f-sparc/fsparc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![MOSEK ApS](https://www.mosek.com/static/images/branding/webgraphmoseklogocolor.png )"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We implement a Python Fusion model for the problem known as F-SPARC (fractional subcarrier and power allocation with rate constraints). Our implementation defines a mixed-integer exponential cone problem.\n",
    "\n",
    "The model comes from the paper *Bi-Perspective Functions for Mixed-Integer Fractional Programs with Indicator Variables* by Adam N. Letchford, Qiang N and, Zhaoyu Zhong, http://www.optimization-online.org/DB_HTML/2017/09/6222.html.\n",
    "\n",
    "Some test data come from http://www.research.lancs.ac.uk/portal/en/datasets/ofdma-optimisation(48d843b0-1fb6-4e3d-af39-ca533a37b7ab).html\n",
    "\n",
    "# Problem formulation\n",
    "\n",
    "We consider a set $I$ of communication channels (subcarriers) to be assigned to a set $J$ of users. Each channel can be assigned to at most one user, while one user will typically have more channels assigned to them, subject to the requirement that user $j$ achieves a total data rate of at least $d_j$ (bits per second). The data rate of a channel is computed as follows: for a channel of bandwidth $B$ (hertz), noise level $N_i$ (watts) and operating with power $p_i$ (watts), the maximum data rate is\n",
    "$$f_i = B \\log_2(1+\\frac{p_i}{N_i}).$$\n",
    "Finally, we assume a minimal system power of $\\sigma$ required to keep the system running and a maximum power level $P$. \n",
    "\n",
    "The goal is to map the channels to users and assign their power levels so that the *energy efficiency*\n",
    "\n",
    "$$\\frac{\\textrm{total data rate}}{\\textrm{total power}}$$\n",
    "is maximized.\n",
    "\n",
    "The mixed-integer formulation is then:\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "\\mathrm{maximize} & \\frac{\\sum_{i,j} B \\log_2(1+p_{i,j}/N_i)}{\\sigma+\\sum_{i,j}p_{i,j}} \\\\\n",
    "\\textrm{subject to} & B \\sum_i \\log_2(1+p_{i,j}/N_i) \\geq d_j, \\quad j\\in J, \\\\\n",
    "& \\sigma + \\sum_{i,j}p_{ij} \\leq P, \\\\\n",
    "& 0 \\leq p_{ij}\\leq Px_{ij}, x_{ij}\\in \\{0,1\\}, \\\\\n",
    "& \\sum_j x_{ij} \\leq 1,\\quad i\\in I,\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "where $p_{ij}$ is the power assigned to channel $i$ when used by user $j$. The first constraint describes the total bitrate of each user, the second bounds total power, and the remaining constraints with indicator variables model the assignment requirements.\n",
    "\n",
    "\n",
    "# Conic reformulation\n",
    "\n",
    "To obtain a problem in conic form we perform a homogenization as in Section 5.2 of Letchfort et al. That is, we introduce new variables $t$, $z_{ij}$ and $\\tilde{p_{ij}}$ with the intention of representing\n",
    "$$t = 1/(\\sigma+\\sum_{ij}p_{ij}),\\quad z_{ij}=Bt\\log_2(1+p_{ij}/N_i),\\quad \\tilde{p_{ij}} = p_{ij}t.$$\n",
    "In terms of the new variables the problem is equivalent with\n",
    "\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "\\mathrm{maximize} & \\sum_{i,j} z_{ij} \\\\\n",
    "\\textrm{subject to} & z_{ij} \\leq B t \\log_2(1+\\tilde{p_{i,j}}/(tN_i)), \\quad i \\in I, j\\in J, \\\\\n",
    "& d_jt \\leq \\sum_i z_{ij},\\quad j\\in J \\\\\n",
    "& t\\sigma + \\sum_{i,j} \\tilde{p_{i,j}} = 1, \\\\\n",
    "& 1/P \\leq t \\leq 1/\\sigma, \\\\\n",
    "& 0 \\leq \\tilde{p_{i,j}} \\leq x_{ij}, x_{ij}\\in \\{0,1\\}, \\\\\n",
    "& \\sum_j x_{ij} \\leq 1,\\quad i\\in I,\n",
    "\\end{array}\n",
    "$$\n",
    "The first constraint can equivalently be written as\n",
    "$$t+\\tilde{p_{i,j}}/N_i \\geq t \\exp(\\log(2)z_{i,j}/(Bt))$$\n",
    "which, using the exponential cone, is\n",
    "$$(t+\\tilde{p_{i,j}}/N_i , t, \\log(2)z_{i,j}/B)\\in K_\\mathrm{exp}.$$\n",
    "\n",
    "# Implementation in Fusion\n",
