Mini-1.ipynb

{
 "cells": [
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   "cell_type": "code",
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   "id": "41fc57f0-cefb-4003-b0d4-23a5df0c6990",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dependencies\n",
    "# import sys\n",
    "# !{sys.executable} -m pip install numpy scipy pandas matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4306ade1-ea43-4d5c-82d4-8b8cd070ceb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import random\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import linprog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bd8fc75e-cc89-4ed4-8478-19fb9c53618c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# LP problem generator\n",
    "def gen_random_lp_problem(n):\n",
    "    c = np.random.uniform(-1, 1, n)\n",
    "    A = np.random.uniform(-1, 1, (n, n))\n",
    "    b = np.random.uniform(-1, 1, n)\n",
    "    \n",
    "    return c, A, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "738e62c3-4de4-41e6-b3a6-9f9ec11b6698",
   "metadata": {},
   "outputs": [],
   "source": [
    "methods = ['highs-ipm', 'highs-ds']\n",
    "variable_range = range(50, 1001, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "92c594b0-3a42-4216-b187-0df8297c04b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# results = list()\n",
    "\n",
    "# for n in variable_range:\n",
    "    \n",
    "#     solution = dict()\n",
    "#     solution['success'] = False\n",
    "\n",
    "#     while (not solution['success']):\n",
    "#         c, A, b = gen_random_lp_problem(n)\n",
    "#         solution = linprog(c=c, A_ub=A, b_ub=b, method='highs')\n",
    "        \n",
    "#     for trial in range(10):\n",
    "#         for method in methods:\n",
    "            \n",
    "#             start = time.process_time()\n",
    "#             linprog(c=c, A_ub=A, b_ub=b, method=method)\n",
    "#             end = time.process_time()\n",
    "            \n",
    "#             results.append([n, trial, method, end - start])\n",
    "            \n",
    "# df = pd.DataFrame(results, columns=['n_variables', 'trial', 'method', 'time'])\n",
    "# df.to_csv('results2.csv', index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "82286c83-1060-492f-ab70-ecb168b32a2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('results2.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18fa406e-50d3-4e08-b34c-3cf877726ca2",
   "metadata": {},
   "source": [
    "# Mini-Project 1 - MATH-510 - Ozeas Carvalho"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30a38484-a1fc-403b-88ea-b60682718e8f",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "The simplex and the interior-point methods are the main algorithms to solve linear programming (LP) problems [1]. The simplex algorithm dominated the scene until  Karmarkar introduced a fast polynomial-time interior-point method in 1984 [2, 3]. Although the original Dantzig's simplex is inherently inefficient, improved simplex variants are still a good choice for sparse LP problems compared to interior-point methods [2]. While simplex variants traverse the vertices of the convex polytope defined by the problem constraints to find the optimal solution, interior-point methods move through solution points inside the feasible region to approximate an optimal solution.\n",
    "\n",
    "For this first project, we would like to evaluate the performance of the linear programming solvers available in SciPy [5], a Python library used for scientific computing. SciPy implements a dual revised simplex method and an interior-point method [3, 6]."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5a633ee-f7de-442e-a5c9-b872b996df9a",
   "metadata": {},
   "source": [
    "## Experiment design\n",
    "\n",
    "Firstly, we decided to write a random LP problem generator to create the problem set. All the generated problems are feasible, bounded, and have the following form:\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{min} \\quad\n",
    "c^T x& \\\\\n",
    "\\text{subject to} \\quad\n",
    "Ax &\\leq b \\\\\n",
    "x &\\geq 0\n",
    "\\end{align*}\n",
    "\n",
