Teoria I - Algoritmos geneticos.ipynb

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   "source": [
    "<img src=\"imagenes/john_holland.jpg\" alt=\"John Holland, inventor de los algoritmos genéticos\" style=\"width: 300px;\"/>"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$John \\, H. \\, Holland \\, (1929 - 2015)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> *I have more ideas than I can ever follow up on in a lifetime, so I never worry if someone steals an idea from me*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">Físico y matemático\n",
    "\n",
    ">Profesor de Ciencias de la Computación, Ingeniería Eléctrica y Psicología (sí, Psicología)\n",
    "\n",
    ">Padre del algoritmo genético y pionero de los sistemas complejos adaptativos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "outputs": [
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     "execution_count": 1,
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   "source": [
    "from IPython.core.display import HTML\n",
    "\n",
    "HTML('''<script>\n",
    "code_show=true; \n",
    "function code_toggle() {\n",
    " if (code_show){\n",
    " $('div.input').hide();\n",
    " } else {\n",
    " $('div.input').show();\n",
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    " code_show = !code_show\n",
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    "$( document ).ready(code_toggle);\n",
    "</script>\n",
    "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>''')"
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random as random\n",
    "from scipy.interpolate import interp1d\n",
    "from IPython.html.widgets import interact\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Resolución directa de problemas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalmente, cuando tenemos un problema intentamos resolverlo directamente. Es decir, a partir de las premisas del problema, aplicamos un método que nos ofrece una solución que cumpla las premisas y nos quedamos a gusto. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$PROBLEM - \\underline{method} \\, -> SOLUTION$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muchos de los problemas que intentamos resolver (por no decir todos) son problemas de optimización. Un problema de optimización es aquel en el que intentamos minimizar o maximizar el valor de algo. Por ejemplo: ¿qué carrocería ofrece menos resistencia aerodinámica? ¿en qué momentos debo comprar y vender para maximizar mi beneficio en este mercado bursátil? ¿qué regalo le gustará más a mi novia?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imaginemos que queremos optimizar la cantidad de sueño que disfrutamos cada noche y que conocemos la función del descanso con el tiempo de sueño (en horas):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$Descanso = \\frac{1}{2200} \\cdot (tiempo^3 - 50 \\cdot tiempo ^2 + 600 \\cdot tiempo)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "num_hora = 20\n",
    "horas = np.linspace(0, 12, num_hora*12+1)\n",
    "descanso = [(tiempo**3 - 50*tiempo**2 + 600*tiempo)/2200 for tiempo in horas]"
   ]
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   "execution_count": 4,
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vvgC++koGr1m4UBZAKgvHjweuuUZ6kFDN6c1EDIVERFRrFEVGDP3gA2DePMDl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\nIiIiKez/Aw6TXzeIFx5LAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8913208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.xkcd():\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.plot(horas, descanso)\n",
    "    plt.xlabel(\"$horas$\", fontsize=20)\n",
    "    plt.ylabel(\"$descanso$\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La teoría de la optimización nos dice que debemos derivar esta función e igualar el resultado a 0 para calcular el máximo local. Obtenemos:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac {d}{d t}(Descanso) = \\frac{1}{2200} \\cdot (3 \\cdot tiempo^2 - 100 \\cdot tiempo + 600) = 0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aplicando el método de resolución de ecuaciones cuadráticas:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ tiempo_{max} = \\frac {100 - \\sqrt {100^2 - 4 \\cdot 3 \\cdot 600}}{2 \\cdot 3} = 7.85 \\, h $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5ufQIvveeDA1V1gk0m6UncMwY4OKLuQ4WEVFT0KoVcM01sgUCci/iF18AX30l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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8ed8630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hora_max = 7.85\n",
    "with plt.xkcd():\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.plot(horas, descanso)\n",
    "    plt.vlines(hora_max, 0, 1, colors = 'r' ,linestyles = 'dashed')\n",
    "    plt.xlabel(\"$horas$\", fontsize=20)\n",
    "    plt.ylabel(\"$descanso$\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Resolución de problemas mediante métodos heurísticos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muchas veces no contamos con un método de resolución directo. A veces no sabemos de qué relaciones depende el problema o el sistema de ecuaciones que lo gobierna es trascendental (es decir, no tiene solución), como las ecuaciones de Navier-Stokes. Muchas veces, las funciones de las que depende el problema simplemente no son derivables o es muy complicado derivarlas. En todos estos casos hay que recurrir a un método heurístico para tratar de resolver el problema:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$proposed \\, solution - \\underline{PROBLEM} \\, -> evaluation$$\n",
    "$$proposed \\, solution - \\underline{PROBLEM} \\, -> evaluation$$\n",
    "$$proposed \\, solution - \\underline{PROBLEM} \\, -> evaluation$$\n",
