Set Cover Problem - Maximum budgeted selection

Maximum budgeted gene selection.ipynb

{
  "cells": [
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "import shutil\nimport sys\nimport os.path\nimport textwrap # For pretty printing missing genes\nfrom random import random # Generate random numbers (Costs)\n\n# pyomo is used as the model generator for the solver\nif not shutil.which(\"pyomo\"):\n    !pip install --user -q pyomo\n    assert(shutil.which(\"pyomo\"))\n\n# cbc/glpk are installed if missing, these are oss solvers\nif not (shutil.which(\"cbc\") or os.path.isfile(\"cbc\")):\n    if \"google.colab\" in sys.modules:\n        !apt-get install --user -y -qq coinor-cbc\n    else:\n        if sys.platform == \"darwin\":\n            try:\n                !brew tap coin-or-tools/coinor\n                !brew install coin-or-tools/coinor/cbc pkg-config\n                !brew install glpk\n            except:\n                pass\n        else:\n            try:\n                !conda install -c conda-forge coincbc glpk\n            except:\n                pass\n\nassert(shutil.which(\"cbc\") or os.path.isfile(\"cbc\"))\nassert(shutil.which(\"glpsol\") or os.path.isfile(\"glpsol\"))\n\nl80_wrap=textwrap.TextWrapper(width = 80)\n\nfrom pyomo.environ import *\nimport pandas as pd # For manipulating the input data",
      "execution_count": 77,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Background - Maximising genes covered under a sample budget restriction\n\nThe previous problem could be also intepreted as a maximisation problem where the objective is maximising the number of covered genes using a library based budget.\n\nIn this case the model can be expressed using the previous definitions for $L$, $G$, $X$ and $Y \\subseteq L\\times G$:\n\n\nIn this case costs are associated to each $g_{i,j}$ according to the importance $w_i$ of the presence of this gene when using $l_i$ in the solution.\n\nThe objective is to maximise:\n\n$$\n\\sum_{g \\subseteq G} w_i(g_j) \\, y_{i,j}\n$$\n\nsubject to:\n\n\\begin{align*}\n&\\sum_{l \\subseteq L} c(l_i) \\, x_i \\leq Budget\\\\\n&\\sum_{g_j \\subseteq L_i} x_i \\geq y_{i,j}\\\\\n&y_i \\in  \\{0,1\\}\\\\\n\\end{align*}\n\n"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Import the data\ndata = pd.read_csv(\"./GENANNO-477.csv\", index_col=0)\n# To try different groups of genes/libraries, sampling of the matrix can be enabled here:\ndata=data.sample(20) # Samples X number of genes\ndata=data.sample(9,axis=1) # Samples X number of libraries\ndataOri=data.copy()\ndata",
      "execution_count": 78,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>GSM3490689</th>\n      <th>GSM1514872</th>\n      <th>GSM3433627</th>\n      <th>GSM1514876</th>\n      <th>GSM2751092</th>\n      <th>GSM1514870</th>\n      <th>GSM2751088</th>\n      <th>GSM3433656</th>\n      <th>GSM2751096</th>\n    </tr>\n    <tr>\n      <th>Gene</th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>AT3G25660</th>\n      <td>19.7</td>\n      <td>59.0</td>\n      <td>85.9</td>\n      <td>43.1</td>\n      <td>58.3</td>\n      <td>31.0</td>\n      <td>53.2</td>\n      <td>47.1</td>\n      <td>59.9</td>\n    </tr>\n    <tr>\n      <th>AT2G34320</th>\n      <td>0.0</td>\n      <td>0.1</td>\n      <td>0.2</td>\n      <td>0.2</td>\n      <td>0.2</td>\n      <td>0.4</td>\n      <td>0.5</td>\n      <td>0.2</td>\n      <td>0.0</td>\n    </tr>\n    <tr>\n      <th>AT5G06210</th>\n      <td>46.1</td>\n      <td>26.4</td>\n      <td>19.8</td>\n      <td>21.8</td>\n      <td>25.4</td>\n      <td>23.3</td>\n      <td>22.4</td>\n      <td>31.1</td>\n      <td>22.6</td>\n    </tr>\n    <tr>\n      <th>AT1G10530</th>\n      <td>35.6</td>\n      <td>1.0</td>\n      <td>9.5</td>\n      <td>7.5</td>\n      <td>3.6</td>\n      <td>22.6</td>\n      <td>6.1</td>\n      <td>5.8</td>\n      <td>4.1</td>\n    </tr>\n    <tr>\n      <th>AT2G08986</th>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n    </tr>\n    <tr>\n      <th>AT5G63150</th>\n      <td>74.6</td>\n      <td>35.1</td>\n      <td>43.1</td>\n      <td>35.5</td>\n      <td>43.2</td>\n      <td>35.5</td>\n      <td>39.3</td>\n      <td>34.2</td>\n      <td>42.2</td>\n    </tr>\n    <tr>\n      <th>AT3G45770</th>\n      <td>28.1</td>\n      <td>42.8</td>\n      <td>41.4</td>\n      <td>30.5</td>\n      <td>37.9</td>\n      <td>33.6</td>\n      <td>35.4</td>\n      <td>58.4</td>\n      <td>35.9</td>\n    </tr>\n    <tr>\n      <th>AT3G27200</th>\n      <td>60.9</td>\n      <td>16.3</td>\n      <td>11.9</td>\n      <td>31.1</td>\n      <td>18.8</td>\n      <td>25.8</td>\n      <td>20.0</td>\n      <td>14.1</td>\n      <td>19.8</td>\n    </tr>\n    <tr>\n      <th>AT2G48030</th>\n      <td>29.5</td>\n      <td>17.3</td>\n      <td>16.8</td>\n      <td>21.1</td>\n      <td>15.9</td>\n      <td>28.9</td>\n      <td>17.1</td>\n      <td>19.8</td>\n      <td>15.6</td>\n    </tr>\n    <tr>\n      <th>AT5G65980</th>\n      <td>4.7</td>\n      <td>0.3</td>\n      <td>5.9</td>\n      <td>0.0</td>\n      <td>3.4</td>\n      <td>1.9</td>\n      <td>4.1</td>\n      <td>0.6</td>\n      <td>3.7</td>\n    </tr>\n    <tr>\n      <th>AT1G66800</th>\n      <td>49.9</td>\n      <td>0.3</td>\n      <td>6.1</td>\n      <td>0.5</td>\n      <td>27.4</td>\n      <td>17.6</td>\n      <td>29.5</td>\n      <td>8.4</td>\n      <td>28.0</td>\n    </tr>\n    <tr>\n      <th>AT3G07740</th>\n      <td>25.7</td>\n      <td>27.1</td>\n      <td>16.4</td>\n      <td>24.8</td>\n      <td>16.7</td>\n      <td>22.5</td>\n      <td>16.1</td>\n      <td>25.2</td>\n      <td>16.1</td>\n    </tr>\n    <tr>\n      <th>AT5G56210</th>\n      <td>40.9</td>\n      <td>28.3</td>\n      <td>19.6</td>\n      <td>21.2</td>\n      <td>6.2</td>\n      <td>23.7</td>\n      <td>7.2</td>\n      <td>27.4</td>\n      <td>8.3</td>\n    </tr>\n    <tr>\n      <th>AT4G12240</th>\n      <td>7.0</td>\n      <td>7.0</td>\n      <td>5.3</td>\n      <td>10.2</td>\n      <td>1.6</td>\n      <td>11.7</td>\n      <td>1.5</td>\n      <td>10.2</td>\n      <td>0.5</td>\n    </tr>\n    <tr>\n      <th>AT1G10800</th>\n      <td>11.0</td>\n      <td>3.4</td>\n      <td>0.8</td>\n      <td>4.1</td>\n      <td>5.5</td>\n      <td>10.2</td>\n      <td>5.8</td>\n      <td>4.7</td>\n      <td>5.7</td>\n    </tr>\n    <tr>\n      <th>AT3G55990</th>\n      <td>18.4</td>\n      <td>12.0</td>\n      <td>8.3</td>\n      <td>26.6</td>\n      <td>24.8</td>\n      <td>27.2</td>\n      <td>24.7</td>\n      <td>11.2</td>\n      <td>22.2</td>\n    </tr>\n    <tr>\n      <th>AT1G22870</th>\n      <td>3.7</td>\n      <td>19.4</td>\n      <td>14.8</td>\n      <td>15.1</td>\n      <td>14.8</td>\n      <td>22.9</td>\n      <td>14.2</td>\n      <td>20.2</td>\n      <td>13.1</td>\n    </tr>\n    <tr>\n      <th>AT5G54070</th>\n      <td>0.2</td>\n      <td>0.0</td>\n      <td>0.3</td>\n      <td>0.0</td>\n      <td>0.5</td>\n      <td>0.1</td>\n      <td>0.3</td>\n      <td>0.0</td>\n      <td>0.5</td>\n    </tr>\n    <tr>\n      <th>AT5G64460</th>\n      <td>63.7</td>\n      <td>53.0</td>\n      <td>46.0</td>\n      <td>46.6</td>\n      <td>60.5</td>\n      <td>38.1</td>\n      <td>52.5</td>\n      <td>59.8</td>\n      <td>55.9</td>\n    </tr>\n    <tr>\n      <th>AT4G37150</th>\n      <td>0.4</td>\n      <td>7.3</td>\n      <td>4.5</td>\n      <td>16.4</td>\n      <td>16.2</td>\n      <td>19.6</td>\n      <td>15.7</td>\n      <td>24.4</td>\n      <td>13.8</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "           GSM3490689  GSM1514872  GSM3433627  GSM1514876  GSM2751092  \\\nGene                                                                    \nAT3G25660        19.7        59.0        85.9        43.1        58.3   \nAT2G34320         0.0         0.1         0.2         0.2         0.2   \nAT5G06210        46.1        26.4        19.8        21.8        25.4   \nAT1G10530        35.6         1.0         9.5         7.5         3.6   \nAT2G08986         0.0         0.0         0.0         0.0         0.0   \nAT5G63150        74.6        35.1        43.1        35.5        43.2   \nAT3G45770        28.1        42.8        41.4        30.5        37.9   \nAT3G27200        60.9        16.3        11.9        31.1        18.8   \nAT2G48030        29.5        17.3        16.8        21.1        15.9   \nAT5G65980         4.7         0.3         5.9         0.0         3.4   \nAT1G66800        49.9         0.3         6.1         0.5        27.4   \nAT3G07740        25.7        27.1        16.4        24.8        16.7   \nAT5G56210        40.9        28.3        19.6        21.2         6.2   \nAT4G12240         7.0         7.0         5.3        10.2         1.6   \nAT1G10800        11.0         3.4         0.8         4.1         5.5   \nAT3G55990        18.4        12.0         8.3        26.6        24.8   \nAT1G22870         3.7        19.4        14.8        15.1        14.8   \nAT5G54070         0.2         0.0         0.3         0.0         0.5   \nAT5G64460        63.7        53.0        46.0        46.6        60.5   \nAT4G37150         0.4         7.3         4.5        16.4        16.2   \n\n           GSM1514870  GSM2751088  GSM3433656  GSM2751096  \nGene                                                       \nAT3G25660        31.0        53.2        47.1        59.9  \nAT2G34320         0.4         0.5         0.2         0.0  \nAT5G06210        23.3        22.4        31.1        22.6  \nAT1G10530        22.6         6.1         5.8         4.1  \nAT2G08986         0.0         0.0         0.0         0.0  \nAT5G63150        35.5        39.3        34.2        42.2  \nAT3G45770        33.6        35.4        58.4        35.9  \nAT3G27200        25.8        20.0        14.1        19.8  \nAT2G48030        28.9        17.1        19.8        15.6  \nAT5G65980         1.9         4.1         0.6         3.7  \nAT1G66800        17.6        29.5         8.4        28.0  \nAT3G07740        22.5        16.1        25.2        16.1  \nAT5G56210        23.7         7.2        27.4         8.3  \nAT4G12240        11.7         1.5        10.2         0.5  \nAT1G10800        10.2         5.8         4.7         5.7  \nAT3G55990        27.2        24.7        11.2        22.2  \nAT1G22870        22.9        14.2        20.2        13.1  \nAT5G54070         0.1         0.3         0.0         0.5  \nAT5G64460        38.1        52.5        59.8        55.9  \nAT4G37150        19.6        15.7        24.4        13.8  "
          },
          "execution_count": 78,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Apply minimum FPKM transformation to binary\nminFPKM=5\ndata[data<minFPKM]=0\ndata[data>=minFPKM]=1\ndata=data.astype('int')\ndataT=data.transpose()\ndata",