    "The generator takes a parameter $n_{variables}$ that defines the number of variables of the objective function and the number of contraints, which in turn determines the size of the vectors $c$, $x$, $b$, and constraint matrix $A$. The generator uniformly draws real numbers from the closed interval $(-1, 1)$ to assign the coefficients. We generated $20$ feasible LP problems varying $n_{variables}$ from $50$ to $1000$. Then we solved each LP problem $10$ times for each method to average the CPU execution time."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "212a5bc2-750b-48fa-9b1a-dd2fe3c653df",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "Table 1 contains the results aggregated by minimum, maximum, mean, and standard deviation of the CPU execution time in seconds. *highs-ds* is the dual revised simplex method, and *highs-ipm* is the interior-point method. Considering the average execution time, we can see that *highs-ds* is faster on average until the number of variables reaches $350$. The standard deviation is small (except for $n=1000$), which indicates a low variance in execution time on all trials. Table 2 has the execution time ratio for each LP problem size. We can make the same observation from Table 2, that *highs-ipm* outperforms *highs-ds* for $n > 300$. For larger instances, *highs-ds* is almost $3$ times faster."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "351048fa-995d-4041-8d48-6196eb30beaa",
   "metadata": {},
   "source": [
    "#### Table 1 - CPU execution time in seconds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "77dcde19-863a-4a25-b4f0-22093f326aef",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">min</th>\n",
       "      <th colspan=\"2\" halign=\"left\">max</th>\n",
       "      <th colspan=\"2\" halign=\"left\">mean</th>\n",
       "      <th colspan=\"2\" halign=\"left\">std</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">time</th>\n",
       "      <th colspan=\"2\" halign=\"left\">time</th>\n",
       "      <th colspan=\"2\" halign=\"left\">time</th>\n",
       "      <th colspan=\"2\" halign=\"left\">time</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>method</th>\n",
       "      <th>highs-ds</th>\n",
       "      <th>highs-ipm</th>\n",
       "      <th>highs-ds</th>\n",
       "      <th>highs-ipm</th>\n",
       "      <th>highs-ds</th>\n",
       "      <th>highs-ipm</th>\n",
       "      <th>highs-ds</th>\n",
       "      <th>highs-ipm</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n_variables</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>50</th>\n",
       "      <td>0.001364</td>\n",
       "      <td>0.002928</td>\n",
       "      <td>0.002056</td>\n",
       "      <td>0.003321</td>\n",
       "      <td>0.001467</td>\n",
       "      <td>0.003012</td>\n",
       "      <td>0.000209</td>\n",
       "      <td>0.000121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.006056</td>\n",
       "      <td>0.016392</td>\n",
       "      <td>0.006766</td>\n",
       "      <td>0.017735</td>\n",
       "      <td>0.006242</td>\n",
       "      <td>0.016860</td>\n",
       "      <td>0.000235</td>\n",
       "      <td>0.000459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>0.022108</td>\n",
       "      <td>0.034537</td>\n",
       "      <td>0.022716</td>\n",
       "      <td>0.034956</td>\n",
       "      <td>0.022269</td>\n",
       "      <td>0.034664</td>\n",
       "      <td>0.000174</td>\n",
       "      <td>0.000124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>0.054487</td>\n",
       "      <td>0.067097</td>\n",
       "      <td>0.054935</td>\n",
       "      <td>0.069136</td>\n",
       "      <td>0.054638</td>\n",
       "      <td>0.067464</td>\n",
       "      <td>0.000133</td>\n",
       "      <td>0.000603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>0.103571</td>\n",
       "      <td>0.149814</td>\n",
       "      <td>0.106833</td>\n",
       "      <td>0.151270</td>\n",
       "      <td>0.104365</td>\n",
       "      <td>0.150408</td>\n",
       "      <td>0.000935</td>\n",
       "      <td>0.000445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>300</th>\n",
       "      <td>0.186499</td>\n",
       "      <td>0.191888</td>\n",
       "      <td>0.187905</td>\n",
       "      <td>0.193328</td>\n",
       "      <td>0.187101</td>\n",
       "      <td>0.192625</td>\n",
       "      <td>0.000447</td>\n",
       "      <td>0.000460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>350</th>\n",
       "      <td>0.306869</td>\n",
       "      <td>0.304368</td>\n",
       "      <td>0.309235</td>\n",
       "      <td>0.307250</td>\n",
       "      <td>0.307801</td>\n",
       "      <td>0.305836</td>\n",
       "      <td>0.000847</td>\n",