    "$$...$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veamos, por ejemplo, cómo se complica el problema anterior añadiendo algunas consideraciones adicionales. Se ha demostrado que el sueño no es un proceso continuo, sino que pasa por una serie de ciclos de unos 90 minutos, en los que el nivel alerta evoluciona siguiendo un patrón típico como el siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xa276a58>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9fQ+kJoa1xdn0apUMa8NQTFhrWS/L4TLI6VwGqSGrJaxZ+0tgWFucTYxWybA2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\n/8kwq+yi3zc6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa236080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vigilia = []\n",
    "vigilia += 5 * [1]\n",
    "vigilia += 10 * [0.6] \n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 10 * [0.2] \n",
    "vigilia += 20 * [0] \n",
    "vigilia += 5 * [0.2] \n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 5 * [0.6] \n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 5 * [0.2] \n",
    "vigilia += 10 * [0] \n",
    "vigilia += 5 * [0.2]\n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 10 * [0.6] \n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 5 * [0.2] \n",
    "vigilia += 5 * [0] \n",
    "vigilia += 5 * [0.2]\n",
    "vigilia += 5 * [0.4]\n",
    "vigilia += 20 * [0.7]\n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 5 * [0.2] \n",
    "vigilia += 5 * [0.4]\n",
    "vigilia += 40 * [0.8]\n",
    "vigilia += 5 * [0.4] \n",
    "vigilia += 5 * [0.2] \n",
    "vigilia += 5 * [0.4]\n",
    "vigilia += 21 * [0.8]\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.plot(horas, vigilia)\n",
    "plt.title('$Evolución \\, de \\, la \\, alerta \\, durante \\, el \\, sueño$', fontsize=20)\n",
    "plt.xlabel(\"$horas$\", fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Naturalmente, es más fácil despertar cuando el nivel de alerta es más alto y además la sensación de descanso es mayor. En cambio, si se fuerza el despertar (por ejemplo mediante un despertador) en un momento del ciclo en el que el sueño es muy profundo, nos despertamos abotargados y cansados. La evolución del descanso seguirá una evolución como la siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WGDECKChQx7Fj1UyWUWt1ZJbEihUY9+9Xx4ICY9tB5iSBUl8DNpFOtqBISBjc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\nP0gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa5f6278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "descanso_ciclos = list(np.array(vigilia)*np.array(descanso))\n",
    "descanso_nuevo = interp1d (horas, descanso_ciclos)\n",
    "\n",
    "with plt.xkcd():\n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.plot(horas, descanso_nuevo(horas))\n",
    "    plt.xlabel(\"$horas$\", fontsize=20)\n",
    "    plt.ylabel(\"$descanso$\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta función ni siquiera es derivable, ¿cómo podemos encontrar el óptimo? Un método heurístico muy sencillo consistiría en muestrear la función con un nivel de precisión suficiente y escoger el punto que se corresponda con el nivel de descanso más alto:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Tiempo de descanso (horas)</th>\n",
       "      <th>Nivel de descanso</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Muestra 1</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 2</th>\n",
       "      <td>0.05</td>\n",
       "      <td>0.013580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 3</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.027046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 4</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.040399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 5</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.053640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 6</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.040061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 7</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0.047871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 8</th>\n",
       "      <td>0.35</td>\n",
       "      <td>0.055614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 9</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.063290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 10</th>\n",
       "      <td>0.45</td>\n",
       "      <td>0.070900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 11</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.078443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 12</th>\n",
       "      <td>0.55</td>\n",
       "      <td>0.085920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 13</th>\n",
       "      <td>0.60</td>\n",
       "      <td>0.093332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 14</th>\n",
       "      <td>0.65</td>\n",
       "      <td>0.100677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 15</th>\n",
       "      <td>0.70</td>\n",
       "      <td>0.107957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 16</th>\n",
       "      <td>0.75</td>\n",
       "      <td>0.076781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 17</th>\n",
       "      <td>0.80</td>\n",
       "      <td>0.081548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 18</th>\n",
       "      <td>0.85</td>\n",
       "      <td>0.086271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 19</th>\n",
       "      <td>0.90</td>\n",
       "      <td>0.090951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 20</th>\n",
       "      <td>0.95</td>\n",
       "      <td>0.095588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 21</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.050091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 22</th>\n",
       "      <td>1.05</td>\n",
       "      <td>0.052367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 23</th>\n",
       "      <td>1.10</td>\n",
       "      <td>0.054621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 24</th>\n",
       "      <td>1.15</td>\n",
       "      <td>0.056854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 25</th>\n",
       "      <td>1.20</td>\n",
       "      <td>0.059066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 26</th>\n",
       "      <td>1.25</td>\n",