      "execution_count": 79,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>GSM3490689</th>\n      <th>GSM1514872</th>\n      <th>GSM3433627</th>\n      <th>GSM1514876</th>\n      <th>GSM2751092</th>\n      <th>GSM1514870</th>\n      <th>GSM2751088</th>\n      <th>GSM3433656</th>\n      <th>GSM2751096</th>\n    </tr>\n    <tr>\n      <th>Gene</th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>AT3G25660</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT2G34320</th>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>AT5G06210</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT1G10530</th>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>AT2G08986</th>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>AT5G63150</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT3G45770</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT3G27200</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT2G48030</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT5G65980</th>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>AT1G66800</th>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT3G07740</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT5G56210</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT4G12240</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>AT1G10800</th>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT3G55990</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT1G22870</th>\n      <td>0</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT5G54070</th>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>AT5G64460</th>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>AT4G37150</th>\n      <td>0</td>\n      <td>1</td>\n      <td>0</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "           GSM3490689  GSM1514872  GSM3433627  GSM1514876  GSM2751092  \\\nGene                                                                    \nAT3G25660           1           1           1           1           1   \nAT2G34320           0           0           0           0           0   \nAT5G06210           1           1           1           1           1   \nAT1G10530           1           0           1           1           0   \nAT2G08986           0           0           0           0           0   \nAT5G63150           1           1           1           1           1   \nAT3G45770           1           1           1           1           1   \nAT3G27200           1           1           1           1           1   \nAT2G48030           1           1           1           1           1   \nAT5G65980           0           0           1           0           0   \nAT1G66800           1           0           1           0           1   \nAT3G07740           1           1           1           1           1   \nAT5G56210           1           1           1           1           1   \nAT4G12240           1           1           1           1           0   \nAT1G10800           1           0           0           0           1   \nAT3G55990           1           1           1           1           1   \nAT1G22870           0           1           1           1           1   \nAT5G54070           0           0           0           0           0   \nAT5G64460           1           1           1           1           1   \nAT4G37150           0           1           0           1           1   \n\n           GSM1514870  GSM2751088  GSM3433656  GSM2751096  \nGene                                                       \nAT3G25660           1           1           1           1  \nAT2G34320           0           0           0           0  \nAT5G06210           1           1           1           1  \nAT1G10530           1           1           1           0  \nAT2G08986           0           0           0           0  \nAT5G63150           1           1           1           1  \nAT3G45770           1           1           1           1  \nAT3G27200           1           1           1           1  \nAT2G48030           1           1           1           1  \nAT5G65980           0           0           0           0  \nAT1G66800           1           1           1           1  \nAT3G07740           1           1           1           1  \nAT5G56210           1           1           1           1  \nAT4G12240           1           0           1           0  \nAT1G10800           1           1           0           1  \nAT3G55990           1           1           1           1  \nAT1G22870           1           1           1           1  \nAT5G54070           0           0           0           0  \nAT5G64460           1           1           1           1  \nAT4G37150           1           1           1           1  "