       "      <td>0.000937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>400</th>\n",
       "      <td>0.435402</td>\n",
       "      <td>0.392919</td>\n",
       "      <td>0.438492</td>\n",
       "      <td>0.394816</td>\n",
       "      <td>0.437046</td>\n",
       "      <td>0.393855</td>\n",
       "      <td>0.001124</td>\n",
       "      <td>0.000616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>450</th>\n",
       "      <td>0.674857</td>\n",
       "      <td>0.632904</td>\n",
       "      <td>0.691577</td>\n",
       "      <td>0.637286</td>\n",
       "      <td>0.678486</td>\n",
       "      <td>0.634223</td>\n",
       "      <td>0.004852</td>\n",
       "      <td>0.001285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>1.030902</td>\n",
       "      <td>0.766470</td>\n",
       "      <td>1.036913</td>\n",
       "      <td>0.768916</td>\n",
       "      <td>1.034160</td>\n",
       "      <td>0.767357</td>\n",
       "      <td>0.002296</td>\n",
       "      <td>0.000838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>550</th>\n",
       "      <td>1.523140</td>\n",
       "      <td>1.071696</td>\n",
       "      <td>1.535642</td>\n",
       "      <td>1.074436</td>\n",
       "      <td>1.528057</td>\n",
       "      <td>1.073052</td>\n",
       "      <td>0.004056</td>\n",
       "      <td>0.000970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>600</th>\n",
       "      <td>1.886364</td>\n",
       "      <td>0.983409</td>\n",
       "      <td>1.920369</td>\n",
       "      <td>1.011807</td>\n",
       "      <td>1.896218</td>\n",
       "      <td>0.988608</td>\n",
       "      <td>0.012731</td>\n",
       "      <td>0.008773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>650</th>\n",
       "      <td>2.688879</td>\n",
       "      <td>1.684096</td>\n",
       "      <td>2.719172</td>\n",
       "      <td>1.698321</td>\n",
       "      <td>2.700382</td>\n",
       "      <td>1.688442</td>\n",
       "      <td>0.009630</td>\n",
       "      <td>0.004219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>700</th>\n",
       "      <td>3.076366</td>\n",
       "      <td>1.760954</td>\n",
       "      <td>3.105560</td>\n",
       "      <td>1.766260</td>\n",
       "      <td>3.087271</td>\n",
       "      <td>1.762932</td>\n",
       "      <td>0.009659</td>\n",
       "      <td>0.002097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>750</th>\n",
       "      <td>4.926290</td>\n",
       "      <td>1.818241</td>\n",
       "      <td>4.961127</td>\n",
       "      <td>1.822714</td>\n",
       "      <td>4.941473</td>\n",
       "      <td>1.820918</td>\n",
       "      <td>0.011861</td>\n",
       "      <td>0.001350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>800</th>\n",
       "      <td>5.849091</td>\n",
       "      <td>2.426489</td>\n",
       "      <td>5.904047</td>\n",
       "      <td>2.436109</td>\n",
       "      <td>5.884292</td>\n",
       "      <td>2.430969</td>\n",
       "      <td>0.018810</td>\n",
       "      <td>0.002502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>850</th>\n",
       "      <td>7.707634</td>\n",
       "      <td>2.873030</td>\n",
       "      <td>7.775103</td>\n",
       "      <td>2.882125</td>\n",
       "      <td>7.734071</td>\n",
       "      <td>2.876818</td>\n",
       "      <td>0.021405</td>\n",
       "      <td>0.003494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>900</th>\n",
       "      <td>9.880268</td>\n",
       "      <td>3.781556</td>\n",
       "      <td>9.997466</td>\n",
       "      <td>3.802773</td>\n",
       "      <td>9.934053</td>\n",
       "      <td>3.791712</td>\n",
       "      <td>0.036043</td>\n",
       "      <td>0.007150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>950</th>\n",
       "      <td>11.953814</td>\n",
       "      <td>4.986329</td>\n",
       "      <td>12.103861</td>\n",
       "      <td>5.135295</td>\n",
       "      <td>12.004362</td>\n",
       "      <td>5.009121</td>\n",
       "      <td>0.047354</td>\n",
       "      <td>0.045051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>13.490490</td>\n",
       "      <td>4.720446</td>\n",
       "      <td>19.000969</td>\n",
       "      <td>5.160067</td>\n",
       "      <td>14.368121</td>\n",
       "      <td>4.817596</td>\n",
       "      <td>1.666265</td>\n",
