QUBO and Ising Models.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"top\" id=\"top\"></a>\n",
    "\n",
    "<div align=\"center\">\n",
    "    <h1>QUBO &amp; Ising Models</h1>\n",
    "    <a href=\"https://github.com/bernalde\">David E. Bernal Neira</a>\n",
    "    <br>\n",
    "    <i>Davidson School of Chemical Engineering, Purdue University</i>\n",
    "    <br>\n",
    "    <i>Universities Space Research Association</i>\n",
    "    <br>\n",
    "    <i>NASA QuAIL</i>\n",
    "    <br>\n",
    "    <br>\n",
    "    <a href=\"https://github.com/pedromxavier\">Pedro Maciel Xavier</a>\n",
    "    <br>\n",
    "    <i>Davidson School of Chemical Engineering, Purdue University</i>\n",
    "    <br>\n",
    "    <i>Computer Science &amp; Systems Engineering Program, Federal University of Rio de Janeiro</i>\n",
    "    <br>\n",
    "    <i>PSR Energy Consulting &amp; Analytics</i>\n",
    "    <br>\n",
    "    <br>\n",
    "    <a href=\"https://github.com/murraybj\">Benjamin J. L. Murray</a>\n",
    "    <br>\n",
    "    <i>Davidson School of Chemical Engineering, Purdue University</i>\n",
    "    <br>\n",
    "    <i>Undergraduate Research Assistant</i>\n",
    "    <br>\n",
    "    <br>\n",
    "    <a href=\"https://colab.research.google.com/github/JuliaQUBO/QUBONotebooks/blob/main/notebooks_py/2-QUBO_python.ipynb\" target=\"_parent\">\n",
    "        <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "    </a>\n",
    "    <a href=\"https://secquoia.github.io/\">\n",
    "        <img src=\"https://img.shields.io/badge/🌲⚛️🌐-SECQUOIA-blue\" alt=\"SECQUOIA\"/>\n",
    "    </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadratic Unconstrained Binary Optimization\n",
    "This notebook will explain the basics of the QUBO modeling. In order to implement the different QUBOs we will use D-Wave's packages **[dimod](https://github.com/dwavesystems/dimod)**, and then solve them using **[neal](https://github.com/dwavesystems/dwave-neal)**'s implementation of simulated annealing.\n",
    "We will also leverage the use of D-Wave's package **[dwavebinarycsp](https://github.com/dwavesystems/dwavebinarycsp)** to translate constraint satisfaction problems to QUBOs. Finally, for Groebner basis computations we will use **[Sympy](https://www.sympy.org/)** for symbolic computation in Python and **[Networkx](https://networkx.github.io/)** for network models/graphs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem statement\n",
    "We define a QUBO as the following optimization problem:\n",
    "$$\n",
    "\\min_{x \\in \\{0,1 \\}^n} \\sum_{(ij) \\in E(G)} Q_{ij}x_i x_j + \\sum_{i \\in V(G)}Q_{ii}x_i + c_Q = \\min_{x \\in \\{0,1 \\}^n}  x^\\top Q x + c_Q\n",
    "$$\n",
    "where we optimize over binary variables $x \\in \\{ 0,1 \\}^n$, on a constrained graph $G(V,E)$ defined by an adjacency matrix $Q$. We also include an arbitrary offset  $c_Q$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "Suppose we want to solve the following problem via QUBO\n",
    "$$\n",
    "\\min_{\\mathbf{x}} 2𝑥_0+4𝑥_1+4𝑥_2+4𝑥_3+4𝑥_4+4𝑥_5+5𝑥_6+4𝑥_7+5𝑥_8+6𝑥_9+5𝑥_{10} \\\\\n",
    "s.t. \\begin{bmatrix}\n",
    "1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1\\\\\n",
    "0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1\\\\\n",
    "0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1\n",
    "\\end{bmatrix}\\mathbf{x}=\n",
    "\\begin{bmatrix}\n",
    "1\\\\\n",
    "1\\\\\n",
    "1\n",
    "\\end{bmatrix} \\\\\n",
    "\\mathbf{x} \\in \\{0,1 \\}^{11}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If using this on Google collab, we need to install the packages\n",
    "try:\n",
    "  import google.colab\n",
    "  IN_COLAB = True\n",
    "except:\n",
    "  IN_COLAB = False\n",
    "\n",
    "# Let's install dimod, neal, and pyomo\n",
    "if IN_COLAB:\n",
    "    !pip install -q pyomo\n",
    "    !pip install dimod\n",
    "    !pip install dwave-neal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the Pyomo library, which can be installed via pip, conda or from Github https://github.com/Pyomo/pyomo\n",