          },
          "execution_count": 79,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "Libraries = list(data.columns.values)\n\nGenes = list(data.index.values)\n\nCosts={}\nfor l in Libraries:\n    Costs[l]=1\n\nBudget = 2",
      "execution_count": 80,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "model = ConcreteModel()\nmodel.genes = Set(initialize=Genes)\nmodel.libraries = Set(initialize=Libraries)\nmodel.x = Var(model.libraries, domain=Boolean)\nmodel.y = Var(model.libraries,model.genes, domain=Boolean)\n\n# Generate the matrix in tuple form as input for the model\nA = data.stack().to_dict()\nmodel.a = Param(model.genes,model.libraries, initialize=A)\n\nmodel.Cost = Objective(\n    expr = sum([dataOri[l][g]*model.y[l,g] for l in Libraries for g in Genes]),\n    sense = maximize\n)\n\nmodel.constraints = ConstraintList()\nmodel.constraints.add(\n    sum([model.x[l]*Costs[l] for l in Libraries]) <= Budget\n)       \n\nfor g in Genes:\n    for l in dataT[dataT[g]>0].index.to_list():\n        model.constraints.add(model.x[l] >= model.y[l,g])",
      "execution_count": 81,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "results = SolverFactory('glpk').solve(model)",
      "execution_count": 82,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "print(\"Genes (and total weights) covered after filtering genes with an FPKM value lower than\", minFPKM)\nprint(\"Using a maximum budget of\", Budget,\"libraries:\\n\")\n\nprint(\"Genes\\t\\tTimes used\\t\\tTotal Weight\")\nfor g in Genes:\n    gene_used=0\n    gene_fpkm=0.\n    for l in dataT[dataT[g]>0].index.to_list():\n        if model.y[l,g]() > 0:\n            gene_used+=1\n            gene_fpkm+=dataOri[l][g]\n    if gene_used>0:\n        print(\"{}\\t{}\\t\\t\\t{:.1f}\".format(g, gene_used, gene_fpkm))\n\nprint()\nprint(\"Library\\t\\tCost\")\nfor l in Libraries:\n    if model.x[l]()>0:\n        print(l,Costs[l],sep='\\t')",
      "execution_count": 83,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "Genes (and total weights) covered after filtering genes with an FPKM value lower than 5\nUsing a maximum budget of 2 libraries:\n\nGenes\t\tTimes used\t\tTotal Weight\nAT3G25660\t2\t\t\t66.8\nAT5G06210\t2\t\t\t77.2\nAT1G10530\t2\t\t\t41.4\nAT5G63150\t2\t\t\t108.8\nAT3G45770\t2\t\t\t86.5\nAT3G27200\t2\t\t\t75.0\nAT2G48030\t2\t\t\t49.3\nAT1G66800\t2\t\t\t58.3\nAT3G07740\t2\t\t\t50.9\nAT5G56210\t2\t\t\t68.3\nAT4G12240\t2\t\t\t17.2\nAT1G10800\t1\t\t\t11.0\nAT3G55990\t2\t\t\t29.6\nAT1G22870\t1\t\t\t20.2\nAT5G64460\t2\t\t\t123.5\nAT4G37150\t1\t\t\t24.4\n\nLibrary\t\tCost\nGSM3490689\t1\nGSM3433656\t1\n"
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
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      "display_name": "Python 3",
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    "language_info": {
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      "file_extension": ".py"
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    "gist": {
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      "data": {
        "description": "Set Cover Problem - Maximum budgeted selection",
        "public": true
      }
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