    "\n",
    "We start that functions which parse examples in the format of http://www.research.lancs.ac.uk/portal/en/datasets/ofdma-optimisation(48d843b0-1fb6-4e3d-af39-ca533a37b7ab).html and set up some global constants. The data files contain user demands and channel noise for each example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ast, sys\n",
    "\n",
    "constants = {\n",
    "  \"System Power\": 10, \n",
    "  \"Bandwidth\": 1.25, \n",
    "  \"Maximum Power\": 36\n",
    "}\n",
    "\n",
    "def parse(filename):\n",
    "    data = []\n",
    "    with open(filename, 'r') as file:\n",
    "        content = file.read()\n",
    "        if 'Instance: ' not in content: raise Exception\n",
    "            \n",
    "        for inst in content.split('Instance: ')[1:]:\n",
    "            if 'noise' not in inst or 'demand' not in inst: raise Exception\n",
    "\n",
    "            data.append({\n",
    "                \"noise\" : ast.literal_eval(inst.split('noise')[1].split('demand')[0].strip()), \n",
    "                \"demand\" : ast.literal_eval(inst.split('demand')[1].strip())\n",
    "            })\n",
    "    return data \n",
    "\n",
    "BW = constants[\"Bandwidth\"]\n",
    "P = constants[\"Maximum Power\"]\n",
    "SIGMA = constants[\"System Power\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next function is a direct implementation of the conic model above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mosek.fusion import *\n",
    "import mosek.fusion.pythonic\n",
    "from math import log\n",
    "\n",
    "def fsparc_model(n, d):\n",
    "    M = Model()\n",
    "    I, J = len(n), len(d)\n",
    "\n",
    "    # create variables\n",
    "    z = M.variable('z', [I, J], Domain.greaterThan(0.0))            \n",
    "    x = M.variable('x', [I, J], Domain.binary())                    \n",
    "    p_tilde = M.variable('p_tilde', [I, J], Domain.greaterThan(0.0))\n",
    "    t = M.variable('t', 1, Domain.inRange(1.0/P, 1.0/SIGMA))        \n",
    "\n",
    "    # add linear constraints\n",
    "    M.constraint(Expr.sum(x, 1) <= 1.0)\n",
    "    M.constraint(SIGMA * t + Expr.sum(p_tilde) == 1.0)\n",
    "    M.constraint(p_tilde <= x)\n",
    "    M.constraint(Expr.sum(z, 0) >= Expr.mulElm(Expr.repeat(t, J, 0), d))\n",
    "    \n",
    "    # objective\n",
    "    M.objective(\"obj\", ObjectiveSense.Maximize, Expr.sum(z))\n",
    "    \n",
    "    # add conic constraint\n",
    "    p_over_n = Expr.mulElm(p_tilde, [[1 / n_i] * J for n_i in n])\n",
    "    multi_t = Expr.repeat(Expr.repeat(t, I, 0), J, 1)\n",
    "    M.constraint(Expr.stack(2, multi_t + p_over_n, multi_t, z * (log(2.0) / BW)), \n",
    "                 Domain.inPExpCone())\n",
    "    \n",
    "    return M\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we run the model and present some statistics for a few examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def stats(M, n, d):\n",
    "    I, J = len(n), len(d)\n",
    "    t    = M.getVariable('t').level()[0]\n",
    "    pval = M.getVariable('p_tilde').level().reshape([I, J]) / t\n",
    "    xval = M.getVariable('x').level().reshape([I, J])\n",
    "    power = [sum(pval[i,:]) for i in range(I)]\n",
    "    user = [int(sum([xval[i][j]*j for j in range(J)])) for i in range(I)]\n",
    "    print(\"Total data rate: demanded {0}, provided {1}\".format(\n",
    "        sum(d), \n",
    "        sum([BW*log(1+power[i]/n[i])/log(2.0) for i in range(I)])))\n",
    "    print(\"Power: system {0:.3f}, used {1:.3f}, maximal: {2:.3f}\".format(SIGMA, SIGMA+sum(power), P))\n",
    "    colors = ['red', 'green', 'blue', 'cyan', 'yellow', 'violet'] \n",
    "    plt.bar(range(I), power, color = [colors[user[i]] for i in range(I)])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1\n",
    "\n",
