320_Optimizing_Steel_Strength_using_simulated_annealing.ipynb

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      "source": [
        "**Finding the best alloy with maximum yield strength using simulated annealing algorithm <br>**\n",
        "\n",
        "In this example, we will work with the steel alloy data set. <br>\n",
        "Download from here: https://www.kaggle.com/datasets/fuarresvij/steel-test-data\n",
        "\n",
        "<p>\n",
        "The data set contains the elemental composition of different alloys and their respective yield and tensile strengths. A machine learning model can be trained on this data, allowing us to predict the strength of an alloy based on its chemical composition. But, for this exercise, let us try to find the optimized alloy composition with the best yield strength. <p>\n",
        "\n",
        "Let us explore simulated annealing algorightm for optimization. <p>\n"
      ],
      "metadata": {
        "id": "lMJa1wzQyU9T"
      }
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    {
      "cell_type": "markdown",
      "source": [
        "#Start with understanding the data"
      ],
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        "id": "mkNGf1CSA0I_"
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      "source": [
        "#Read the csv file and capture data into a pandas dataframe\n",
        "import pandas as pd\n",
        "\n",
        "df = pd.read_csv(\"/content/drive/MyDrive/ColabNotebooks/data/steel_strength.csv\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()"
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              "                                             formula     c    mn    si     cr  \\\n",
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              "4  Fe0.636C0.000474Mn0.000518Si0.00101Cr0.000109N...  0.01  0.05  0.05   0.01   \n",
              "\n",
              "      ni    mo     v     n    nb     co     w    al    ti  yield strength  \\\n",
              "0  19.70  2.95  0.01  0.00  0.01  15.00  0.00  0.15  1.55          2411.5   \n",
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              "3  17.70  3.95  0.01  0.00  0.01  15.00  0.00  0.13  1.47          2487.3   \n",
              "4  19.40  1.45  0.01  0.00  0.01  14.90  0.00  0.13  1.55          2249.6   \n",
              "\n",
              "   tensile strength  elongation  \n",
              "0            2473.5         7.0  \n",
              "1            1929.2         8.0  \n",
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      "source": [
        "Check if there is any null data. There are a few missing from the elongation column but we will not use it for our exercise."
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        "id": "58_ErHurWJWu"
      }
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              "formula             0\n",
              "c                   0\n",
              "mn                  0\n",
              "si                  0\n",
              "cr                  0\n",
              "ni                  0\n",
              "mo                  0\n",
              "v                   0\n",
              "n                   0\n",
              "nb                  0\n",
              "co                  0\n",
              "w                   0\n",
              "al                  0\n",
              "ti                  0\n",
              "yield strength      0\n",
              "tensile strength    0\n",
              "elongation          9\n",
              "dtype: int64"
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              "                  count         mean         std      min       25%       50%  \\\n",
              "c                 312.0     0.096442    0.109008     0.00     0.010     0.030   \n",
              "mn                312.0     0.146250    0.397102     0.01     0.010     0.010   \n",
              "si                312.0     0.221218    0.580796     0.01     0.010     0.010   \n",
              "cr                312.0     8.043830    5.426169     0.01     3.100     9.050   \n",
              "ni                312.0     8.184006    6.337055     0.01     0.960     8.500   \n",
              "mo                312.0     2.766090    1.832908     0.02     1.500     2.210   \n",
              "v                 312.0     0.183750    0.452462     0.00     0.010     0.010   \n",
              "n                 312.0     0.005545    0.018331     0.00     0.000     0.000   \n",
              "nb                312.0     0.035449    0.161537     0.00     0.010     0.010   \n",
              "co                312.0     7.008782    6.254431     0.01     0.010     7.085   \n",
              "w                 312.0     0.161282    0.920211     0.00     0.000     0.000   \n",
              "al                312.0     0.239135    0.340110     0.01     0.030     0.050   \n",
              "ti                312.0     0.310897    0.556593     0.00     0.000     0.030   \n",
              "yield strength    312.0  1420.998397  301.894169  1005.90  1219.475  1344.200   \n",
              "tensile strength  312.0  1641.653205  346.475179  1019.00  1338.125  1666.300   \n",
              "elongation        303.0    14.007261    5.095974     2.00    10.800    14.800   \n",
              "\n",
              "                        75%      max  \n",
              "c                    0.1825     0.43  \n",
              "mn                   0.0800     3.00  \n",
              "si                   0.1100     4.75  \n",
              "cr                  12.5200    17.50  \n",
              "ni                  12.1175    21.00  \n",
              "mo                   4.0900     9.67  \n",
              "v                    0.1275     4.32  \n",
              "n                    0.0000     0.15  \n",
              "nb                   0.0100     2.50  \n",
              "co                  13.4800    20.10  \n",
              "w                    0.0000     9.18  \n",
              "al                   0.3000     1.80  \n",
              "ti                   0.2325     2.50  \n",
              "yield strength    1576.0750  2510.30  \n",
              "tensile strength  1899.9500  2570.00  \n",
              "elongation          17.3000    35.00  "
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              "    <tr>\n",
              "      <th>cr</th>\n",
              "      <td>312.0</td>\n",
              "      <td>8.043830</td>\n",
              "      <td>5.426169</td>\n",
              "      <td>0.01</td>\n",
              "      <td>3.100</td>\n",
              "      <td>9.050</td>\n",
              "      <td>12.5200</td>\n",
              "      <td>17.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ni</th>\n",
              "      <td>312.0</td>\n",
              "      <td>8.184006</td>\n",
              "      <td>6.337055</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.960</td>\n",
              "      <td>8.500</td>\n",
              "      <td>12.1175</td>\n",
              "      <td>21.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mo</th>\n",
              "      <td>312.0</td>\n",
              "      <td>2.766090</td>\n",
              "      <td>1.832908</td>\n",
              "      <td>0.02</td>\n",
              "      <td>1.500</td>\n",
              "      <td>2.210</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>9.67</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>v</th>\n",
              "      <td>312.0</td>\n",
              "      <td>0.183750</td>\n",
              "      <td>0.452462</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.010</td>\n",
              "      <td>0.010</td>\n",
              "      <td>0.1275</td>\n",
              "      <td>4.32</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>n</th>\n",
              "      <td>312.0</td>\n",
              "      <td>0.005545</td>\n",
              "      <td>0.018331</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.0000</td>\n",
              "      <td>0.15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>nb</th>\n",
              "      <td>312.0</td>\n",
              "      <td>0.035449</td>\n",
              "      <td>0.161537</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.010</td>\n",
              "      <td>0.010</td>\n",
              "      <td>0.0100</td>\n",
              "      <td>2.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>co</th>\n",
              "      <td>312.0</td>\n",
              "      <td>7.008782</td>\n",
              "      <td>6.254431</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.010</td>\n",
              "      <td>7.085</td>\n",
              "      <td>13.4800</td>\n",
              "      <td>20.10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>w</th>\n",
              "      <td>312.0</td>\n",
              "      <td>0.161282</td>\n",
              "      <td>0.920211</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.0000</td>\n",
              "      <td>9.18</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>al</th>\n",
              "      <td>312.0</td>\n",
              "      <td>0.239135</td>\n",
              "      <td>0.340110</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.030</td>\n",
              "      <td>0.050</td>\n",
              "      <td>0.3000</td>\n",
              "      <td>1.80</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ti</th>\n",
              "      <td>312.0</td>\n",
              "      <td>0.310897</td>\n",
              "      <td>0.556593</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.030</td>\n",
              "      <td>0.2325</td>\n",
              "      <td>2.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>yield strength</th>\n",
              "      <td>312.0</td>\n",
              "      <td>1420.998397</td>\n",
              "      <td>301.894169</td>\n",
              "      <td>1005.90</td>\n",
              "      <td>1219.475</td>\n",
              "      <td>1344.200</td>\n",
              "      <td>1576.0750</td>\n",
              "      <td>2510.30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tensile strength</th>\n",
              "      <td>312.0</td>\n",
              "      <td>1641.653205</td>\n",
              "      <td>346.475179</td>\n",
              "      <td>1019.00</td>\n",
              "      <td>1338.125</td>\n",
              "      <td>1666.300</td>\n",
              "      <td>1899.9500</td>\n",
              "      <td>2570.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>elongation</th>\n",
              "      <td>303.0</td>\n",
              "      <td>14.007261</td>\n",
              "      <td>5.095974</td>\n",
              "      <td>2.00</td>\n",
              "      <td>10.800</td>\n",
              "      <td>14.800</td>\n",
              "      <td>17.3000</td>\n",
              "      <td>35.00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ff0138c3-6a8d-4d71-b9c7-ed5e4937082d')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-ff0138c3-6a8d-4d71-b9c7-ed5e4937082d button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-ff0138c3-6a8d-4d71-b9c7-ed5e4937082d');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.hist(figsize=(17,12))"
      ],
      "metadata": {
        "id": "v0zpiRo4PPwg",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 998
        },
        "outputId": "b765b7af-7583-40d9-a888-384b91067e9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<Axes: title={'center': 'c'}>, <Axes: title={'center': 'mn'}>,\n",
              "        <Axes: title={'center': 'si'}>, <Axes: title={'center': 'cr'}>],\n",
              "       [<Axes: title={'center': 'ni'}>, <Axes: title={'center': 'mo'}>,\n",
              "        <Axes: title={'center': 'v'}>, <Axes: title={'center': 'n'}>],\n",
              "       [<Axes: title={'center': 'nb'}>, <Axes: title={'center': 'co'}>,\n",
              "        <Axes: title={'center': 'w'}>, <Axes: title={'center': 'al'}>],\n",
              "       [<Axes: title={'center': 'ti'}>,\n",
              "        <Axes: title={'center': 'yield strength'}>,\n",
              "        <Axes: title={'center': 'tensile strength'}>,\n",
              "        <Axes: title={'center': 'elongation'}>]], dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1700x1200 with 16 Axes>"
            ],
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FAAAAAAAAAItQgAUAAAAAAAAAi1CABQAAAAAAAACLUIAFAAAAAAAAAIv8P1L5DkPgTzkbAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Check for correlations of composition with the yield strength. This gives us an idea about which elements (features) are important in predicting and modeling  the strength."
