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Notebook[{

Cell[CellGroupData[{
Cell["Algoritmo Gen\[EAcute]tico.", "Title"],

Cell[CellGroupData[{

Cell["\<\
Supongamos que tenemos una funcion como funcion(x)=(x^3+5x^2) Sin(x) a la \
cual le queremos calcular el minimo, pero no queremos hacer ni derivadas ni \
ninguna de las tecnicas analiticas, queremos llegar a ese minimo teniendo \
solo en cuenta el valor de la funcion en sus puntos.

Pues una forma de hacerlo es utilizando el algoritmo genetico que se basa en \
adaptacion de los individuos al medio\
\>", "Section"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\( (*funcion[x_] := x^4 - 8  x^3 + 5  x^2 + 50  x; *) \ 
     (*\ funcion\ a\ minimizar\ *) \n
    funcion[x_] := \((x^3 + 5  x^2)\)*Sin[x]; \n
     (*intervalo = {\(-3\), 8}; *) \ 
     (*\ Intervalo\ donde\ se\ busca\ el\ minimo\ *) \n
    intervalo = {\(-7\), 3}; \nindividuos = 10; \ 
     (*\ como\ minimo, \ 
      se\ toma\ la\ menor\ potencia\ de\ 2\  > \ individuos, \ 16*) \n
    poblacion = 2*individuos + 2; \ 
     (*\ Numero\ de\ individuos\ que\ puede\ haber\ como\ maximo\ *) \n
    iter = 10;  (*\ Numero\ de\ iteraciones\ *) \nnuitermuta = 4; \ 
     (*\ cada\ cuantas\ iteraciones\ se\ producen\ mutaciones\ *) \n
    numuta = 10; \ 
     (*\ numero\ maximo\ de\ mutaciones\ que\ se\ producen\ cada\ vez\ *) \n
    A = Plot[funcion[x], {x, intervalo[\([1]\)], intervalo[\([2]\)]}]; \n\n
    longint = intervalo[\([2]\)] - intervalo[\([1]\)]; \n
    propo = longint/\((individuos + 1)\); \n
    lista = {intervalo[\([1]\)], intervalo[\([2]\)]}; \n
    For[i = 1, i <= individuos, \(i++\), \n\t
      lista = Append[lista, N[intervalo[\([1]\)] + i*propo]]\n\t]; \n
    Print["\<inicio: \>", Sort[lista]]; \n\n
    For[kk = 1, kk <= iter, \(kk++\), \  (*\ Iteraciones\ *) \n
      \t{\n\t\tPrint["\<*******   Iteracion: \>", \ kk]; \n\t\t
        funlis = N[funcion[lista]]; \n\t\t
        While[Length[lista] <= poblacion, \n
          \t\t\t{\n\t\t\t\t
            alfa = Random[Real, {0, Sqrt[Max[funlis] - Min[funlis]]}]^2 + 
                Min[funlis]; \n\t\t\t\t
            Print["\<Se reproducen los menores de: \>", alfa]; \n\t\t\t\t
            longlist = Length[lista]; \n\t\t\t\t
            For[i = 1, i <= longlist, \(i++\), \n
              \t\t\t\t\t{\n\t\t\t\t\t\t
                If[funlis[\([i]\)] <= alfa, \n
                  \t\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\t
                    beta = Random[Integer, {1, longlist}]; \n\t\t\t\t\t\t\t\t
                    gama = Random[Real, {0, 1}]; \n\t\t\t\t\t\t\t\t
                    res = N[
                        gama*lista[\([i]\)] + 
                          \((1 - gama)\)*lista[\([beta]\)]]; \ 
                     (*\ nuevo\ individuo\ *) \n\t\t\t\t\t\t\t\t
                    lista = Append[lista, res]; \n\t\t\t\t\t\t\t\t
                    funlis = Append[funlis, funcion[res]]\n\t\t\t\t\t\t\t}\n
                  \t\t\t\t\t\t]\n\t\t\t\t\t}\n\t\t\t\t]\n\t\t\t}\n\t\t]; \n