    "We run an example with realistic data (72 channels, 4 users) with a very short time limit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : max             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 1229            \n",
      "  Cones                  : 288             \n",
      "  Scalar variables       : 1729            \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 288             \n",
      "\n",
      "Optimizer started.\n",
      "Mixed integer optimizer started.\n",
      "Threads used: 20\n",
      "Presolve started.\n",
      "Presolve terminated. Time = 0.01\n",
      "Presolved problem: 1440 variables, 940 constraints, 2883 non-zeros\n",
      "Presolved problem: 0 general integer, 288 binary, 1152 continuous\n",
      "Clique table size: 72\n",
      "BRANCHES RELAXS   ACT_NDS  DEPTH    BEST_INT_OBJ         BEST_RELAX_OBJ       REL_GAP(%)  TIME  \n",
      "0        1        1        0        NA                   3.2821073370e+02     NA          0.1   \n",
      "Cut generation started.\n",
      "0        2        1        0        NA                   3.2821073370e+02     NA          0.6   \n",
      "Cut generation terminated. Time = 0.00\n",
      "8        12       9        2        NA                   3.2564092596e+02     NA          1.0   \n",
      "21       25       22       5        NA                   3.2564092596e+02     NA          1.1   \n",
      "36       40       37       5        NA                   3.2564092596e+02     NA          1.2   \n",
      "49       53       50       6        NA                   3.2564092596e+02     NA          1.3   \n",
      "79       83       80       8        NA                   3.2564092596e+02     NA          1.5   \n",
      "159      163      160      12       NA                   3.2564092596e+02     NA          1.7   \n",
      "319      323      320      20       NA                   3.2564092596e+02     NA          2.3   \n",
      "639      643      640      36       NA                   3.2564092596e+02     NA          3.3   \n",
      "1079     1083     1080     58       NA                   3.2564092596e+02     NA          5.1   \n",
      "1540     1544     1519     4        9.6388958662e+01     3.2355936051e+02     235.68      7.0   \n",
      "2003     2003     1610     76       9.7146226251e+01     3.1948388561e+02     228.87      8.8   \n",
      "2483     2483     2056     10       9.7146226251e+01     3.1418591147e+02     223.42      10.4  \n",
      "2963     2963     2534     16       9.7146226251e+01     3.1198674503e+02     221.15      11.8  \n",
      "3442     3442     3011     40       9.7146226251e+01     3.1198674503e+02     221.15      13.4  \n",
      "3917     3917     3486     64       9.7146226251e+01     3.1198674503e+02     221.15      15.1  \n",
      "4389     4389     3870     13       9.7146226251e+01     3.1198474109e+02     221.15      17.0  \n",
      "4863     4863     4200     10       9.7146226251e+01     3.1068358231e+02     219.81      18.6  \n",
      "5343     5343     4680     11       9.7146226251e+01     3.0978236788e+02     218.88      20.1  \n",
      "5823     5823     5160     12       9.7146226251e+01     3.0943340745e+02     218.52      21.6  \n",
      "6303     6303     5624     9        9.7146226251e+01     3.0892256489e+02     218.00      23.2  \n",
      "6783     6783     6104     20       9.7146226251e+01     3.0848648896e+02     217.55      24.6  \n",
      "7260     7260     6581     44       9.7146226251e+01     3.0848648896e+02     217.55      26.1  \n",
      "7740     7740     7061     68       9.7146226251e+01     3.0848648896e+02     217.55      27.7  \n",
      "8209     8209     7522     12       9.7146226251e+01     3.0843778266e+02     217.50      29.5  \n",
      "8678     8678     7845     13       9.7146226251e+01     3.0824261215e+02     217.30      31.2  \n",
      "9156     9156     8281     14       9.7146226251e+01     3.0782433694e+02     216.87      33.0  \n",