      ],
      "metadata": {
        "id": "Y1FbHZksWOWb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.corrwith(df[\"yield strength\"])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mGB_m2GEPgZk",
        "outputId": "4f22958e-8a73-4e6f-8f96-d096ceeb741e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-6-0b8e28b47c07>:1: FutureWarning: The default value of numeric_only in DataFrame.corrwith is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning.\n",
            "  df.corrwith(df[\"yield strength\"])\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "c                   0.146949\n",
              "mn                 -0.172716\n",
              "si                 -0.131461\n",
              "cr                 -0.408730\n",
              "ni                  0.252954\n",
              "mo                  0.064278\n",
              "v                   0.200595\n",
              "n                  -0.117023\n",
              "nb                  0.032042\n",
              "co                  0.200274\n",
              "w                  -0.025941\n",
              "al                 -0.035487\n",
              "ti                  0.510252\n",
              "yield strength      1.000000\n",
              "tensile strength    0.821071\n",
              "elongation         -0.575289\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Not much correlation of yield strength with Mo, Nb, W or Al but good correlation with C, Mn, Si, Cr, Ni, V, and Co. We can choose to not include the less correlated features but let's include them for this exercise."
      ],
      "metadata": {
        "id": "tIG2ds9ZQFMY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Define the X values by dropping all irrelevant columns\n",
        "X = df.drop(columns=[\"formula\", \"elongation\", \"tensile strength\", \"yield strength\"])"
      ],
      "metadata": {
        "id": "Q1-1j1XuOpDO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "VL_6K9OlOudk",
        "outputId": "c3501303-b421-4efe-a939-ea00b8fe4cdf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      c    mn    si     cr     ni    mo     v     n    nb     co     w    al  \\\n",
              "0  0.02  0.05  0.05   0.01  19.70  2.95  0.01  0.00  0.01  15.00  0.00  0.15   \n",
              "1  0.18  0.01  0.01  13.44   0.01  3.01  0.46  0.04  0.01  19.46  2.35  0.04   \n",
              "2  0.00  0.01  0.01   8.67  13.45  0.82  0.01  0.00  0.01  13.90  0.00  0.39   \n",
              "3  0.01  0.05  0.05   0.01  17.70  3.95  0.01  0.00  0.01  15.00  0.00  0.13   \n",
              "4  0.01  0.05  0.05   0.01  19.40  1.45  0.01  0.00  0.01  14.90  0.00  0.13   \n",
              "\n",
              "     ti  \n",
              "0  1.55  \n",
              "1  0.00  \n",
              "2  0.57  \n",
              "3  1.47  \n",
              "4  1.55  "
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              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.02</td>\n",
              "      <td>0.05</td>\n",
              "      <td>0.05</td>\n",
              "      <td>0.01</td>\n",
              "      <td>19.70</td>\n",
              "      <td>2.95</td>\n",
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              "      <td>0.18</td>\n",
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              "      <td>13.44</td>\n",
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              "      <th>2</th>\n",
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              "      <td>0.01</td>\n",
              "      <td>0.01</td>\n",
              "      <td>8.67</td>\n",
              "      <td>13.45</td>\n",
              "      <td>0.82</td>\n",
              "      <td>0.01</td>\n",
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              "      <td>0.39</td>\n",
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              "      <td>0.13</td>\n",
              "      <td>1.47</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.01</td>\n",
              "      <td>0.05</td>\n",
              "      <td>0.05</td>\n",
              "      <td>0.01</td>\n",
              "      <td>19.40</td>\n",
              "      <td>1.45</td>\n",
              "      <td>0.01</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.01</td>\n",
              "      <td>14.90</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.13</td>\n",
              "      <td>1.55</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6478917a-22c3-4bd1-a575-848055c091a1')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "      border-radius: 50%;\n",
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              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-6478917a-22c3-4bd1-a575-848055c091a1');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
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              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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              "            + ' to learn more about interactive tables.';\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Define y\n",
        "y = df['yield strength']"
      ],
      "metadata": {
        "id": "Jtm-RMBtFEId"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Split data into train and test sets."
      ],
      "metadata": {
        "id": "GujaP-yEW4OD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "X_train, X_test, y_train, y_test = train_test_split(X,y,\n",
        "test_size=0.2, random_state = 42)"
      ],
      "metadata": {
        "id": "eQtHS8moFG6l"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Define a model for the problem - the model that can be used later as an objective function for optimization <br>\n",
        "Import the ML algorithm for regression - here, we will import the Random Forest Regressor from scikit-learn.<br>\n",
        "Please note that Colab comes with most of the required libraries. You need to make sure you install all the required libraries in case you are running the code locally."
      ],
      "metadata": {
        "id": "i_f5MmF0W6zd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.ensemble import RandomForestRegressor"
      ],
      "metadata": {
        "id": "bHjMv9uAFI1F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Instantiate the model by defining the appropriate hyperparameters. We will discuss hyperparameter optimization in the next tutorial."
      ],
      "metadata": {
        "id": "amzVzZAMXDrW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        " model = RandomForestRegressor(n_estimators=100, max_depth=100)"
      ],
      "metadata": {
        "id": "VtfjhDL1FK78"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model.fit(X_train, y_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "M94UWnSSFMRU",
        "outputId": "50c456ff-903f-48e2-c08a-9865a6e01e14"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RandomForestRegressor(max_depth=100)"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestRegressor(max_depth=100)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestRegressor</label><div class=\"sk-toggleable__content\"><pre>RandomForestRegressor(max_depth=100)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Predict using the trained model on our test data."
      ],
      "metadata": {
        "id": "U9UKEHtJXPG8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = model.predict(X_test)"
      ],
      "metadata": {
        "id": "WhBZE5fhFO4e"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Test the model performance on our test data by checking the RMSE values."
      ],
      "metadata": {
        "id": "O-yxDftPXXKf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "import numpy as np\n",
        "\n",
        "rmse = np.sqrt(mean_squared_error(y_test, y_pred))\n",
        "\n",
        "print(\"RMSE: \", rmse)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i5LKCSPxFQlz",
        "outputId": "5389c973-28ad-4d73-fe55-b7c81f8d9729"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "RMSE:  109.8926796883185\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Plot actual vs. predicted to see if they fall into approximately a straight line."
      ],
      "metadata": {
        "id": "U5z9XKdBXerT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.scatter(y_test, y_pred)\n",
        "plt.title(\"Actual vs. Predicted\")\n",
        "plt.xlabel(\"Actual\")\n",
        "plt.ylabel(\"Predicted\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "2nnjuWYhFUgD",
        "outputId": "92ac00c2-a669-459d-ef96-d3e8ac52c35f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Predicted')"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Out of curiosity, let us check how good the fit is between actual and predicted by fitting to a linear regression and calculating R squared."
      ],
      "metadata": {
        "id": "v-ZQp4kvZvJT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "#initiate linear regression model\n",
        "lin_model = LinearRegression()\n",
        "#fit regression model\n",
        "lin_model.fit((y_test.values.reshape(-1, 1)), (y_pred))\n",
        "#calculate R-squared of regression model\n",
        "r_squared = lin_model.score((y_test.values.reshape(-1, 1)), (y_pred))\n",
        "print(\"R suqared value is: \", r_squared)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IW_pvcCHXwRU",
        "outputId": "ab9cf399-2796-482e-d210-61cde003d769"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "R suqared value is:  0.8588955516003332\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us also check the feature ranking to assess the importance of each dfeature, as reported by Random Forest."