       "      <td>0.061257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 27</th>\n",
       "      <td>1.30</td>\n",
       "      <td>0.063427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 28</th>\n",
       "      <td>1.35</td>\n",
       "      <td>0.065576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 29</th>\n",
       "      <td>1.40</td>\n",
       "      <td>0.067704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 30</th>\n",
       "      <td>1.45</td>\n",
       "      <td>0.069811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 212</th>\n",
       "      <td>10.55</td>\n",
       "      <td>0.176283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 213</th>\n",
       "      <td>10.60</td>\n",
       "      <td>0.175729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 214</th>\n",
       "      <td>10.65</td>\n",
       "      <td>0.175166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 215</th>\n",
       "      <td>10.70</td>\n",
       "      <td>0.174595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 216</th>\n",
       "      <td>10.75</td>\n",
       "      <td>0.348031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 217</th>\n",
       "      <td>10.80</td>\n",
       "      <td>0.346857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 218</th>\n",
       "      <td>10.85</td>\n",
       "      <td>0.345666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 219</th>\n",
       "      <td>10.90</td>\n",
       "      <td>0.344460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 220</th>\n",
       "      <td>10.95</td>\n",
       "      <td>0.343238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 221</th>\n",
       "      <td>11.00</td>\n",
       "      <td>0.684000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 222</th>\n",
       "      <td>11.05</td>\n",
       "      <td>0.681494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 223</th>\n",
       "      <td>11.10</td>\n",
       "      <td>0.678957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 224</th>\n",
       "      <td>11.15</td>\n",
       "      <td>0.676389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 225</th>\n",
       "      <td>11.20</td>\n",
       "      <td>0.673792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 226</th>\n",
       "      <td>11.25</td>\n",
       "      <td>0.671165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 227</th>\n",
       "      <td>11.30</td>\n",
       "      <td>0.668508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 228</th>\n",
       "      <td>11.35</td>\n",
       "      <td>0.665822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 229</th>\n",
       "      <td>11.40</td>\n",
       "      <td>0.663107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 230</th>\n",
       "      <td>11.45</td>\n",
       "      <td>0.660363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 231</th>\n",
       "      <td>11.50</td>\n",
       "      <td>0.657591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 232</th>\n",
       "      <td>11.55</td>\n",
       "      <td>0.654791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 233</th>\n",
       "      <td>11.60</td>\n",
       "      <td>0.651962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 234</th>\n",
       "      <td>11.65</td>\n",
       "      <td>0.649106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 235</th>\n",
       "      <td>11.70</td>\n",
       "      <td>0.646223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 236</th>\n",
       "      <td>11.75</td>\n",
       "      <td>0.643313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 237</th>\n",
       "      <td>11.80</td>\n",
       "      <td>0.640375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 238</th>\n",
       "      <td>11.85</td>\n",
       "      <td>0.637412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 239</th>\n",
       "      <td>11.90</td>\n",
       "      <td>0.634421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 240</th>\n",
       "      <td>11.95</td>\n",
       "      <td>0.631405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Muestra 241</th>\n",
       "      <td>12.00</td>\n",
       "      <td>0.628364</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>241 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Tiempo de descanso (horas)  Nivel de descanso\n",
       "Muestra 1                          0.00           0.000000\n",
       "Muestra 2                          0.05           0.013580\n",
       "Muestra 3                          0.10           0.027046\n",
       "Muestra 4                          0.15           0.040399\n",
       "Muestra 5                          0.20           0.053640\n",
       "Muestra 6                          0.25           0.040061\n",
       "Muestra 7                          0.30           0.047871\n",
       "Muestra 8                          0.35           0.055614\n",
       "Muestra 9                          0.40           0.063290\n",
       "Muestra 10                         0.45           0.070900\n",
       "Muestra 11                         0.50           0.078443\n",
       "Muestra 12                         0.55           0.085920\n",
       "Muestra 13                         0.60           0.093332\n",
       "Muestra 14                         0.65           0.100677\n",
       "Muestra 15                         0.70           0.107957\n",
       "Muestra 16                         0.75           0.076781\n",
       "Muestra 17                         0.80           0.081548\n",
       "Muestra 18                         0.85           0.086271\n",
       "Muestra 19                         0.90           0.090951\n",
       "Muestra 20                         0.95           0.095588\n",
       "Muestra 21                         1.00           0.050091\n",
       "Muestra 22                         1.05           0.052367\n",
       "Muestra 23                         1.10           0.054621\n",