        \t\tPrint["\<Hijos: \>", Sort[lista]]; \n\t\t (*\ Mutaciones\ *) \n
        \t\tIf[Mod[kk, nuitermuta] == 0, \n
          \t\t\t{\n\t\t\t\talfa = Random[Integer, {1, numuta + 1}]; \n\t\t\t\t
            For[s = 1, \ s <= alfa, \ \(s++\), \n
              \t\t\t\t\t{\n\t\t\t\t\t\t
                beta = Random[
                    Real, {intervalo[\([1]\)], intervalo[\([2]\)]}]; \n
                \t\t\t\t\t\t
                Print["\<Nueva Mutacion: \>", beta, \ "\< con valor: \>", 
                  funcion[beta]]; \n\t\t\t\t\t\tlista = Append[lista, beta]; 
                \n\t\t\t\t\t\tfunlis = Append[funlis, funcion[beta]]\n
                \t\t\t\t\t}\n\t\t\t\t]\n\t\t\t}\n\t\t]; \n\t\t\n\t\t
        qui = Length[lista] - poblacion - 1; \n\t\t
        Print["\<Quitar \>", qui, "\< individuos.\>"]; \n\t\tsalto = 0; \n\t\t
        While[qui >= 0, \n
          \t\t\t{\n\t\t\t\t
            If[salto == 0, \n\t\t\t\t\t
              alfa = Sqrt[
                    Random[Real, {0, \((Max[funlis] - Min[funlis])\)^2}]] + 
                  Min[funlis]\n\t\t\t\t]\n\t\t\t\t\t\t\t\t\n
            \t\t\t\t
            Print["\<Se mueren el inmediatamente mayores de: \>", alfa]; \n
            \t\t\t\tmi = 10^100; \  (*\ Un\ numero\ muy\ grande\ *) \n\t\t\t\t
            funlis = N[funcion[lista]]; \n\t\t\t\t
            For[j = 1, j <= Length[lista], \(j++\), \n
              \t\t\t\t\t{\n\t\t\t\t\t\t
                If[funlis[\([j]\)] > alfa\  && \ funlis[\([j]\)] <= mi, \n
                  \t\t\t\t\t\t\t{\n\t\t\t\t\t\t\t\tmi = funlis[\([j]\)]; \n
                    \t\t\t\t\t\t\t\tjj = j\n\t\t\t\t\t\t\t}\n\t\t\t\t\t\t]\n
                \t\t\t\t\t}\n\t\t\t\t]; \n\t\t\t\t
            If[mi != 10^100, \  (*\ el\ numero\ muy\ grande\ de\ arriba\ *) \n
              \t\t\t\t\t{\n\t\t\t\t\t\t\(qui--\); \n\t\t\t\t\t\t
                lista = Delete[lista, jj]; \n\t\t\t\t\t\t
                funlis = Delete[funlis, jj]; \n\t\t\t\t\t\tsalto = 0\n
                \t\t\t\t\t}, \n
              \t\t\t\t\t{\n\t\t\t\t\t\talfatem = alfa; \n\t\t\t\t\t\t
                alfa = alfatem/2; \n\t\t\t\t\t\tsalto = 1\n\t\t\t\t\t}\n
              \t\t\t\t]\n\t\t\t}\n\t\t]; \n\t\t
        Print["\<Supervivientes: \>", Sort[lista]]; \n\t\t
        B = ListPlot[
            Table[{lista[\([i]\)], \ funlis[\([i]\)]}, \ {i, \ longlist}], \ 
            PlotStyle -> {PointSize[0.03], RGBColor[1, \ 0, \ 0]}]; \n\t\t
        Show[A, B]; \t\n\ }\n]; \nres = funcion[lista]; \n
    Print["\<Resultado: minimo:\>", Min[res], "\< en el punto: \>", 
      lista[\([\(\(Position[res, Min[res]]\)[\([1]\)]\)[\([1]\)]]\)]\n]\n
     (*A = Plot[x^4 - 8  x^3 + 5  x^2 + 50  x, {x, \(-3\), 8}]; \n
      B = ListPlot[
          Table[{lista[\([i]\)], \ funlis[\([i]\)]}, \ {i, \ longlist}], \ 
          PlotStyle -> {PointSize[0.03], RGBColor[1, \ 0, \ 0]}]; \n
      Show[A, B]; *) \t\)\)], "Input"],

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