       "      <td>0.129694</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "                   min                  max                 mean            \\\n",
       "                  time                 time                 time             \n",
       "method        highs-ds highs-ipm   highs-ds highs-ipm   highs-ds highs-ipm   \n",
       "n_variables                                                                  \n",
       "50            0.001364  0.002928   0.002056  0.003321   0.001467  0.003012   \n",
       "100           0.006056  0.016392   0.006766  0.017735   0.006242  0.016860   \n",
       "150           0.022108  0.034537   0.022716  0.034956   0.022269  0.034664   \n",
       "200           0.054487  0.067097   0.054935  0.069136   0.054638  0.067464   \n",
       "250           0.103571  0.149814   0.106833  0.151270   0.104365  0.150408   \n",
       "300           0.186499  0.191888   0.187905  0.193328   0.187101  0.192625   \n",
       "350           0.306869  0.304368   0.309235  0.307250   0.307801  0.305836   \n",
       "400           0.435402  0.392919   0.438492  0.394816   0.437046  0.393855   \n",
       "450           0.674857  0.632904   0.691577  0.637286   0.678486  0.634223   \n",
       "500           1.030902  0.766470   1.036913  0.768916   1.034160  0.767357   \n",
       "550           1.523140  1.071696   1.535642  1.074436   1.528057  1.073052   \n",
       "600           1.886364  0.983409   1.920369  1.011807   1.896218  0.988608   \n",
       "650           2.688879  1.684096   2.719172  1.698321   2.700382  1.688442   \n",
       "700           3.076366  1.760954   3.105560  1.766260   3.087271  1.762932   \n",
       "750           4.926290  1.818241   4.961127  1.822714   4.941473  1.820918   \n",
       "800           5.849091  2.426489   5.904047  2.436109   5.884292  2.430969   \n",
       "850           7.707634  2.873030   7.775103  2.882125   7.734071  2.876818   \n",
       "900           9.880268  3.781556   9.997466  3.802773   9.934053  3.791712   \n",
       "950          11.953814  4.986329  12.103861  5.135295  12.004362  5.009121   \n",
       "1000         13.490490  4.720446  19.000969  5.160067  14.368121  4.817596   \n",
       "\n",
       "                  std            \n",
       "                 time            \n",
       "method       highs-ds highs-ipm  \n",
       "n_variables                      \n",
       "50           0.000209  0.000121  \n",
       "100          0.000235  0.000459  \n",
       "150          0.000174  0.000124  \n",
       "200          0.000133  0.000603  \n",
       "250          0.000935  0.000445  \n",
       "300          0.000447  0.000460  \n",
       "350          0.000847  0.000937  \n",
       "400          0.001124  0.000616  \n",
       "450          0.004852  0.001285  \n",
       "500          0.002296  0.000838  \n",
       "550          0.004056  0.000970  \n",
       "600          0.012731  0.008773  \n",
       "650          0.009630  0.004219  \n",
       "700          0.009659  0.002097  \n",
       "750          0.011861  0.001350  \n",
       "800          0.018810  0.002502  \n",
       "850          0.021405  0.003494  \n",
       "900          0.036043  0.007150  \n",
       "950          0.047354  0.045051  \n",
       "1000         1.666265  0.129694  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.pivot_table(index=['n_variables'], columns=['method'], values=['time'], aggfunc=[min, max, np.mean, np.std])"
   ]
  },
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   "metadata": {},
   "source": [
    "#### Table 2 - Execution time ratio $\\frac{highs-ds}{highs-ipm}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "232905e1-7c5b-43ca-a964-509c8c5135b4",
   "metadata": {},
   "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>Time ratio</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n_variables</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.487133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.370247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>0.642422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>0.809875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>0.693877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>300</th>\n",
       "      <td>0.971318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>350</th>\n",
       "      <td>1.006425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>400</th>\n",
       "      <td>1.109663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>450</th>\n",