       "Muestra 24                         1.15           0.056854\n",
       "Muestra 25                         1.20           0.059066\n",
       "Muestra 26                         1.25           0.061257\n",
       "Muestra 27                         1.30           0.063427\n",
       "Muestra 28                         1.35           0.065576\n",
       "Muestra 29                         1.40           0.067704\n",
       "Muestra 30                         1.45           0.069811\n",
       "...                                 ...                ...\n",
       "Muestra 212                       10.55           0.176283\n",
       "Muestra 213                       10.60           0.175729\n",
       "Muestra 214                       10.65           0.175166\n",
       "Muestra 215                       10.70           0.174595\n",
       "Muestra 216                       10.75           0.348031\n",
       "Muestra 217                       10.80           0.346857\n",
       "Muestra 218                       10.85           0.345666\n",
       "Muestra 219                       10.90           0.344460\n",
       "Muestra 220                       10.95           0.343238\n",
       "Muestra 221                       11.00           0.684000\n",
       "Muestra 222                       11.05           0.681494\n",
       "Muestra 223                       11.10           0.678957\n",
       "Muestra 224                       11.15           0.676389\n",
       "Muestra 225                       11.20           0.673792\n",
       "Muestra 226                       11.25           0.671165\n",
       "Muestra 227                       11.30           0.668508\n",
       "Muestra 228                       11.35           0.665822\n",
       "Muestra 229                       11.40           0.663107\n",
       "Muestra 230                       11.45           0.660363\n",
       "Muestra 231                       11.50           0.657591\n",
       "Muestra 232                       11.55           0.654791\n",
       "Muestra 233                       11.60           0.651962\n",
       "Muestra 234                       11.65           0.649106\n",
       "Muestra 235                       11.70           0.646223\n",
       "Muestra 236                       11.75           0.643313\n",
       "Muestra 237                       11.80           0.640375\n",
       "Muestra 238                       11.85           0.637412\n",
       "Muestra 239                       11.90           0.634421\n",
       "Muestra 240                       11.95           0.631405\n",
       "Muestra 241                       12.00           0.628364\n",
       "\n",
       "[241 rows x 2 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {\n",
    "    'Tiempo de descanso (horas)' : horas,\n",
    "    'Nivel de descanso' : descanso_nuevo(horas)\n",
    "}\n",
    "\n",
    "catalogue = pd.DataFrame(data, \n",
    "                         columns = ['Tiempo de descanso (horas)',  'Nivel de descanso' ], \n",
    "                         index = ['Muestra ' + str(i) for i in range(1, len(descanso_ciclos)+1)]\n",
    "                        )\n",
    "catalogue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El óptimo resulta ser:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Tiempo de descanso (horas)</th>\n",
       "      <th>Nivel de descanso</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Muestra 166</th>\n",
       "      <td>8.25</td>\n",
       "      <td>0.766688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Tiempo de descanso (horas)  Nivel de descanso\n",
       "Muestra 166                        8.25           0.766688"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index_max = descanso_ciclos.index(max(descanso_ciclos))\n",
    "hora_max = horas[index_max]\n",
    "catalogue[index_max : index_max+1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eKOfn52ujlxI+nE5nVK9zKlxbJFxEBsq6ujptdCRyJoV0cEbOIpH3w0OnFEeOPEsnpsvl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\nQwNmzZqFd955BwBwySWXAACqwu22I4oBNTWi581g6P2NSr0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B2eTJYkQvJ+fc32exiOmg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\niIiIiCiO/X8sZ+jF/fRevgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8eb7390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.xkcd():\n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.plot(horas, descanso_nuevo(horas))\n",
    "    plt.xlabel(\"$horas$\", fontsize=20)\n",
    "    plt.ylabel(\"$descanso$\", fontsize=20)\n",
    "    plt.vlines(hora_max, 0, 1, colors = 'r' ,linestyles = 'dashed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este es un método heurístico muy sencillo y muy eficaz, pero no es muy eficiente. Para obtener un óptimo con la precisión deseada hemos evaluado 241 muestras, de las que hemos retenida sólo una. Es decir, **hemos desechado el 99,6 % de las soluciones propuestas**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este método es apropiado para un problema sencillo como éste.  Sin embargo, cuando el espacio de soluciones es muy amplio o cuando la evaluación de la solución propuesta es difícil, los tiempos de cálculo se vuelven inaceptables y es necesario recurrir a métodos heurísticos más inteligentes, como el algoritmo genético."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#¿Qué es un algoritmo genético?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es habitual, en el proceso de diseño o de optimización encontrarse con:\n",
    "\n",
    "* Ecuaciones no derivables (o que nos da pereza derivar)\n",
    "* Sistemas de ecuaciones trascendentales (o que no sabemos resolver)\n",
    "* Relaciones que desconocemos (o que no comprendemos)\n",
    "* Múltiples factores que interactúan simultáneamente\n",
    "* Condiciones cambiantes\n",
    "* ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y entonces surgen preguntas como las siguientes:\n",
    "\n",