      "9636     9636     8723     15       9.7146226251e+01     3.0758164100e+02     216.62      34.6  \n",
      "10115    10115    9152     16       9.7146226251e+01     3.0726996741e+02     216.30      36.2  \n",
      "10556    10556    9527     38       9.7146226251e+01     3.0726996741e+02     216.30      38.1  \n",
      "11034    11034    9989     62       9.7146226251e+01     3.0726996741e+02     216.30      39.7  \n",
      "\n",
      "Objective of best integer solution : 9.714622625080e+01      \n",
      "Best objective bound               : 3.072699674120e+02      \n",
      "Construct solution objective       : Not employed\n",
      "Construct solution # roundings     : 0\n",
      "User objective cut value           : 0\n",
      "Number of cuts generated           : 0\n",
      "Number of branches                 : 11034\n",
      "Number of relaxations solved       : 11034\n",
      "Number of interior point iterations: 242428\n",
      "Number of simplex iterations       : 0\n",
      "Time spend presolving the root     : 0.01\n",
      "Time spend optimizing the root     : 0.09\n",
      "Mixed integer optimizer terminated. Time: 40.03\n",
      "\n",
      "Optimizer terminated. Time: 40.08   \n",
      "\n",
      "\n",
      "Integer solution solution summary\n",
      "  Problem status  : PRIMAL_FEASIBLE\n",
      "  Solution status : PRIMAL_FEASIBLE\n",
      "  Primal.  obj: 9.7146226251e+01    nrm: 8e+03    Viol.  con: 6e-05    var: 6e-10    cones: 0e+00    itg: 0e+00  \n",
      "Total data rate: demanded 1144.5349999999999, provided 1144.5614497476022\n",
      "Power: system 10.000, used 11.782, maximal: 36.000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fea2130e9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "instance = parse(\"data/lancaster/4_0.8.txt\")[0]\n",
    "n, d = instance[\"noise\"], instance[\"demand\"]\n",
    "M = fsparc_model(n, d)\n",
    "M.setLogHandler(sys.stdout)\n",
    "M.setSolverParam(\"optimizerMaxTime\", 40.0)\n",
    "M.solve()\n",
    "M.acceptedSolutionStatus(AccSolutionStatus.Feasible)\n",
    "stats(M, n, d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bar plot shows power assignments to the channels. Each color represents one user.\n",
    "\n",
    "# Example 2\n",
    "\n",
    "The next example is a small, randomly generated set of data with 15 channels and 3 users, which we should solve to optimality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : max             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 199             \n",
      "  Cones                  : 45              \n",
      "  Scalar variables       : 271             \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 45              \n",
      "\n",
      "Optimizer started.\n",
      "Mixed integer optimizer started.\n",
      "Threads used: 20\n",
      "Presolve started.\n",
      "Presolve terminated. Time = 0.00\n",
      "Presolved problem: 225 variables, 153 constraints, 452 non-zeros\n",
      "Presolved problem: 0 general integer, 45 binary, 180 continuous\n",
      "Clique table size: 15\n",
      "BRANCHES RELAXS   ACT_NDS  DEPTH    BEST_INT_OBJ         BEST_RELAX_OBJ       REL_GAP(%)  TIME  \n",
      "0        1        1        0        NA                   6.2736906817e+01     NA          0.0   \n",
      "Cut generation started.\n",
      "0        2        1        0        NA                   6.2736906817e+01     NA          0.1   \n",
      "Cut generation terminated. Time = 0.00\n",
      "8        12       9        2        NA                   5.8418013107e+01     NA          0.2   \n",
      "20       24       21       5        NA                   5.7248034543e+01     NA          0.3   \n",
      "36       40       37       7        NA                   5.7248034543e+01     NA          0.3   \n",