      ],
      "metadata": {
        "id": "kt2ZUdOEZ9Gd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Get feature names from training data\n",
        "features = X_train.columns\n",
        "# Extract importances from model\n",
        "importances = model.feature_importances_\n",
        "# Create a series with feature names and importances\n",
        "feat_imp = pd.Series(importances, index=features)\n",
        "# Plot 10 most important features\n",
        "feat_imp.sort_values().plot(kind=\"barh\")\n",
        "plt.xlabel(\"Importance\")\n",
        "plt.ylabel(\"Feature\")\n",
        "plt.title(\"Feature Importance\");"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "oykl8K_Ffu2C",
        "outputId": "e70e4383-bad1-40df-b6b2-501cb415de28"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now that we are satisfied with our model, we can define a new model object, which we will train on the full data set."
      ],
      "metadata": {
        "id": "I8niN6m0Fdi7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_full= RandomForestRegressor(n_estimators=100, max_depth=100,\n",
        "random_state =42)\n",
        "model_full.fit(X, y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "Dp3bdbneFazL",
        "outputId": "af8b6e3d-1d1d-451f-fdbd-6072eac5e835"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "RandomForestRegressor(max_depth=100, random_state=42)"
            ],
            "text/html": [
              "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RandomForestRegressor(max_depth=100, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestRegressor</label><div class=\"sk-toggleable__content\"><pre>RandomForestRegressor(max_depth=100, random_state=42)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Define the boundaries for each element composition. We will define them as the minum and maximum values from the data set, for each element. Remember that these are the boudnary conditions for our algorithm."
      ],
      "metadata": {
        "id": "uk7xICvvbTMA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Using simulated annealing"
      ],
      "metadata": {
        "id": "tg80THNRZV5q"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The simulated_annealing function is the implementation of the simulated annealing algorithm, which takes the objective function and several other parameters as input and returns the final solution and its quality.\n"
      ],
      "metadata": {
        "id": "QBsQWFkdbEK5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import random\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def obj_fun(X):\n",
        "    X = [X]\n",
        "    results = model_full.predict(X)\n",
        "\n",
        "    return - results  #Negative sign since we are trying to minize the value."
      ],
      "metadata": {
        "id": "krP08YMPaDZ6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "boundaries = np.array([[df['c'].min(), df['c'].max()],\n",
        "[df['mn'].min(), df['mn'].max()],\n",
        "[df['si'].min(), df['si'].max()],\n",
        "[df['cr'].min(), df['cr'].max()],\n",
        "[df['ni'].min(), df['ni'].max()],\n",
        "[df['mo'].min(), df['mo'].max()],\n",
        "[df['v'].min(), df['v'].max()],\n",
        "[df['n'].min(), df['n'].max()],\n",
        "[df['nb'].min(), df['nb'].max()],\n",
        "[df['co'].min(), df['co'].max()],\n",
        "[df['w'].min(), df['w'].max()],\n",
        "[df['al'].min(), df['al'].max()],\n",
        "[df['ti'].min(), df['ti'].max()]])\n",
        "print(boundaries)"
      ],
      "metadata": {
        "id": "Am-VKU7QiTuZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e8aed2fb-8268-432b-8466-0d31c0e9e284"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.00e+00 4.30e-01]\n",
            " [1.00e-02 3.00e+00]\n",
            " [1.00e-02 4.75e+00]\n",
            " [1.00e-02 1.75e+01]\n",
            " [1.00e-02 2.10e+01]\n",
            " [2.00e-02 9.67e+00]\n",
            " [0.00e+00 4.32e+00]\n",
            " [0.00e+00 1.50e-01]\n",
            " [0.00e+00 2.50e+00]\n",
            " [1.00e-02 2.01e+01]\n",
            " [0.00e+00 9.18e+00]\n",
            " [1.00e-02 1.80e+00]\n",
            " [0.00e+00 2.50e+00]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the simulated annealing algorithm\n",
        "def simulated_annealing(obj_func, bounds, t_init, t_final, cooling_rate):\n",
        "    \"\"\"Simulate annealing algorithm for optimization.\n",
        "\n",
        "    Parameters:\n",
        "    obj_func (function): The objective function to be optimized.\n",
        "    bounds (ndarray): An array with the bounds for each parameter of the objective function.\n",
        "    t_init (float): The initial temperature for the algorithm.\n",
        "    t_final (float): The final temperature for the algorithm.\n",
        "    cooling_rate (float): The cooling rate for the algorithm.\n",
        "\n",
        "    Returns:\n",