    "* ¿Cómo resolver *fácilmente* un problema que con una formulación complicada?\n",
    "* ¿Cómo evaluar una solución cuándo queremos optimizar varios factores al mismo tiempo?\n",
    "* ¿Cómo solucionar un problema cuyas condiciones evolucionan todo el tiempo?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por muy complicado que nos parezcan, hasta los seres vivos más primitivos llevan resolviendo problemas como estos desde *siempre*. La supervivencia es un problema complejo, donde intervienen una cantidad inconmensurable de factores que no se sabe muy bien cómo interactúan entre sí y que, para colmo, cambian geográficamente y evolucionan rápidamente a lo largo del tiempo.\n",
    "\n",
    "Los algoritmos evolutivos nacen de una analogía entre la optimización y la selección natural."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">*My own idiosyncratic view is that the reason scientists burn out early is that they dig very deep in one area and they’ve gone as far as its humanly possible at that time and then they can’t easily cross over into other areas. \n",
    "I think at the heart of most creative science are well thought-out metaphors, and cross-disciplinary work is a rich source of metaphor*. John Henry Holland"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Miremos alrededor y veamos la biodiversidad del mundo. Tenemos seres humanos, enormes elefantes herbívoros, feroces tigres, mansos perritos, minúsculas e industriosas hormigas, árboles grandes y pequeños, setas de colores, peces y mamíferos marinos, bacterias y viruses...\n",
    "\n",
    "**Soluciones diferentes para el mismo problema: ¿cómo hay que ser para reproducirse lo más posible?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Cómo podemos emular a la selección natural para resolver un problema de diseño? Veámoslo con un ejemplo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Ejemplo: cómo aplicar el algoritmo genético"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Cómo se plantearía el problema de optimización de las horas de sueño de tal manera que se pueda resolver con un algoritmo genético?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primero necesitamos poder generar soluciones, \"individuo\" con unas características determinadas que cumplen mejor o peor nuestro objetivo de descansar bien. Por el momento vamos a definir una clase que nos dé un marco general para definirlos e iremos profundizando en lo que quiere decir cada uno de sus atributos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Individual (object):\n",
    "    \n",
    "    def __init__(self, genome):\n",
    "        \n",
    "        self.genome = genome        \n",
    "        self.traits = {}\n",
    "        self.performances = {}\n",
    "        self.fitness = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El genoma es donde está codificada la información que sirve para construir una solución. Mientras se sea coherente, el genoma se puede definir con total libertad según se necesite: números reales, enteros, letras... En el mundo informático todo está codificado en estados binarios, así que haremos que nuestro genoma será una cadena de ceros y unos. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para ello vamos a utilizar un diccionario genético que defina los genes de nuestro individuo y su longitud. En este caso, nuestro individuo sólo presenta una característica, que son las horas de sueño, por lo que sólo habrá un gen. Vamos a estudiar el óptimo en un rango de 0 - 12 horas con una precisión de 0,05 horas, por lo que necesitamos poder representar $\\frac{12}{0.05} = 240 $ estados diferentes como mínimo. Vamos a ir más allá y vamos a utilizar 10 dígitos, que nos permiten codificar 1024 estados diferentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dict_genes = {\n",
    "    'Horas de sueño' : 10,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos a necesitar crear individuos aleatorios, para lo que utilizaremos una función \"Generar genoma\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "generate_random_binary_list = lambda n: [random.randint(0,1) for b in range(1,n+1)]\n",
    "\n",
    "def generate_genome (dict_genes):\n",
    "    \n",
    "    #We first calculate the total number of bits that the genome must contain\n",
    "    number_of_bits = sum([dict_genes[trait] for trait in dict_genes])\n",
    "    \n",
    "    #And we return a random genome of this length\n",
    "    return generate_random_binary_list(number_of_bits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 1, 0, 1, 1, 1, 0, 1, 1, 1],\n",
       " [0, 1, 1, 1, 1, 1, 1, 0, 1, 0],\n",
       " [1, 0, 1, 0, 0, 1, 0, 1, 1, 0],\n",
       " [0, 0, 1, 0, 0, 1, 1, 0, 0, 1]]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[generate_genome(dict_genes) for i in range (4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando ya tengamos nuestros individuos, con su material genético, necesitaremos una función que nos descifre este código y lo traduzca a características reconocibles del mismo. En el mundo real sería como leer el \"gen del color de los ojos\" (en realidad son varios genes) para descubrir que el contenido de ese gen en concreto indica que el individuo tiene \"ojos azules\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calculate_traits (individual, dict_genes):\n",
    "    #This function must decipher the genome and return the traits of the individual.\n",
    "    #Normally, the genome contains binary numerical values for the different traits.\n",
    "    \n",
    "    dict_traits = {}\n",
    "    index = 0\n",
    "    \n",
    "    for trait in dict_genes:\n",
    "        step = 12 / (int(dict_genes[trait]*'1',2))\n",
    "        dict_traits[trait] = step*int(''.join(str(bit) for bit in individual.genome[index : index+dict_genes[trait]]), 2)\n",
    "        index += dict_genes[trait]\n",
    "        \n",
    "    individual.traits = dict_traits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 1, 1, 0, 0, 0, 0, 0, 0]\n",
      "{'Horas de sueño': 2.252199413489736}\n"
     ]