      "48       52       49       8        NA                   5.7248034543e+01     NA          0.3   \n",
      "80       84       81       10       NA                   5.7248034543e+01     NA          0.4   \n",
      "160      164      161      14       NA                   5.7248034543e+01     NA          0.5   \n",
      "320      313      249      17       1.9890365163e+01     5.5150531676e+01     177.27      0.8   \n",
      "560      515      269      5        2.0074632174e+01     5.4015323987e+01     169.07      1.1   \n",
      "820      769      353      18       2.0886038578e+01     5.2713196601e+01     152.38      1.6   \n",
      "1160     1102     503      18       2.0886038578e+01     5.1086229306e+01     144.60      2.0   \n",
      "1619     1558     686      13       2.0886038578e+01     5.0036307959e+01     139.57      2.7   \n",
      "2081     2015     816      22       2.0886038578e+01     4.7777192266e+01     128.75      3.3   \n",
      "2545     2475     950      18       2.0886038578e+01     4.5168505100e+01     116.26      4.0   \n",
      "3008     2933     1043     21       2.0886038578e+01     4.2765322708e+01     104.76      4.6   \n",
      "3467     3391     1090     18       2.0886038578e+01     4.0000720055e+01     91.52       5.3   \n",
      "3913     3843     1186     21       2.0886038578e+01     3.8961479080e+01     86.54       6.0   \n",
      "4353     4292     1242     15       2.0886038578e+01     3.7279206008e+01     78.49       6.8   \n",
      "4803     4743     1316     9        2.0886038578e+01     3.6233564889e+01     73.48       7.5   \n",
      "5263     5200     1394     17       2.0886038578e+01     3.6162281699e+01     73.14       8.1   \n",
      "5717     5652     1446     21       2.0886038578e+01     3.5396585587e+01     69.47       8.8   \n",
      "6155     6097     1474     10       2.0886038578e+01     3.4835152140e+01     66.79       9.6   \n",
      "6574     6521     1477     19       2.0886038578e+01     3.4008845027e+01     62.83       10.4  \n",
      "7033     6977     1514     18       2.0886038578e+01     3.3563414586e+01     60.70       11.1  \n",
      "7474     7424     1523     14       2.0886038578e+01     3.3441191697e+01     60.11       11.9  \n",
      "7927     7879     1482     21       2.0886038578e+01     3.3056697831e+01     58.27       12.6  \n",
      "8376     8329     1467     18       2.0886038578e+01     3.2055350146e+01     53.48       13.2  \n",
      "8821     8777     1392     15       2.0886156731e+01     3.1721254007e+01     51.88       14.1  \n",
      "9275     9230     1338     14       2.0886156731e+01     3.1296712465e+01     49.84       14.8  \n",
      "9730     9684     1293     10       2.0886156731e+01     3.1084824213e+01     48.83       15.5  \n",
      "10172    10133    1255     16       2.0886156731e+01     3.0927284262e+01     48.08       16.2  \n",
      "10618    10580    1173     17       2.0886156731e+01     3.0531538141e+01     46.18       16.9  \n",
      "11060    11028    1089     14       2.0886156731e+01     3.0358038321e+01     45.35       17.7  \n",
      "11473    11455    1030     20       2.0886156731e+01     3.0272515219e+01     44.94       18.5  \n",
      "11898    11896    991      18       2.0886156731e+01     2.9876691828e+01     43.05       19.3  \n",
      "12327    12338    900      18       2.0886156731e+01     2.9590258263e+01     41.67       20.2  \n",
      "12743    12777    834      16       2.0886156731e+01     2.9590258263e+01     41.67       21.1  \n",
      "13180    13222    759      18       2.0886156731e+01     2.9590258263e+01     41.67       21.9  \n",
      "13600    13664    691      17       2.0886156731e+01     2.8856240125e+01     38.16       22.8  \n",
      "14033    14108    610      17       2.0886156731e+01     2.8758742060e+01     37.69       23.6  \n",