        "    tuple: A tuple containing the final solution and its quality, and the list of temperatures.\n",
        "\n",
        "    \"\"\"\n",
        "    # Initialize the current solution and temperature\n",
        "    num_params = bounds.shape[0]\n",
        "    current_params = np.array([random.uniform(bounds[i][0], bounds[i][1]) for i in range(num_params)])\n",
        "    current_solution = obj_func(current_params)\n",
        "    t_current = t_init\n",
        "    temperatures = [t_current]\n",
        "\n",
        "    # Iterate until the temperature is below the final temperature\n",
        "    while t_current > t_final:\n",
        "        # Randomly perturb the current solution\n",
        "        perturbed_params = np.array([random.uniform(bounds[i][0], bounds[i][1]) for i in range(num_params)])\n",
        "        perturbed_solution = obj_func(perturbed_params)\n",
        "\n",
        "        # Calculate the change in solution quality\n",
        "        delta = perturbed_solution - current_solution\n",
        "\n",
        "        # If the perturbed solution is better, accept it as the new current solution\n",
        "        if delta < 0:\n",
        "            current_params = perturbed_params\n",
        "            current_solution = perturbed_solution\n",
        "        # If the perturbed solution is worse, accept it with a certain probability\n",
        "        else:\n",
        "            probability = math.exp(-delta / t_current)\n",
        "            if random.random() < probability:\n",
        "                current_params = perturbed_params\n",
        "                current_solution = perturbed_solution\n",
        "\n",
        "        # Decrease the temperature according to the cooling rate\n",
        "        t_current *= cooling_rate\n",
        "        temperatures.append(t_current)\n",
        "\n",
        "    # Return the final solution and its quality, and the list of temperatures\n",
        "    return current_params, current_solution, temperatures\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "uyWsQ73_ZrBd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Set the bounds parameter to a NumPy array with shape (num_params, 2), where num_params is the number of parameters to be optimized, and the first column of each row specifies the lower boundary, and the second column specifies the upper boundary. The cooling rate is a parameter that determines the rate at which the temperature decreases during the simulated annealing process. In the example code provided, the cooling rate is set to 0.95, which means that the temperature will be decreased by 5% at each iteration.\n",
        "\n",
        "The cooling rate can be adjusted to control the rate of cooling and the speed of convergence to the optimal solution. A larger cooling rate will result in a faster decrease in temperature and a faster convergence to the optimal solution, but may also increase the risk of getting stuck in a local minimum. A smaller cooling rate will result in a slower decrease in temperature and a slower convergence to the optimal solution, but may decrease the risk of getting stuck in a local minimum.\n",
        "\n",
        "To adjust the cooling rate in the code, simply change the value of the cooling_rate variable when calling the simulated_annealing function. For example, setting the cooling rate to 0.99 would decrease the temperature by 1% at each iteration:"
      ],
      "metadata": {
        "id": "Dv465dznbU5o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Set the bounds and run the simulated annealing algorithm\n",
        "bounds = boundaries\n",
        "t_init, t_final, cooling_rate = 100, 0.1, 0.95\n",
        "final_solution, final_quality, temperatures = simulated_annealing(obj_fun, bounds, t_init, t_final, cooling_rate)\n",
        "\n",
        "# Print the final solution and its quality\n",
        "print(\"Final solution: \", final_solution)\n",
        "print(\"Final yield strength of our amazing alloy, vibranium :) \", final_quality)\n",
        "print(\"____________________________________________________________\")\n",
        "print(\"____________________________________________________________\")\n",
        "# Plot the temperature versus iteration\n",
        "plt.plot(temperatures)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Temperature')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "xuB-5FPBaUoI",
        "outputId": "30d52c95-c03a-430f-da48-740a01065ee9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/base.py:439: UserWarning: X does not have valid feature names, but RandomForestRegressor was fitted with feature names\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final solution:  [ 0.2462575   2.78498709  0.08603555  5.87522494 17.28400802  4.03393305\n",
            "  4.14760941  0.13282433  2.3333837  18.21838083  2.04765138  0.4159214\n",
            "  2.24231046]\n",
            "Final yield strength of our amazing alloy, vibranium :)  [-2420.945]\n",