       "      <td>1.069792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>1.347691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>550</th>\n",
       "      <td>1.424028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>600</th>\n",
       "      <td>1.918069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>650</th>\n",
       "      <td>1.599334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>700</th>\n",
       "      <td>1.751214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>750</th>\n",
       "      <td>2.713726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>800</th>\n",
       "      <td>2.420554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>850</th>\n",
       "      <td>2.688412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>900</th>\n",
       "      <td>2.619939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>950</th>\n",
       "      <td>2.396501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>2.982425</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Time ratio\n",
       "n_variables            \n",
       "50             0.487133\n",
       "100            0.370247\n",
       "150            0.642422\n",
       "200            0.809875\n",
       "250            0.693877\n",
       "300            0.971318\n",
       "350            1.006425\n",
       "400            1.109663\n",
       "450            1.069792\n",
       "500            1.347691\n",
       "550            1.424028\n",
       "600            1.918069\n",
       "650            1.599334\n",
       "700            1.751214\n",
       "750            2.713726\n",
       "800            2.420554\n",
       "850            2.688412\n",
       "900            2.619939\n",
       "950            2.396501\n",
       "1000           2.982425"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df.groupby(['n_variables', 'method'])[['time']].agg([np.mean]).unstack()[('time', 'mean',  'highs-ds')] / \\\n",
    "df.groupby(['n_variables', 'method'])[['time']].agg([np.mean]).unstack()[('time', 'mean',  'highs-ipm')]).to_frame(name='Time ratio')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44e8dd64-f859-4c43-94cc-befb72ba5805",
   "metadata": {},
   "source": [
    "Figure 1 shows the scatter plot of the average execution time for each problem size. Although we have a small sample, we can see that the execution time seems to grow exponentially with respect to the problem size. To confirm that, we can use regression to find the approximate exponential function that describes the execution time as a function of the problem size. Figure 2 shows the exponential functions found after we applied exponential regression to the data using SciPy.\n",
    "\n",
    "Additionally, we can also plot the original data in a *log-log* scale. In such space, exponential curves become linear functions, and we can use the inclination of the lines to compare relative exponential growth. Figure 3 has a *log-log* plot of the original data. Again, we can draw the same conclusions as before, that *highs-ds* is faster until a certain point, represented by the point where the lines intersect."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56d0f226-a4da-43b6-bbe8-39fb8651fb6c",
   "metadata": {},
   "source": [
    "#### Figure 1 - Average execution time plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "191b2f3b-d8b1-429e-a1c6-3664fba53e60",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "marker = {'highs-ds': '^',\n",
    "          'highs-ipm': '.'}\n",
    "\n",
    "for method in methods:\n",
    "    ax.plot(df[df['method']==method].groupby(['n_variables'])[['time']].agg([np.mean]), marker[method], label=method)\n",
    "\n",
    "ax.set_xlabel('Number of variables')\n",
    "ax.set_ylabel('CPU execution time mean (seconds)')\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6715ce27-0231-443d-b5a3-078532f2c63b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = df.groupby(['n_variables', 'method'])[['time']].agg([np.mean]).unstack()[('time', 'mean',  'highs-ds')].index.tolist()\n",
    "y1 = df.groupby(['n_variables', 'method'])[['time']].agg([np.mean]).unstack()[('time', 'mean',  'highs-ds')].tolist()\n",
    "\n",
    "x2 = df.groupby(['n_variables', 'method'])[['time']].agg([np.mean]).unstack()[('time', 'mean',  'highs-ipm')].index.tolist()\n",