      "14483    14558    524      16       2.0886156731e+01     2.8140325871e+01     34.73       24.3  \n",
      "14918    14992    435      18       2.0886156731e+01     2.7798746872e+01     33.10       25.0  \n",
      "15335    15415    344      16       2.0886156731e+01     2.7511073832e+01     31.72       25.7  \n",
      "15675    15756    290      17       2.0886156731e+01     2.7223697972e+01     30.34       26.3  \n",
      "15955    16043    240      22       2.0886156731e+01     2.7223697972e+01     30.34       26.9  \n",
      "16195    16303    194      15       2.0886156731e+01     2.6706954318e+01     27.87       27.5  \n",
      "16375    16495    140      14       2.0886156731e+01     2.6240947330e+01     25.64       28.1  \n",
      "16515    16642    118      21       2.0886156731e+01     2.6240947330e+01     25.64       28.5  \n",
      "16614    16744    77       13       2.0886156731e+01     2.5988521964e+01     24.43       28.8  \n",
      "16673    16804    54       15       2.0886156731e+01     2.5988521964e+01     24.43       28.9  \n",
      "16713    16844    44       18       2.0886156731e+01     2.5988521964e+01     24.43       29.1  \n",
      "16750    16882    23       18       2.0886156731e+01     2.5988521964e+01     24.43       29.2  \n",
      "16761    16893    16       16       2.0886156731e+01     2.5988521964e+01     24.43       29.2  \n",
      "16776    16909    7        14       2.0886156731e+01     2.4433909459e+01     16.99       29.3  \n",
      "16786    16921    3        8        2.0886156731e+01     2.4433909459e+01     16.99       29.4  \n",
      "An optimal solution satisfying the relative gap tolerance of 1.00e-02(%) has been located.\n",
      "The relative gap is 0.00e+00(%).\n",
      "An optimal solution satisfying the absolute gap tolerance of 0.00e+00 has been located.\n",
      "The absolute gap is 0.00e+00.\n",
      "\n",
      "Objective of best integer solution : 2.088615673080e+01      \n",
      "Best objective bound               : 2.088615673080e+01      \n",
      "Construct solution objective       : Not employed\n",
      "Construct solution # roundings     : 0\n",
      "User objective cut value           : 0\n",
      "Number of cuts generated           : 0\n",
      "Number of branches                 : 16791\n",
      "Number of relaxations solved       : 16927\n",
      "Number of interior point iterations: 418244\n",
      "Number of simplex iterations       : 0\n",
      "Time spend presolving the root     : 0.00\n",
      "Time spend optimizing the root     : 0.02\n",
      "Mixed integer optimizer terminated. Time: 29.53\n",
      "\n",
      "Optimizer terminated. Time: 29.55   \n",
      "\n",
      "\n",
      "Integer solution solution summary\n",
      "  Problem status  : PRIMAL_FEASIBLE\n",
      "  Solution status : INTEGER_OPTIMAL\n",
      "  Primal.  obj: 2.0886156731e+01    nrm: 6e+04    Viol.  con: 1e-05    var: 7e-10    cones: 0e+00    itg: 0e+00  \n",
      "Total data rate: demanded 297.7325530926529, provided 301.222514307648\n",
      "Power: system 10.000, used 14.422, maximal: 36.000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fea18dbed68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "instance = parse(\"data/small-random/random_15_3_0.85.txt\")[0]\n",
    "n, d = instance[\"noise\"], instance[\"demand\"]\n",
    "M = fsparc_model(n, d)\n",
    "M.setLogHandler(sys.stdout)\n",
    "M.solve()\n",
    "stats(M, n, d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/80x15.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>. The **MOSEK** logo and name are trademarks of <a href=\"http://mosek.com\">Mosek ApS</a>. The code is provided as-is. Compatibility with future release of **MOSEK** or the `Fusion API` are not guaranteed. For more information contact our [support](mailto:support@mosek.com). "
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}