    }
   ],
   "source": [
    "individuo = Individual(generate_genome(dict_genes))\n",
    "calculate_traits (individuo, dict_genes)\n",
    "\n",
    "print(individuo.genome)\n",
    "print(individuo.traits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el mundo natural, las características de un individuo determinarán en gran parte cómo de bien o de mal se desenvolverá en la vida, esto es, sus \"actuaciones\", \"desempeño\" o, en inglés, su \"performance\". Si tiene las piernas más largas, podrá correr más rápido; si tiene unos dientes afilados, podrá defenderse mejor... En nuestro ejemplo esto no es ni más ni menos que el eje vertical de nuestra función de descanso. También vamos a añadir una \"performance\" cuyo valor sea el tiempo de descanso, lo cual puede ser interesante para evaluar la calidad de la solución, como veremos luego."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calculate_performances (individual):\n",
    "    \n",
    "    dict_perfo = {\n",
    "        \n",
    "        'Descanso' : float(descanso_nuevo (individual.traits['Horas de sueño'])),\n",
    "        'Tiempo' : individual.traits['Horas de sueño']\n",
    "    }\n",
    "    \n",
    "    individual.performances = dict_perfo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Horas de sueño': 7.788856304985337}\n",
      "{'Tiempo': 7.788856304985337, 'Descanso': 0.1920462789922687}\n"
     ]
    }
   ],
   "source": [
    "individuo = Individual(generate_genome(dict_genes))\n",
    "calculate_traits (individuo, dict_genes)\n",
    "calculate_performances (individuo)\n",
    "\n",
    "print(individuo.traits)\n",
    "print(individuo.performances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Bs84yaizXCAlwAlPmj0yzOvJaIa+vdODkNQy8Jgd2lFNTU7XZSwk+HA5HUK9zJFxbJLgI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\nP0gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa301400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.xkcd():\n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.plot(horas, descanso_nuevo(horas))\n",
    "    plt.xlabel(\"$horas$\", fontsize=20)\n",
    "    plt.ylabel(\"$descanso$\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Según sean de buenas sus actuaciones, el individuo será más apto, estará mejor adaptado. En nuestro problema se trata de **definir qué es una solución buena**, y aquí se haya una de las armas más potentes del algoritmo genético. **El algoritmo genético nos obliga a definir qué es lo que estamos buscando en nuestro proceso de optimización mediante una función.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En nuestro ejemplo, la calidad del sueño es importante, pero tal vez no queramos optimizarla a toda costa. En ciertas circunstancias podemos desear descansar un poco menos si ello nos permite ahorrar un par de horas. El peso relativo entre estos dos factores lo vamos a representar mediante unos pesos $\\alpha$ y $\\beta$ que intervienen en la función de aptitud, que podemos definir así:\n",
    "$$ Aptitud = \\alpha \\cdot Descanso + \\beta \\cdot \\frac{12 \\, horas - Tiempo}{12 \\, horas } $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calculate_fitness (individual):\n",
    "    \n",
    "    alpha = 1\n",
    "    beta = 0\n",
    "    \n",
    "    individual.fitness = alpha*individual.performances['Descanso'] + beta*((12 - individual.performances['Tiempo'])/12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Tiempo': 0.7272727272727273, 'Descanso': 0.09095212809917358}\n",
      "0.09095212809917358\n"
     ]
    }
   ],
   "source": [
    "individuo = Individual(generate_genome(dict_genes))\n",
    "calculate_traits (individuo, dict_genes)\n",
    "calculate_performances (individuo)\n",
    "calculate_fitness (individuo)\n",
    "\n",
    "print(individuo.performances)\n",
    "print(individuo.fitness)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora ya podemos generar nuestras soluciones y tenemos medios para evaluarlas. Es hora de hacer que la selección natural haga su trabajo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primero necesitamos crear una población. Una manera de hacer esto es mediante una función de inmigración, que genere una sociedad formada por una determinada cantidad de individuos exóticos, generados de manera aleatoria:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def immigration (society, target_population, dict_genes):\n",
    "    \n",
    "    while len(society) < target_population:\n",
    "        \n",
    "        new_individual = Individual (generate_genome (dict_genes))\n",
    "        calculate_traits (new_individual, dict_genes)\n",
    "        calculate_performances (new_individual)\n",
    "        calculate_fitness (new_individual)\n",
    "        \n",
    "        society.append (new_individual)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x8efdd30>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x891e400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "society = []\n",
    "immigration (society, 12, dict_genes)\n",
    "\n",
    "plt.matshow([individual.genome for individual in society], cmap=plt.cm.gray)\n",
    "plt.title('Immigration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora, los individuos de esta sociedad se reproducen entre ellos, generando nuevos individuos. Los individuos más aptos tienen más probabilidades de reproducirse que los menos aptos, con lo que las mejores soluciones generan más descendencia. Durante la concepción, los nuevos individuos sufren pequeñas mutaciones aleatorias. Después nacen y se incorporan a la sociedad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#This function was taken from Eli Bendersky's website\n",
    "#It returns an index of a list called \"weights\", \n",
    "#where the content of each element in \"weights\" is the probability of this index to be returned.\n",
    "#For this function to be as fast as possible we need to pass it a list of weights in descending order.\n",
    "def weighted_choice_sub(weights):\n",
    "    \"\"\"\n",