            "____________________________________________________________\n",
            "____________________________________________________________\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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jIiK6VixCHm7EjZEAgK0nKtHUbJE4DRERkWdhEfJwPWI1iAhSoa7JjJ2nq6SOQ0RE5FFYhDycTCZgWJfW0+h5eIyIiMguLEJeYDhPoyciIromLEJeYFiXdpAJQH55DYrP10sdh4iIyGOwCHmB0ECV9W7064/yNHoiIqKrxSLkJUZ2jwIAZB9hESIiIrpaLEJeYmS3ltPot508hzpjs8RpiIiIPAOLkJe4ITII8WEBaDJbsOl4pdRxiIiIPAKLkJcQBAEju7fsFVp/tFziNERERJ6BRciLjOzWMk9o/dGzsFhEidMQERG5PxYhLzIwMQzBagUqa43YX6KXOg4REZHbYxHyIiqFDMNab8KafYSHx4iIiH4Pi5CXuaX17LGfeRo9ERHR72IR8jJ/6BYJmQAcKTOgpLpB6jhERERujUXIy4QFqtAvvuUq0zw8RkRE9NtYhLzQqB4tZ4/9dEgncRIiIiL3dk1FqLm5GT///DPee+891NTUAABKS0tRW1vr0HB0bUYlRQMAthdUobq+SeI0RERE7svuInT69GkkJydjzJgxyMjIwNmzZwEA8+fPx6xZsxwekOyXEBGIG6OCYbaIvAkrERHRb7C7CE2fPh0pKSk4f/48/P39rcvvueceZGdnOzQcXbvRPDxGRET0u+wuQps2bcKLL74IlUplszwhIQElJSUOC0bXZ1SPlsNjOcfOoqHJLHEaIiIi92R3EbJYLDCbL/3FWlxcjODgYIeEouvXI1aD9iH+aDRZsOn4WanjEBERuSW7i9CoUaOwaNEi6/eCIKC2thZ//etfcfvttzsyGwCgpKQEDz74IMLDw+Hv74/k5GTs3LnTul4URbz00kuIiYmBv78/0tLScPz4cYfn8DSCIFx09hhPoyciIrocu4vQ//3f/2HLli1ISkpCY2MjHnjgAethsfnz5zs03Pnz5zF06FAolUr8+OOPOHz4MP7xj38gNDTUus2CBQuwePFiZGVlITc3F4GBgRg9ejQaGxsdmsUTjW49PJZ9tBzNZovEaYiIiNyPIIqi3bcpb25uxqpVq7Bv3z7U1taiX79+SE9Pt5k87QizZ8/Gli1bsGnTpsuuF0URsbGxeOaZZ6xnrOn1ekRFRWH58uWYMGHCZV9nNBphNBqt3xsMBsTFxUGv10Oj0Tj0M0jJbBExYN7PqKprwqePp2JI5wipIxERETmMwWCAVqu9rt/fdu0RMplM6Ny5M44fP4709HQsWLAA77zzDv785z87vAQBwLfffouUlBT86U9/QmRkJPr27Ytly5ZZ1xcWFkKn0yEtLc26TKvVIjU1Fdu2bbvi+2ZmZkKr1VofcXFxDs/uDuQyAWndW+499tNBnj1GRET0a3YVIaVS6dJDTgUFBXj33XfRpUsX/PTTT5gyZQqeeuopfPzxxwAAna7ll3tUVJTN66KioqzrLmfOnDnQ6/XWR1FRkfM+hMRu7dlyeGztIR0sFrt3/hEREXk1u+cIZWRkYP78+WhubnZGHhsWiwX9+vXD66+/jr59+2Ly5Ml4/PHHkZWVdV3vq1arodFobB7eaugNEQhWK1BuMGLXmfNSxyEiInIrCntfkJeXh+zsbPz3v/9FcnIyAgMDbdavXr3aYeFiYmKQlJRks6x79+748ssvAQDR0S17O8rLyxETE2Pdpry8HH369HFYDk+mVsjxP0lRWL2nBN/vL8OAhDCpIxEREbkNu/cIhYSEYPz48Rg9ejRiY2Nt5tpotVqHhhs6dCjy8/Ntlh07dgwdO3YEACQmJiI6OtrmitYGgwG5ubkYPHiwQ7N4stuTW0rijwfLeHiMiIjoInbvEfroo4+ckeOynn76aQwZMgSvv/467r33XuzYsQPvv/8+3n//fQAt18qZMWMGXnvtNXTp0gWJiYmYO3cuYmNjMXbsWJfldHc3d71weGz3mfNI4V4hIiIiANd493lXGTBgAL766it89tln6NmzJ1599VUsWrQI6enp1m2ee+45TJs2DZMnT8aAAQNQW1uLtWvXws/PT8Lk7kWtkCMtqWVC+fcHyiROQ0RE5D7svo5QYmIiBEG44vqCgoLrDuVqjrgOgbtbd7gcj/9rJ6I1ftg6+xbIZFf+b0hEROQJHPH72+5DYzNmzLD53mQyYc+ePVi7di2effbZawpBzndzlwgEqRXQGRqxp6ga/TuG/v6LiIiIvJzdRWj69OmXXb506VKbe4CRe/FTypHWPRJf7y3FDwfKWISIiIjgwDlCt912m/W0dnJPt7WePfbDAZ49RkREBDiwCP3nP/9BWBjPRnJnw7u2Q5BagTJ9Iy+uSEREhGs4NNa3b1+bydKiKEKn0+Hs2bN45513HBqOHMtPKcfoHtH4cncxvt1byosrEhGRz7O7CI0ZM8amCMlkMrRr1w4jRoxAt27dHBqOHO/uPrH4cncxvj9QhpfuSoJS7tZXUCAiInIqu4vQyy+/7IQY5CpDO4cjPFCFc3VN2HKiEiNujJQ6EhERkWTs3h0gl8tRUVFxyfJz585BLpc7JBQ5j0Iuwx29WiZNf7uvVOI0RERE0rK7CF3p+otGoxEqleq6A5Hz3d07FgDw00EdGk1midMQERFJ56oPjS1evBhAy/29PvjgAwQFBVnXmc1mbNy4kXOEPES/+FC0D/FHSXUD1h+tsN6UlYiIyNdcdRF68803AbTsEcrKyrI5DKZSqZCQkICsrCzHJySHk8kE3NU7Flk5J/Ht3lIWISIi8llXXYQKCwsBAH/4wx+wevVqhIbyysSe7O7WIrQ+vwKGRhM0fkqpIxEREbmc3XOENmzYwBLkBbrHBKNLZBCami1Ye0AndRwiIiJJ2H36PAAUFxfj22+/xZkzZ9DU1GSzbuHChQ4JRs4lCALG9m2Pv/+Ujy93F+PeAXFSRyIiInI5u4tQdnY27r77bnTq1AlHjx5Fz549cerUKYiiiH79+jkjIznJPX3b4//+m4/cwioUVdUjLixA6khEREQuZfehsTlz5mDWrFk4cOAA/Pz88OWXX6KoqAjDhw/Hn/70J2dkJCeJDfHHkM7hAICv95RInIaIiMj17C5CR44cwUMPPQQAUCgUaGhoQFBQEP72t79h/vz5Dg9IzjWubwcAwOo9JVe8RhQREZG3srsIBQYGWucFxcTE4OTJk9Z1lZWVjktGLnFrz2j4K+UorKzDnqJqqeMQERG5lN1FaNCgQdi8eTMA4Pbbb8czzzyDefPm4dFHH8WgQYMcHpCcK1CtwG09owEAq3cXS5yGiIjItewuQgsXLkRqaioA4JVXXsHIkSOxatUqJCQk4MMPP3R4QHK+cf1aDo99t68MxmbecoOIiHyHXWeNmc1mFBcXo1evXgBaDpPxatKeb3DncERr/KAzNGLD0Qrc2pNXmiYiIt9g1x4huVyOUaNG4fz5887KQxKQy1quKQQAX+zk4TEiIvIddh8a69mzJwoKCpyRhST0x/4th8d+OXYWFYZGidMQERG5ht1F6LXXXsOsWbOwZs0alJWVwWAw2DzIM90QGYSUjqEwW0T8h5OmiYjIRwiinRePkckudCdBEKzPRVGEIAgwmz1vsq3BYIBWq4Ver4dGo5E6jmQ+31mE5/6zH4kRgVj/zHCb/75ERETuxhG/v+2+xcaGDRuu6QeR+7sjOQavfHsIhZV12FFYhdRO4VJHIiIiciq7i9Dw4cOdkYPcQKBagbt6x2JlXhFW7SxiESIiIq9n9xwhANi0aRMefPBBDBkyBCUlLfeo+uSTT6wXWiTP1XYX+h8OlMHQaJI4DRERkXPZXYS+/PJLjB49Gv7+/ti9ezeMRiMAQK/X4/XXX3d4QHKtvnEh6BIZhEaTBd/uLZU6DhERkVNd01ljWVlZWLZsGZRKpXX50KFDsXv3boeGI9cTBAH3te4V+nxnkcRpiIiInMvuIpSfn49hw4Zdslyr1aK6utoRmUhi9/RtD6VcwP5iPQ6W6KWOQ0RE5DR2F6Ho6GicOHHikuWbN29Gp06dHBKKpBUepLbeZmNF7hmJ0xARETmP3UXo8ccfx/Tp05GbmwtBEFBaWooVK1Zg1qxZmDJlijMykgQeTI0HAHyztwQ1nDRNREReyu7T52fPng2LxYKRI0eivr4ew4YNg1qtxqxZszBt2jRnZCQJDEwMww2RQThRUYuv95Rg4uAEqSMRERE5nN1Xlm7T1NSEEydOoLa2FklJSQgKCnJ0NpfhlaUv76MthXjlu8PoFh2MH6ffzCtNExGRW3HE7+9ruo4QAKhUKgQHByMmJsajSxBd2bh+HeCnlOGorga7Tp+XOg4REZHD2V2EmpubMXfuXGi1WiQkJCAhIQFarRYvvvgiTCbOJfEmWn8l7u4dC4CTpomIyDvZXYSmTZuG999/HwsWLMCePXuwZ88eLFiwAB9++CGeeuopZ2QkCaWndgQAfH+gDFV1TRKnISIiciy75whptVqsXLkSt912m83yH374Affffz/0es+77gznCF2ZKIq46+3NOFhiwPO3dsOUEZ2ljkRERARAojlCarUaCQkJlyxPTEyESqW6phDkvgRBwEOtZ4z9e/tpNJst0gYiIiJyILuL0NSpU/Hqq69a7zEGAEajEfPmzcPUqVMdGo7cw929YxEWqEJJdQN+PlIudRwiIiKHsfs6Qnv27EF2djY6dOiA3r17AwD27duHpqYmjBw5EuPGjbNuu3r1asclJcn4KeW4f2Aclm44ieVbT1mvOk1EROTp7C5CISEhGD9+vM2yuLg4hwUi9/TgoI7IyinA9oIqHCkzoHsM51IREZHns7sIffTRR87IQW4uRuuPW3tE4/sDZfh46ym8Mb6X1JGIiIiu2zVfUJF8z8NDEwAAX+8twXmeSk9ERF7A7iJ07tw5ZGRkICkpCREREQgLC7N5kPdK6RiKHrEaNJosWJlXJHUcIiKi62b3obGJEyfixIkTeOyxxxAVFcX7T/kQQRDw8JAEPPuf/fh46yk8dlMiVAruVCQiIs9ldxHatGkTNm/ebD1jjHzL3X1iseCnfOgMjfj+QCnu6dtB6khERETXzO7/ne/WrRsaGhqckYU8gFohx8NDEgAAyzYWws4LkxMREbkVu4vQO++8gxdeeAE5OTk4d+4cDAaDzYO8X3pqPPyVchwuM2DryXNSxyEiIrpmdhehkJAQGAwG3HLLLYiMjERoaChCQ0MREhKC0NBQZ2QkNxMSoMK9KS2HxJZtKpA4DRER0bWze45Qeno6lEolPv30U06W9mGP3pSIf20/jV/yz+JYeQ26RgVLHYmIiMhudhehgwcPYs+ePbjxxhudkYc8RMfwQNzaIxo/HtThg00FWPBHTp4nIiLPY/ehsZSUFBQV8RoyBPz55k4AgK/3lKLc0ChxGiIiIvvZvUdo2rRpmD59Op599lkkJydDqVTarO/Vi7de8BX9O4ZiQEIo8k6dxwebCvDCHUlSRyIiIrKLINp5/rNMdulOJEEQIIoiBEGA2Wx2WDhXMRgM0Gq10Ov10Gh4M1F7bMivwCMf5SFAJceW529BaKBK6khEROQjHPH72+5DY4WFhZc8CgoKrF+d6Y033oAgCJgxY4Z1WWNjIzIyMhAeHo6goCCMHz8e5eXlTs1BF4zo2g5JMRrUN5nx8bZTUschIiKyi91FqGPHjr/5cJa8vDy89957lxx6e/rpp/Hdd9/hiy++QE5ODkpLSzFu3Din5SBbgiDgyT90BgB8tOUU6ozNEiciIiK6etd0o6hPPvkEQ4cORWxsLE6fPg0AWLRoEb755huHhmtTW1uL9PR0LFu2zOZaRXq9Hh9++CEWLlyIW265Bf3798dHH32ErVu3Yvv27U7JQpe6rWcMEiMCoW8w4bMdZ6SOQ0REdNXsLkLvvvsuZs6cidtvvx3V1dXWOUEhISFYtGiRo/MBADIyMnDHHXcgLS3NZvmuXbtgMplslnfr1g3x8fHYtm3bFd/PaDTyitgOJJcJeGJ4yxlkyzYVwNjsefPEiIjIN9ldhJYsWYJly5bhhRdegFwuty5PSUnBgQMHHBoOAFauXIndu3cjMzPzknU6nQ4qlQohISE2y6OioqDT6a74npmZmdBqtdZHXFyco2P7nHv6dkCM1g/lBiO+2FksdRwiIqKrck2Tpfv27XvJcrVajbq6OoeEalNUVITp06djxYoV8PPzc9j7zpkzB3q93vrgdZGun0ohw1+GtewVemfDCTQ1WyRORERE9PvsLkKJiYnYu3fvJcvXrl2L7t27OyKT1a5du1BRUYF+/fpBoVBAoVAgJycHixcvhkKhQFRUFJqamlBdXW3zuvLyckRHR1/xfdVqNTQajc2Drt+EgfGIDFajVN+IL3axXBIRkfu76iL0t7/9DfX19Zg5cyYyMjKwatUqiKKIHTt2YN68eZgzZw6ee+45h4YbOXIkDhw4gL1791ofKSkpSE9Ptz5XKpXIzs62viY/Px9nzpzB4MGDHZqFfp+fUo4nR7ScQbZ0PfcKERGR+7vqCyrK5XKUlZUhMjISK1aswMsvv4yTJ08CAGJjY/HKK6/gsccec2pYABgxYgT69OljnZg9ZcoU/PDDD1i+fDk0Gg2mTZsGANi6detVvycvqOg4jSYzhi3YgIoaI+bd0xPpqc67pAIREfk2l15Q8eK+lJ6ejuPHj6O2thY6nQ7FxcUuKUGX8+abb+LOO+/E+PHjMWzYMERHR2P16tWSZCHuFSIiIs9y1XuEZDIZysvL0a5dO2dncjnuEXKsi/cKvTa2Jx4cxL1CRETkeC6/xUbXrl0RFhb2mw+ii/cKvb3+BBpNvK4QERG5J7vuPv/KK69Aq9U6Kwt5kftT4/H+xgKU6hvxybbTeLz11HoiIiJ3YlcRmjBhAiIjI52VhbyIWiHHjLSueO7L/XjnlxOYMDAOwX5KqWMRERHZuOpDY4IgODMHeaFx/dqjc7tAnK834YNNhVLHISIiusQ1nTVGdDUUchmeGXUjAOCDTQU4V2uUOBEREZGtqy5CFouFh8XIbrf2iEbP9hrUNZnxzi8npY5DRERkw+5bbBDZQyYT8OzobgCAT7adRlFVvcSJiIiILmARIqcb1iUCgzuFo8lswf/9N1/qOERERFYsQuR0giDghTtabsj7zd5S7C+uljYQERFRKxYhcome7bUY17c9AGDe90c4+Z6IiNwCixC5zDOjb4RaIUNuYRV+PlIhdRwiIiIWIXKd9iH+ePSmRABA5o9HYDLzhqxERCQtFiFyqSkjOiMsUIWCs3VYsf201HGIiMjHsQiRS2n8lHj6f7oCABauO4aquiaJExERkS9jESKXe2BgPLpFB8PQ2Ix/8HR6IiKSEIsQuZxcJuDlu3sAAD7bcQaHSvUSJyIiIl/FIkSSGNQpHHf0ioFFBF759jBPpyciIkmwCJFk/vf27vBTyrDjVBXW7C+TOg4REfkgFiGSTPsQf0wZfgOAloss1hqbJU5ERES+hkWIJPWX4Z0QHxYAnaERb647JnUcIiLyMSxCJCk/pRx/G9MycXr51lM4XGqQOBEREfkSFiGS3IgbI3F7cjTMFhEvfn0AFgsnThMRkWuwCJFbeOnOHghUybH7TDVW7SySOg4REfkIFiFyC9FaP+sVp9/48SjO1hglTkRERL6ARYjcxsNDEtAjVgN9gwkvf3dI6jhEROQDWITIbSjkMswf3wtymYDv95fhv4d0UkciIiIvxyJEbqVney0ev7kTAGDuNwdhaDRJnIiIiLwZixC5nRlpXZAYEYhygxGZPxyVOg4REXkxFiFyO35KOd4Ylwyg5aasW09WSpyIiIi8FYsQuaXUTuFIT40HADz7xX7U8BAZERE5AYsQua05t3dHXJg/SqobMO/7I1LHISIiL8QiRG4rSK3A3//YG4IArMwrwoajFVJHIiIiL8MiRG5tUKdwPDo0EQDw/Jf7UV3fJHEiIiLyJixC5PaeHX0jOrULREWNES9+fRCiyHuRERGRY7AIkdvzU8qx8N4+kMsErNlfhtW7S6SOREREXoJFiDxCn7gQPJ3WBQDw0jcHcfpcncSJiIjIG7AIkceYMuIGDEwMQ12TGU+t3AuT2SJ1JCIi8nAsQuQx5DIBb97XBxo/BfYVVeOtn49LHYmIiDwcixB5lPYh/ni99arTS385gS0neNVpIiK6dixC5HHu7BWLCQPiIIrA9JV7UGFolDoSERF5KBYh8kgv390D3aKDUVnbhKdW7kEz5wsREdE1YBEij+SnlGNpej8EquTYXlCFt7I5X4iIiOzHIkQeq3O7IOt8obc3nMAv+bwFBxER2YdFiDzamD7tkZ4a3zpfaC/OnKuXOhIREXkQFiHyeC/dlYQ+cSHQN5gw+ZOdqG9qljoSERF5CBYh8nhqhRxZD/ZHRJAaR3U1mP3lAd6PjIiIrgqLEHmFaK0f3knvB4VMwLf7SvHBpkKpIxERkQdgESKvMTAxDC/e0R0AkPnjEWw4ysnTRET021iEyKtMGpKACQPiYBGBaZ/twbHyGqkjERGRG2MRIq8iCAL+NqYnUhPDUGtsxmMf56GqrknqWERE5KZYhMjrqBQyZD3YH/FhASiqasATn+yCsdksdSwiInJDLELklUIDVfhwUgqC1QrsOFWFWV/sh8XCM8mIiMgWixB5rS5Rwcia2B8KmYDv9pViwU/5UkciIiI3wyJEXm3oDRGYP74XACAr5yQ+2X5a4kREROROWITI643v3wEz/6crAOCv3xzET4d0EiciIiJ3wSJEPmHaLTdcOK3+0z3YerJS6khEROQG3LoIZWZmYsCAAQgODkZkZCTGjh2L/HzbeR6NjY3IyMhAeHg4goKCMH78eJSXl0uUmNyVIAh4bWxPjEqKQpPZgsc/3on9xdVSxyIiIom5dRHKyclBRkYGtm/fjnXr1sFkMmHUqFGoq6uzbvP000/ju+++wxdffIGcnByUlpZi3LhxEqYmd6WQy7D4/r4Y0jkcdU1mTPrnDpyoqJU6FhERSUgQPejulGfPnkVkZCRycnIwbNgw6PV6tGvXDp9++in++Mc/AgCOHj2K7t27Y9u2bRg0aNBVva/BYIBWq4Ver4dGo3HmRyA3UGtsxgPLtmN/sR7RGj+s+ssgdAwPlDoWERHZyRG/v916j9Cv6fV6AEBYWBgAYNeuXTCZTEhLS7Nu061bN8THx2Pbtm1XfB+j0QiDwWDzIN8RpFZg+SMD0SUyCDpDIx5Ylovi8/VSxyIiIgl4TBGyWCyYMWMGhg4dip49ewIAdDodVCoVQkJCbLaNioqCTnflM4MyMzOh1Wqtj7i4OGdGJzcUFqjCisdT0SkiECXVDbh/2XaU6RukjkVERC7mMUUoIyMDBw8exMqVK6/7vebMmQO9Xm99FBUVOSAheZrIYD98+vggdAxvuRXHA8tyWYaIiHyMRxShqVOnYs2aNdiwYQM6dOhgXR4dHY2mpiZUV1fbbF9eXo7o6Ogrvp9arYZGo7F5kG+K1raUoQ6h/iisrMN9723nYTIiIh/i1kVIFEVMnToVX331FdavX4/ExESb9f3794dSqUR2drZ1WX5+Ps6cOYPBgwe7Oi55qPYh/lg5eRDiwwJwpqoe9723HWfOsQwREfkCtz5r7Mknn8Snn36Kb775BjfeeKN1uVarhb+/PwBgypQp+OGHH7B8+XJoNBpMmzYNALB169ar/jk8a4wAoEzfgPRluSiorEOM1g8r/pyKTu2CpI5FRERX4Ijf325dhARBuOzyjz76CA8//DCAlgsqPvPMM/jss89gNBoxevRovPPOO795aOzXWISoTYWhEekf5OJ4RS3CA1X4+NGB6NleK3UsIiK6DK8vQq7CIkQXO1drxKSPduBgiQHBagU+mJSC1E7hUsciIqJf8bnrCBG5QniQGp89PgipiWGoMTbjoX/uwLrDvG0LEZE3YhEiuoxgPyU+fnQg0rpHwdhswV8+2YnlWwqljkVERA7GIkR0BX5KObIe7Ge9a/3L3x3Gy98egtni80eTiYi8BosQ0W9QyGXIHJeM2bd1AwAs33oKk/+1E3XGZomTERGRI7AIEf0OQRDwxPDOeCe9H9QKGbKPVuDe97ZBp2+UOhoREV0nFiGiq3R7cgw+mzwI4YEqHCo1YOzSLThcyhv2EhF5MhYhIjv0iw/F1xlDcUPrnev/lLUVaw9e+Qa/RETk3liEiOwUFxaAL6cMwZDO4ahrMuOJf+9C5o9H0Gy2SB2NiIjsxCJEdA20/i2n1//5ppb7372XU4AHP8xFRQ3nDREReRIWIaJrpJTL8OKdSVj6QD8EquTYXlCFOxdvxs5TVVJHIyKiq8QiRHSd7ugVg2+m3oQukUGoqDFiwvvb8eHmQvDuNURE7o9FiMgBbogMwtcZQ3F371g0W0S8uuYwpn66B/oGk9TRiIjoN7AIETlIoFqBtyb0wSt394BSLuD7A2W4bdFGbD1ZKXU0IiK6AhYhIgcSBAGThiTgiyeGICE8AKX6RqR/kIt53x9Go8ksdTwiIvoVFiEiJ+gTF4Ifpt+MB1LjIYrAsk2FGLt0C46U8QKMRETuhEWIyEkCVAq8fk8yPngoBRFBKhzV1WDM21vw/saTsPDGrUREboFFiMjJ0pKisHbGMKR1j0ST2YLXfziKCe9vx4mKGqmjERH5PBYhIheICFJj2UMpyByXjACVHDtOVeH2tzbjzXXHYGzm3CEiIqmwCBG5iCAIuH9gPP779DDc0q1l79Bb2cdx+1ubkFtwTup4REQ+iUWIyMU6hAbgw0kpePuBvogIUuPk2Trc9/52zP5yP/T1vO4QEZErsQgRSUAQBNzZKxbZzwzHA6nxAICVeUUYufAXfLGziJOpiYhcRBB5HwAYDAZotVro9XpoNBqp45APyjtVhTmrD+BERS0AILm9FnPvTMLAxDCJkxERuS9H/P5mEQKLELmHpmYLlm8txJLsE6gxNgMA7kiOwezbuiEuLEDidERE7odFyEFYhMidVNYasXDdMazccQYWEVApZHjspkQ8OaIzgv2UUscjInIbLEIOwiJE7uiozoBX1xzGlhMtZ5RFBKkwZcQNSE+Nh59SLnE6IiLpsQg5CIsQuStRFJF9pALzfjiCwso6AEC0xg8Zt9yA+1LioFLwfAci8l0sQg7CIkTuzmS24D+7irEk+zhK9Y0AgA6h/njqli4Y1689FHIWIiLyPSxCDsIiRJ7C2GzGyh1FeHvDCZytMQIAEiMCMfUPN+DuPrFQshARkQ9hEXIQFiHyNA1NZvx7+2m8m3MSVXVNAIBYrR8eu7kTJgyIQ6BaIXFCIiLnYxFyEBYh8lS1xmb8a9sp/HPzKVTWtuwh0vor8dDgjpg0JAERQWqJExIROQ+LkIOwCJGnazSZsXp3Cd7feBKnztUDANQKGe5NicMjQxPQqV2QxAmJiByPRchBWITIW5gtIv57SIesnJPYV6y3Lr+5SwQeGpyAW7pFQi4TJExIROQ4LEIOwiJE3kYURWwvqMIHmwqwPr8CbX/L24f4I31QPO5LiUM4D5sRkYdjEXIQFiHyZkVV9fh37mmsyitCdevd7VVyGe7oFYN7U+KQmhgGGfcSEZEHYhFyEBYh8gWNJjO+21eKT7afxv6LDpvFhfljfL8OGN+vA+9pRkQehUXIQViEyNfsLarGqrwz+G5fGWpbb/AKAEM6h+OP/Tvg1p7RCFDxFHwicm8sQg7CIkS+qqHJjJ8O6fDFriJsPXnOOpcoQCXHyO5RuLNXDIZ3bcd7mxGRW2IRchAWISKg+Hw9Vu8uwX92FeNMVb11ebBagf9JisJdvWMx9IYI3t+MiNwGi5CDsAgRXSCKIvYX6/HdvlJ8f6AMZa33NgNaLtY4snskRiVF4eYu7XgFayKSFIuQg7AIEV2exSJi95nzWLO/DN8fKLPe3wwAVAoZhnYOx/8kRSOteyQiNX4SJiUiX8Qi5CAsQkS/z2wRsfNUFdYdLse6I+U4fa7eZn3vuBAM79oOw7tGoHeHECh4A1gicjIWIQdhESKyjyiKOF5Ri3WHy/Hfw+XYV1Rts17jp8DQGyIwrGs7DOvaDu1D/KUJSkRejUXIQViEiK5PuaEROflnkXP8LDYfr4S+wWSzvlNEIAZ1DsegTuEYlBjGw2hE5BAsQg7CIkTkOGaLiP3F1dh4rBIbj5/FnjPnYfnVvzKd2gW2lKJO4RiQEIoYLfcYEZH9WIQchEWIyHn0DSbkFVZhe8E5bCs4h8NlBvz6X51YrR/6dQxF/9ZH9xgNlJxjRES/g0XIQViEiFxHX2/CjlMtxWh7wTkcKTNcssfITylDrw4hSG6vRXJ7LXq216JTRCDviUZENliEHIRFiEg6dcZm7Cuqxu4z57Hr9HnsPlN9yRwjAAhUydEjtqUUJXfQILm9FokRQZCzHBH5LBYhB2ERInIfFouIgspa7DlTjYMlehwo0eNwmQGNJssl2wao5EiK0aBrdDBujApG16hg3BgdjLBAlQTJicjVWIQchEWIyL01my04ebYOB0r0F8pRqQENJvNlt48IUqHrRcWoa1QQukQFQ+OndHFyInImFiEHYREi8jxmi4iTZ2txuNSAY+U1OFZeg/zyGhRVNVzxNRFBKiRGBCIhPBAJEYHoFNHyNSE8EP4q3liWyNM44vc3bxRERB5JLhOse30uVmdsxomKWuSX1+B4eQ3yy2txTFcDnaERlbVNqKxtQt6p85e8X4zWz1qQ4sL80SE0AB1C/dEh1B/tgtQQBM5FIvJG3CME7hEi8gU1jSacqqxH4bk6FJ6tw6lzdSiorEPh2VoYGpt/87Vqhay1FAVYv7YP9Ue0xg/RGj9EatTwU3KPEpGrcY8QEdFVCvZTIrmDFskdtDbLRVHE+XoTCivrcKqypSCVnG9A8fkGFJ+vR5mhEcbmljlKJ8/WXfH9QwOUiNL4IVrbUo4u9zw0QMk9S0RuhkWIiHyaIAgIC1QhLFCF/h1DL1nf1GyBTt+IovP1KD5f31qQGlByvgE6QyN0hkY0NVtwvt6E8/UmHNXVXPFnqeQyRASpEB6kRniQCuGB6tbvW55f/DUsUMW9TEQuwCJERPQbVAoZ4sMDEB8ecNn1oiiiut4EnaER5a0Pnd5o/V6nb/l6rq4JTWYLSvWNKNU3XtXPDlYrEB6kQmigCiH+SoQEqKD1V0Lrr0RIQOvDXwVN2/et6xS8KjfRVWMRIiK6DoIgIDSwpax0j7nyHAVjsxkVBiPO1TXhXG3b1wvPK2uNqGpbVmeEySyixtiMGmMzTp2rtytTkFoBrb8SwX4KBPspEKRWIMhPiSC1Ahrr9y1fW7ZRWpcFt371V8p5GI98AosQEZELqBVyxIUFIC7s8nuWLiaKIgyNzdaSVFXXBH2DCfp6E6obmlBdb0L1Rd/rG0yorjehpnXSd62xGbXG354A/nvkMgEBKnnrQwE/pdz6vb9SDn/rcwX8VTIEqBS/Wv7rbVqWqRUyqJUyqBVyXhWc3ILXFKGlS5fi73//O3Q6HXr37o0lS5Zg4MCBUsciIrKbIAjWQ2Cd2l3965rNFhgam1Fd34TqBhPqjM2oaWxGbWPLnqXaxmbUGk2obVveuqzteU1jyzqL2HKdpprWdYDRKZ9TIRNai5EcKnlbQWopSW2FSSVv/f6y6+RQyAWo5DIo5AKUchmUrV8VchlUcgEKmQxKhQxKmQClQgaFrG27C9sqL/d6mcA9Yj7CK4rQqlWrMHPmTGRlZSE1NRWLFi3C6NGjkZ+fj8jISKnjERG5hEIus078vlaiKKLBZG4tTc2obzKjwWRGQ5O59XnrstZHvenXz5vRYDJf2OZXz80X3WG32SKiucmMuqbLXyFcasq2IiUXoJDLIJcJkAtCy1eZAIXswnObh2D7/aXbySAXALmspXDJrvReQss6uSBAJgAymQBBAGRt3wstZa3tuUx20XMBresu3rZtnQC57LfXt71eLrv4vS6st24rAwS0bdOynYAL2wsQWpcDURo/KN1w/ppXXEcoNTUVAwYMwNtvvw0AsFgsiIuLw7Rp0zB79uxLtjcajTAaL/wfjsFgQFxcHK8jRETkZM1mC5rMFhhNFhibLTA2m9HUfOH5heWt37c9N7U8b/rVumazBc1mEU2tX01mC0wWEaZmC5otFjSZRTSbLTBdbjuzBSaziGZLy1dyruxnhqNzuyCHvievIwSgqakJu3btwpw5c6zLZDIZ0tLSsG3btsu+JjMzE6+88oqrIhIRUStF62GrADe7L64oimi2iNZyZLqoMDWZLTBbROuj+aLn1ocowmxpeY1FtN2m2SLC0vZVFNFsvvg1F7+nBWYLrF+bLRZYRBEWsSWfxQLb71ufW9qe/8Z6sfWr2XLhue22l77Wdlvb97Eus4gQW8dPxMXfX7Ss9XUyNz3U6PFFqLKyEmazGVFRUTbLo6KicPTo0cu+Zs6cOZg5c6b1+7Y9QkRE5JsEQbDODyLf4vFF6Fqo1Wqo1WqpYxAREZHEPL76RkREQC6Xo7y83GZ5eXk5oqOjJUpFREREnsDji5BKpUL//v2RnZ1tXWaxWJCdnY3BgwdLmIyIiIjcnVccGps5cyYmTZqElJQUDBw4EIsWLUJdXR0eeeQRqaMRERGRG/OKInTffffh7NmzeOmll6DT6dCnTx+sXbv2kgnURERERBfziusIXS9HXIeAiIiIXMsRv789fo4QERER0bViESIiIiKfxSJEREREPotFiIiIiHwWixARERH5LBYhIiIi8lksQkREROSzWISIiIjIZ3nFlaWvV9s1JQ0Gg8RJiIiI6Gq1/d6+nmtDswgBqKmpAQDExcVJnISIiIjsVVNTA