    "y2 = df.groupby(['n_variables', 'method'])[['time']].agg([np.mean]).unstack()[('time', 'mean',  'highs-ipm')].tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aaee8238-bc1e-4dfe-8966-79162dde6845",
   "metadata": {},
   "outputs": [],
   "source": [
    "fit1 = np.polyfit(x1, np.log(y1), 1, w=np.sqrt(y1))\n",
    "\n",
    "a1 = np.exp(fit1[1])\n",
    "b1 = fit1[0]\n",
    "x1_fitted = np.linspace(np.min(x1), np.max(x1), 100)\n",
    "y1_fitted = a1 * np.exp(b1 * x1_fitted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5bc551c9-8345-4872-8bd7-03d29b70aaf9",
   "metadata": {},
   "outputs": [],
   "source": [
    "fit2 = np.polyfit(x2, np.log(y2), 1, w=np.sqrt(y2))\n",
    "\n",
    "a2 = np.exp(fit2[1])\n",
    "b2 = fit2[0]\n",
    "x2_fitted = np.linspace(np.min(x2), np.max(x2), 100)\n",
    "y2_fitted = a2 * np.exp(b2 * x2_fitted)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c623ecc6-0471-4ae3-be9d-9a7eba20caf0",
   "metadata": {},
   "source": [
    "#### Figure 2 - Exponential regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6dff0436-19aa-4683-ba86-b1bc97d65bbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['text.usetex'] = True\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "marker = {'highs-ds': 'v',\n",
    "          'highs-ipm': '*'}\n",
    "\n",
    "for method in methods:\n",
    "    ax.plot(df[df['method']==method].groupby(['n_variables'])[['time']].agg([np.mean]), marker[method], label=method)\n",
    "    \n",
    "ax.plot(x1_fitted, y1_fitted, label=\"${%fe}^{%fx}$\" % (a1, b1))\n",
    "ax.plot(x2_fitted, y2_fitted, label=\"${%fe}^{%fx}$\" % (a2, b2))\n",
    "\n",
    "ax.set_xlabel('Number of variables')\n",
    "ax.set_ylabel('CPU execution time mean (seconds)')\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adde9b46-9f0a-45be-be42-d4c10c448107",
   "metadata": {},
   "source": [
    "#### Figure 3 - *log-log* plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4fba91f8-8d43-4049-a281-1b971b542b59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['text.usetex'] = True\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "marker = {'highs-ds': 'v',\n",
    "          'highs-ipm': '*'}\n",
    "\n",
    "for method in methods:\n",
    "    ax.plot(df[df['method']==method].groupby(['n_variables'])[['time']].agg([np.mean]), marker=marker[method], label=method)\n",
    "    \n",
    "ax.set_xlabel('Number of variables')\n",
    "ax.set_ylabel('CPU execution time mean (seconds)')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
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    "## Conclusion\n",
    "\n",
    "To the best of our knowledge, there is no definitive proof of the time complexity of the simplex algorithm. Some authors argue that the simplex method has combinatorial complexity since it can potentially visit all the polytope vertices to reach the optimal solution [1] while others estimate a polynomial time like the interior-point method [2].\n",
    "\n",
    "As limitations, we can mention the problem space, the quality of the problem generator, and the solvers' parameter space. Although the observed results are somewhat consistent with the discussion about the time complexity, the conclusions are not statistically significant due to the small sample space. And that raises some questions. What happens if we keep increasing the number of variables? What happens if we increase or decrease the number of constraints? The tested problems have a specific structure (the number of constraints is equal to the number of variables), so we cannot safely extrapolate our conclusions. It took a considerable time to generate random feasible LP problems. A deep understanding of LP problems can help write a better random LP problem generator. Also, the SciPy LP solvers provide a variety of parameters that we did not experiment with."
   ]
  },
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   "id": "a2689a80-d891-4285-82cb-e2523b313764",
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   "source": [
    "## References\n",
    "\n",
    "[1] https://arxiv.org/abs/cs/0111050v7\n",
    "\n",
    "[2] https://epubs.siam.org/doi/10.1137/S0036144502414942\n",
    "\n",
    "[3] https://link.springer.com/article/10.1007/BF02579150\n",
    "\n",
    "[4] https://link.springer.com/article/10.1007/s12532-017-0130-5\n",
    "\n",
    "[5] https://scipy.org/\n",
    "\n",
    "[6] https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html"
   ]
  }
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