    "    weights = [0.9, 0.05, 0.05]\n",
    "    N = 100000\n",
    "    lista = [weighted_choice_sub(weights) for ii in range(N)]\n",
    "    print( lista.count(0)/N, lista.count(1)/N, lista.count(2)/N)\n",
    "    \"\"\"\n",
    "    rnd = random.random() * sum(weights)\n",
    "    for i, w in enumerate(weights):\n",
    "        rnd -= w\n",
    "        if rnd < 0:\n",
    "            return i\n",
    "\n",
    "def crossover (society, reproduction_rate, mutation_rate):\n",
    "    \n",
    "    #First we create a list with the fitness values of every individual in the society\n",
    "    fitness_list = [individual.fitness for individual in society]\n",
    "    \n",
    "    #We sort the individuals in the society in descending order of fitness.   \n",
    "    society_sorted = [x for (y, x) in sorted(zip(fitness_list, society), key=lambda x: x[0], reverse=True)] \n",
    "    \n",
    "    #We then create a list of relative probabilities in descending order, \n",
    "    #so that the fittest individual in the society has N times more chances to reproduce than the least fit,\n",
    "    #where N is the number of individuals in the society.\n",
    "    probability = [i for i in reversed(range(1,len(society_sorted)+1))]\n",
    "    \n",
    "    #We create a list of weights with the probabilities of non-mutation and mutation\n",
    "    mutation = [1 - mutation_rate, mutation_rate]    \n",
    "    \n",
    "    #For every new individual to be created through reproduction:\n",
    "    for i in range (int(len(society) * reproduction_rate)):\n",
    "        \n",
    "        #We select two parents randomly, using the list of probabilities in \"probability\".\n",
    "        father, mother = society_sorted[weighted_choice_sub(probability)], society_sorted[weighted_choice_sub(probability)]\n",
    "        \n",
    "        #We randomly select two cutting points for the genome.\n",
    "        a, b = random.randrange(0, len(father.genome)), random.randrange(0, len(father.genome))\n",
    "        \n",
    "        #And we create the genome of the child putting together the genome slices of the parents in the cutting points.\n",
    "        child_genome = father.genome[0:min(a,b)]+mother.genome[min(a,b):max(a,b)]+father.genome[max(a,b):]\n",
    "        \n",
    "        #For every bit in the not-yet-born child, we generate a list containing \n",
    "        #1's in the positions where the genome must mutate (i.e. the bit must switch its value)\n",
    "        #and 0's in the positions where the genome must stay the same.\n",
    "        n = [weighted_choice_sub(mutation) for ii in range(len(child_genome))]\n",
    "        \n",
    "        #This line switches the bits of the genome of the child that must mutate.\n",
    "        mutant_child_genome = [abs(n[i] -  child_genome[i]) for i in range(len(child_genome))]\n",
    "        \n",
    "        #We finally append the newborn individual to the society\n",
    "        newborn = Individual(mutant_child_genome)\n",
    "        calculate_traits (newborn, dict_genes)\n",
    "        calculate_performances (newborn)\n",
    "        calculate_fitness (newborn)\n",
    "        society.append(newborn)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x89429b0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa44ae80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "crossover(society, 1/12, 1/16)\n",
    "plt.matshow([individual.genome for individual in society], cmap=plt.cm.gray)\n",
    "plt.title('Crossover')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el mundo natural, la escasez de recursos obliga a los individuos a competir. Una función de torneo escoge parejas de soluciones al azar, las compara y elimina las menos aptas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tournament(society, target_population):\n",
    "    \n",
    "    while len(society) > target_population:\n",
    "        \n",
    "        #index1, index2 = random.randrange(0, len(society)), random.randrange(0, len(society))\n",
    "        #if society[index1].fitness > society[index2].fitness:\n",
    "        #    society.pop(index2)\n",
    "        #else:\n",
    "        #    society.pop(index1)\n",
    "                \n",
    "        fitness_list = [individual.fitness for individual in society]\n",
    "        society.pop(fitness_list.index(min(fitness_list)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x8e2c978>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa405f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tournament (society, 12)\n",
    "plt.matshow([individual.genome for individual in society], cmap=plt.cm.gray)\n",
    "plt.title('Tournament')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veamos ahora, animado, cómo evoluciona la población:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"imagenes/imm_cross_tour.gif\" alt=\"\" style=\"width: 300px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"imagenes/genome_animation.gif\" alt=\"\" style=\"width: 300px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"imagenes/points_animation.gif\" alt=\"\" style=\"width: 1000px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora podemos crear una función que aplique el algoritmo genético a este problema concreto:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def optimise_sleep (number_of_genes = 10,\n",
    "                    size_of_society = 30, \n",
    "                    reproduction_rate = 0.2, \n",
    "                    mutation_rate = 0.05, \n",
    "                    number_of_generations = 20,\n",
    "                    size_after_tournament = 20\n",
    "                   ):\n",
    "\n",
    "    \n",
    "    dict_genes = {'Horas de sueño' : number_of_genes}\n",
    "    \n",
    "            \n",
    "    society = []\n",
    "    fitness_max = []\n",
    "    fitness_avg = []\n",
    "\n",
    "    for generation in range(number_of_generations):\n",
    "    \n",
    "        immigration (society, size_of_society, dict_genes)\n",
