\(\(TextForm\`\[Sum]\)\)\!\(TextForm\`x\_i\)=", Times[ 761.13122921217882, " \!\(TextForm\`Y\_i\)="], 2684.9393110457459], Editable->False]], "Print"] }, Open ]], Cell["Utilisons un \[LeftGuillemet]For\[RightGuillemet]", "Text", FormatType->TextForm], Cell[BoxData[{ RowBox[{\(m = 50000;\), " ", \( (*\ nombre\ d' individus\ dans\ le\ population\ *) \)}], "\[IndentingNewLine]", \ \(n = 10; \ (*\ nombre\ de\ g\[EAcute]n\[EAcute]rations\ *) ;\), "\[IndentingNewLine]", RowBox[{\(prof = 5;\), " ", \( (*\ profondeur\ de\ recherche\ d' un\ individu\ adapt\[EAcute]\ *) \)}], "\[IndentingNewLine]", \(p = 0.01; \ (*\ probabilit\[EAcute]\ de\ mutation\ *) \[IndentingNewLine]dom = {{100, 300}, {80, 150}, {80, 200}, {20, 100}, {100, 300}};\), "\[IndentingNewLine]", RowBox[{\(but = 756;\), " ", "\[IndentingNewLine]", "\[IndentingNewLine]", \( (*\ valeurs\ intiales\ *) \)}], "\[IndentingNewLine]", RowBox[{\(parent = Table[Random[Real, dom[\([i]\)]], {i, Length[yi]}];\), "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"For", "[", RowBox[{\(j = 1\), ",", \(j \[LessEqual] n\), ",", \(j++\), ",", "\[IndentingNewLine]", RowBox[{\(Sum[ yi[\([i]\)] /. x \[Rule] parent[\([i]\)], {i, Length[yi]}]\), ";", "\[IndentingNewLine]", \(pop = Sort[Table[ RotateLeft[{poptemp = Table[Random[Real, dom[\([i]\)]], {i, Length[yi]}], Abs[Apply[Plus, poptemp] - but], Sum[yi[\([i]\)] /. x \[Rule] poptemp[\([i]\)], {i, Length[yi]}]}], {n}]]\), ";", "\[IndentingNewLine]", \(Map[ muter[p, #, \(pop[\([1]\)]\)[\([3]\)]] &, \(pop[\([Random[ Integer, {1, prof}]]\)]\)[\([3]\)]]\), ";", "\[IndentingNewLine]", \(valeur = pop[\([1, 2]\)]\), ";", "\[IndentingNewLine]", \(parent = pop[\([1, 3]\)]\), ";", "\[IndentingNewLine]", \(somme = Apply[Plus, parent]\), ";", "\[IndentingNewLine]", \(ecart = somme - but\), ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{ "\"\<G\[EAcute]n\[EAcute]ration \>\"", ",", "j", ",", "\"\<: \>\"", ",", "parent", ",", " ", "\"\< \!\(TextForm\`Y\)=\>\"", ",", "valeur", ",", "\"\< \!\(\(TextForm\`\[Sum]\)\)\!\(TextForm\`x\_i\)=\>\"", ",", "somme", ",", "\"\< Ecart=\>\"", ",", "ecart"}], "]"}], ";"}]}], "\[IndentingNewLine]", "]"}]}], "Input"] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{0, 997}, {0, 746}}, CellGrouping->Manual, WindowSize->{891, 719}, WindowMargins->{{27, Automatic}, {-24, Automatic}}, ShowSelection->True, ShowCellLabel->False, Magnification->1.25, StyleDefinitions -> "DemoText.nb" ] (******************************************************************* Cached data follows. 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