61We02v5S020HK3+tLSUgQHB0MQBIe9r8FgQFxcHIqKinz+1h0ciws4FhdwLFpwHC7gWFzAsbjgSmMhiiJqamoQGxsLmezaZvtwjxAAmUyGDh06OO39NRqNz/8hbsOxuIBjcQHHogXH4QKOxQUciwsuNxbXuieoDSdLExERkc9iESIiIiKfxSLkRGq1Gn/961+hVquljiI5jsUFHIsLOBYtOA4XcCwu4Fhc4Myx4GRpIiIi8lncI0REREQ+i0WIiIiIfBaLEBEREfksFiEiIiLyWSxCTrR06VIkJCTAz88Pqamp2LFjh9SRnCozMxMDBgxAcHAwIiMjMXbsWOTn59ts09jYiIyMDISHhyMoKAjjx49HeXm5RIld54033oAgCJgxY4Z1mS+NRUlJCR588EGEh4fD398fycnJ2Llzp3W9KIp46aWXEBMTA39/f6SlpeH48eMSJnYOs9mMuXPnIjExEf7+/ujcuTNeffVVm/skeetYbNy4EXfddRdiY2MhCAK+/vprm/VX87mrqqqQnp4OjUaDkJAQPPbYY6itrXXhp7h+vzUOJpMJzz//PJKTkxEYGIjY2Fg89NBDKC0ttXkPbxgH4Pf/TFzsiSeegCAIWLRokc1yR4wFi5CTrFq1CjNnzsRf//pX7N69G71798bo0aNRUVEhdTSnycnJQUZGBrZv345169bBZDJh1KhRqKurs27z9NNP47vvvsMXX3yBnJwclJaWYty4cRKmdr68vDy899576NWrl81yXxmL8+fPY+jQoVAqlfjxxx9x+PBh/OMf/0BoaKh1mwULFmDx4sXIyspCbm4uAgMDMXr0aDQ2NkqY3PHmz5+Pd999F2+//TaOHDmC+fPnY8GCBViyZIl1G28di7q6OvTu3RtLly697Pqr+dzp6ek4dOgQ1q1bhzVr1mDjxo2YPHmyqz6CQ/zWONTX12P37t2YO3cudu/ejdWrVyM/Px933323zXbeMA7A7/+ZaPPVV19h+/btiI2NvWSdQ8ZCJKcYOHCgmJGRYf3ebDaLsbGxYmZmpoSpXKuiokIEIObk5IiiKIrV1dWiUqkUv/jiC+s2R44cEQGI27ZtkyqmU9XU1IhdunQR161bJw4fPlycPn26KIq+NRbPP/+8eNNNN11xvcViEaOjo8W///3v1mXV1dWiWq0WP/vsM1dEdJk77rhDfPTRR22WjRs3TkxPTxdF0XfGAoD41VdfWb+/ms99+PBhEYCYl5dn3ebHH38UBUEQS0pKXJbdkX49DpezY8cOEYB4+vRpURS9cxxE8cpjUVxcLLZv3148ePCg2LFjR/HNN9+0rnPUWHCPkBM0NTVh165dSEtLsy6TyWRIS0vDtm3bJEzmWnq9HgAQFhYGANi1axdMJpPNuHTr1g3x8fFeOy4ZGRm44447bD4z4Ftj8e233yIlJQV/+tOfEBkZib59+2LZsmXW9YWFhdDpdDZjodVqkZqa6nVjMWTIEGRnZ+PYsWMAgH379mHz5s247bbbAPjWWFzsaj73tm3bEBISgpSUFOs2aWlpkMlkyM3NdXlmV9Hr9RAEASEhIQB8axwsFgsmTpyIZ599Fj169LhkvaPGgjdddYLKykqYzWZERUXZLI+KisLRo0clSuVaFosFM2bMwNChQ9GzZ08AgE6ng0qlsv6FbhMVFQWdTidBSudauXIldu/ejby8vEvW+dJYFBQU4N1338XMmTPxv//7v8jLy8NTTz0FlUqFSZMmWT/v5f6+eNtYzJ49GwaDAd26dYNcLofZbMa8efOQnp4OAD41Fhe7ms+t0+kQGRlps16hUCAsLMxrx6axsRHPP/887r//fuuNRn1pHObPnw+FQoGnnnrqsusdNRYsQuQUGRkZOHjwIDZv3ix1FEkUFRVh+vTpWLduHfz8/KSOIymLxYKUlBS8/vrrAIC+ffvi4MGDyMrKwqRJkyRO51qff/45VqxYgU8//RQ9evTA3r17MWPGDMTGxvrcWNBvM5lMuPfeeyGKIt59912p47jcrl278NZbb2H37t0QBMGpP4uHxpwgIiICcrn8kjOAysvLER0dLVEq15k6dSrWrFmDDRs2oEOHDtbl0dHRaGpqQnV1tc323jguu3btQkVFBfr16weFQgGFQoGcnBwsXrwYCoUCUVFRPjMWMTExSEpKslnWvXt3nDlzBgCsn9cX/r48++yzmD17NiZMmIDk5GRMnDgRTz/9NDIzMwH41lhc7Go+d3R09CUnmzQ3N6OqqsrrxqatBJ0+fRrr1q2z7g0CfGccNm3ahIqKCsTHx1v/DT19+jSeeeYZJCQkAHDcWLAIOYFKpUL//v2RnZ1tXWaxWJCdnY3BgwdLmMy5RFHE1KlT8dVXX2H9+vVITEy0Wd+/f38olUqbccnPz8eZM2e8blxGjhyJAwcOYO/evdZHSkoK0tPTrc99ZSyGDh16yWUUjh07ho4dOwIAEhMTER0dbTMWBoMBubm5XjcW9fX1kMls/9mVy+WwWCwAfGssLnY1n3vw4MGorq7Grl27rNusX78eFosFqampLs/sLG0l6Pjx4/j5558RHh5us95XxmHixInYv3+/zb+hsbGxePbZZ/HTTz8BcOBYXPscb/otK1euFNVqtbh8+XLx8OHD4uTJk8WQkBBRp9NJHc1ppkyZImq1WvGXX34Ry8rKrI/6+nrrNk888YQYHx8vrl+/Xty5c6c4ePBgcfDgwRKmdp2LzxoTRd8Zix07dogKhUKcN2+eePz4cXHFihViQECA+O9//9u6zRtvvCGGhISI33zzjbh//35xzJgxYmJiotjQ0CBhcsebNGmS2L59e3HNmjViYWGhuHr1ajEiIkJ87rnnrNt461jU1NSIe/bsEffs2SMCEBcuXCju2bPHejbU1XzuW2+9Vezbt6+Ym5srbt68WezSpYt4//33S/WRrslvjUNTU5N49913ix06dBD37t1r8++o0Wi0voc3jIMo/v6fiV/79VljouiYsWARcqIlS5aI8fHxokqlEgcOHChu375d6khOBeCyj48++si6TUNDg/jkk0+KoaGhYkBAgHjPPfeIZWVl0oV2oV8XIV8ai++++07s2bOnqFarxW7duonvv/++zXqLxSLOnTtXjIqKEtVqtThy5EgxPz9forTOYzAYxOnTp4vx8fGin5+f2KlTJ/GFF16w+SXnrWOxYcOGy/77MGnSJFEUr+5znzt3Trz//vvFoKAgUaPRiI888ohYU1Mjwae5dr81DoWFhVf8d3TDhg3W9/CGcRDF3/8z8WuXK0KOGAtBFC+6pCkRERGRD+EcISIiIvJZLEJERETks1iEiIiIyGexCBEREZHPYhEiIiIin8UiRERERD6LRYiIiIh8FosQERER+SwWISIiAAkJCVi0aJHUMYjIxViEiMjlHn74YYwdOxYAMGLECMyYMcNlP3v58uUICQm5ZHleXh4mT57sshxE5B4UUgcgInKEpqYmqFSqa359u3btHJiGiDwF9wgRkWQefvhh5OTk4K233oIgCBAEAadOnQIAHDx4ELfddhuCgoIQFRWFiRMnorKy0vraESNGYOrUqZgxYwYiIiIwevRoAMDChQuRnJyMwMBAxMXF4cknn0RtbS0A4JdffsEjjzwCvV5v/Xkvv/wygEsPjZ05cwZjxoxBUFAQNBoN7r33XpSXl1vXv/zyy+jTpw8++eQTJCQkQKvVYsKECaipqXHuoBGRQ7EIEZFk3nrrLQwePBiPP/44ysrKUFZWhri4OFRXV+OWW25B3759sXPnTqxduxbl5eW49957bV7/8ccfQ6VSYcuWLcjKygIAyGQyLF68GIcOHcLHH3+M9evX47nnngMADBkyBIsWLYJGo7H+vFmzZl2Sy2KxYMyYMaiqqkJOTg7WrVuHgoIC3HfffTbbnTx5El9//TXWrFmDNWvWICcnB2+88YaTRouInIGHxohIMlqtFiqVCgEBAYiOjrYuf/vtt9G3b1+8/vrr1mX//Oc/ERcXh2PHjqFr164AgC5dumDBggU273nxfKOEhAS89tpreOKJJ/DOO+9ApVJBq9VCEASbn/dr2dnZOHDgAAoLCxEXFwcA+Ne//oUePXogLy8PAwYMANBSmJYvX47g4GAAwMSJE5GdnY158+Zd38AQkctwjxARuZ19+/Zhw4YNCAoKsj66desGoGUvTJv+/ftf8tqff/4ZI0eORPv27REcHIyJEyfi3LlzqK+vv+qff+TIEcTFxVlLEAAkJSUhJCQER44csS5LSEiwliAAiImJQUVFhV2flYikxT1CROR2amtrcdddd2H+/PmXrIuJibE+DwwMtFl36tQp3HnnnZgyZQrmzZuHsLAwbN68GY899hiampoQEBDg0JxKpdLme0EQYLFYHPoziMi5WISISFIqlQpms9lmWb9+/fDll18iISEBCsXV/zO1a9cuWCwW/OMf/4BM1rLD+/PPP//dn/dr3bt3R1FREYqKiqx7hQ4fPozq6mokJSVddR4icn88NEZEkkpISEBubi5OnTqFyspKWCwWZGRkoKqqCvfffz/y8vJw8uRJ/PTTT3jkkUd+s8TccMMNMJlMWLJkCQoKCvDJJ59YJ1Ff/PNqa2uRnZ2NysrKyx4yS0tLQ3JyMtLT07F7927s2LEDDz30EIYPH46UlBSHjwERSYdFiIgkNWvWLMjlciQlJaFdu3Y4c+YMYmNjsWXLFpjNZowaNQrJycmYMWMGQkJCrHt6Lqd3795YuHAh5s+fj549e2LFihXIzMy02WbIkCF44okncN9996Fdu3aXTLYGWg5xffPNNwgNDcWwYcOQlpaGTp06YdWqVQ7//EQkLUEURVHqEERERERS4B4hIiIi8lksQkREROSzWISIiIjIZ7EIERERkc9iESIiIiKfxSJEREREPotFiIiIiHwWixARERH5LBYhIiIi8lksQkREROSzWISIiIjIZ/0/RFFG0V1+MbgAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}