    "        fitness_max += list([max([individual.fitness for individual in society])])\n",
    "        fitness_avg += list([np.mean([individual.fitness for individual in society])])\n",
    "        crossover(society, reproduction_rate, mutation_rate)\n",
    "        tournament (society, size_after_tournament)\n",
    "    \n",
    "    fitness_list = [individual.fitness for individual in society]\n",
    "    winner = society[fitness_list.index(max(fitness_list))]\n",
    "    \n",
    "    with plt.xkcd():\n",
    "        plt.figure(figsize=(15,5))\n",
    "        plt.title(\"Óptimo a las \" + str(round(winner.performances['Tiempo'], 2)) + \" horas\", fontsize = 15)\n",
    "        plt.xlabel(\"$horas$\", fontsize=20)\n",
    "        plt.ylabel(\"$descanso$\", fontsize=20)\n",
    "        \n",
    "        plt.plot(horas, descanso_nuevo(horas))\n",
    "        plt.vlines(winner.performances['Tiempo'], 0, 1, colors = 'r' ,linestyles = 'dashed')\n",
    "        \n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.plot(fitness_max)\n",
    "    plt.title('$\\Phi_{max} = $' + str(round(fitness_max[-1], 5)), fontsize = 15)  \n",
    "    \n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.plot(fitness_avg)\n",
    "    plt.title('$\\overline{\\Phi}$', fontsize = 15)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PtSG0bVEhNXAo6uGHHw4A+PXXXzFixAgcd9xxuPbaa9HU1ISysjLceuutWLJkSYvZWdsK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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb662208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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f6bdgbSrhGTTDY11YRZIkSZrnpu3B65o9eNNL2AH4FPC3Vbyr43IkSZIkzbJB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\na6L8zXwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdbe19b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wYauna0oaXgQHA8tkskPdWdrJQq4PVFcGbwTeX2283IlzbkhZO/c74BOZ/KND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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe2b7ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimise_sleep ()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que alcanzamos el resultado con muchas menos evaluaciones de la función que el algoritmo heurístico más básico (144, frente a 241). Hemos duplicado el rendimiento para esta función 1D, pero las mejoras de rendimiento son más espectaculares cuanto mayor es la dimensión del problema que se quiere optimizar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sin embargo, puede que te hayas dado cuenta de que por más que ejecutes el algortimo, nunca se alcanza el verdadero óptimo, sino que nos quedamos muy, muy, cerca. ¿A qué crees que se debe? ¿Cómo lo solucionarías?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación podrás experimentar con los diferentes parámetros del problema y ver cómo afectan a la optimización:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calculate_fitness (individual):\n",
    "    alpha = 1\n",
    "    beta = 0\n",
    "    individual.fitness = (alpha*individual.performances['Descanso'] + beta*((12 - individual.performances['Tiempo'])/12))/(alpha + beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PtSG0bVEhNXAo6uGHHw4A+PXXXzFixAgcd9xxuPbaa9HU1ISysjLceuutWLJkSYvZWdsK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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa3ff550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa359f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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reo5X0Bldm1dVnZdkeZJfqKrr5nl+7XalXKSE5XSmab4IuB/wJmC/qnZOzZQk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\nWsiyJkmSJEktZFmTJEmSpBb6/3FgrDwCbTPPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa0ffc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = interact(optimise_sleep,\n",
    "             number_of_genes = (1, 50, 1),\n",
    "             size_of_society = (1, 100, 1), \n",
    "             reproduction_rate = (0, 1, 0.01), \n",
    "             mutation_rate = (0, 1, 0.01),\n",
    "             number_of_generations = (1, 100, 1),\n",
    "             size_after_tournament = (1, 100, 1)\n",
    "            )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El tamaño del genoma, esto es, el número de bits utilizados para describir al individuo, determina la cantidad de soluciones posibles, por lo que abre la puerta a mejores optimizaciones. Un genoma mayor supone asimismo una mayor dificultad para converger, debido a que hay muchas más combinaciones posibles a probar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El tamaño de la población es, probablemente el factor más importante. El tiempo de cálculo aumenta de forma directamente proporcional al tamaño de la población, por lo que hay que tener cuidado al elegir el tamaño apropiado.\n",
    "\n",
    "Una población pequeña, aunque mejora los tiempos, puede ser víctima del llamado “efecto del fundador”, en los que una baja variabilidad genética en el origen y, en general, un tamaño poblacional pequeño, hacen que la “deriva genética” lleve a la población a presentar una serie de rasgos comunes que no necesariamente se corresponden con los de los individuos más aptos, que sí se observan fuera de ella."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para evitar este problema, se pueden introducir altas tasas de inmigración y mutación. Si la población es pequeña, es muy sensible, por lo que la media de la función de aptitud evoluciona de manera muy turbulenta y puede, incluso, alejarse de la convergencia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por el contrario, una población grande es garantía de una gran variedad genética inicial. Estadísticamente, también es más probable que se encuentre antes la solución, aunque la convergencia sea más lenta. Además, el gran número estabiliza la evolución de la función de mérito media y hace que la población sea más robusta frente a la inmigración y la mutación."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}