    "import pyomo.environ as pyo\n",
    "# Import the Dwave packages dimod and neal\n",
    "import dimod\n",
    "import neal\n",
    "# Import Matplotlib to generate plots\n",
    "import matplotlib.pyplot as plt\n",
    "# Import numpy and scipy for certain numerical calculations below\n",
    "import numpy as np\n",
    "from scipy.special import gamma\n",
    "import math\n",
    "from collections import Counter\n",
    "import pandas as pd\n",
    "from itertools import chain\n",
    "import time\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we would write this problem as an unconstrained one by penalizing the linear constraints as quadratics in the objective. Let's first define the problem parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1],\n",
    "            [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1],\n",
    "            [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]])\n",
    "b = np.array([1, 1, 1])\n",
    "c = np.array([2, 4, 4, 4, 4, 4, 5, 4, 5,6, 5])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to define the $\\mathbf{Q}$ matrix, we first write the problem\n",
    "\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "    \\displaystyle%\n",
    "    \\min_{\\mathbf{x}} &\\mathbf{c}' \\mathbf{x} \\\\\n",
    "    \\textrm{s.t.}     & \\mathbf{A}\\mathbf{x} = \\mathbf{b} \\\\\n",
    "    ~                 & \\mathbf{x} \\in \\{0,1 \\}^{11}\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "as follows:\n",
    "\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "    \\displaystyle%\n",
    "    \\min_{\\mathbf{x}} & \\mathbf{c}' \\mathbf{x} + \\rho (\\mathbf{A}\\mathbf{x}-\\mathbf{b})' (\\mathbf{A}\\mathbf{x}-\\mathbf{b}) \\\\\n",
    "    \\textrm{s.t.}     & \\mathbf{x} \\in \\{0,1 \\}^{11}\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "Exploiting the fact that $x^2=x$ for $x \\in \\{0,1\\}$, we can make the linear terms appear in the diagonal of the $\\mathbf{Q}$ matrix.\n",
    "\n",
    "$$\n",
    "\\rho(\\mathbf{A}\\mathbf{x}-\\mathbf{b})'(\\mathbf{A}\\mathbf{x}-\\mathbf{b}) = \\rho( \\mathbf{x}'(\\mathbf{A}'\\mathbf{A}) \\mathbf{x} - 2(\\mathbf{A}'\\mathbf{b}) \\mathbf{x} + \\mathbf{b}'\\mathbf{b} )\n",
    "$$\n",
    "\n",
    "For this problem in particular, one can prove that a reasonable penalization factor is given by $\\rho = \\sum_{i=1}^n |c_i| + \\epsilon$ with $\\epsilon > 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ -46    0    0   48   48   48    0   48   48   48   48]\n",
      " [   0  -44    0   48    0   48   48    0   48   48   48]\n",
      " [   0    0  -44    0   48    0   48   48   48   48   48]\n",
      " [  48   48    0  -92   48   96   48   48   96   96   96]\n",
      " [  48    0   48   48  -92   48   48   96   96   96   96]\n",
      " [  48   48    0   96   48  -92   48   48   96   96   96]\n",
      " [   0   48   48   48   48   48  -91   48   96   96   96]\n",
      " [  48    0   48   48   96   48   48  -92   96   96   96]\n",
      " [  48   48   48   96   96   96   96   96 -139  144  144]\n",
      " [  48   48   48   96   96   96   96   96  144 -138  144]\n",
      " [  48   48   48   96   96   96   96   96  144  144 -139]]\n",
      "144\n"
     ]
    }
   ],
   "source": [
    "epsilon = 1\n",
    "rho = np.sum(np.abs(c)) + epsilon\n",
    "Q = rho*np.matmul(A.T,A)\n",
    "Q += np.diag(c)\n",
    "Q -= rho*2*np.diag(np.matmul(b.T,A))\n",
    "Beta = rho*np.matmul(b.T,b)\n",
    "print(Q)\n",
    "print(Beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the graph that defines this instance using the Q matrix as the adjacency matrix of a graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.from_numpy_array(Q)\n",
    "nx.draw(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define a QUBO model and then solve it using DWaves code for complete enumeration and simulated annealing (eventually with Quantum annealiing too!)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BinaryQuadraticModel({0: -46.0, 1: -44.0, 2: -44.0, 3: -92.0, 4: -92.0, 5: -92.0, 6: -91.0, 7: -92.0, 8: -139.0, 9: -138.0, 10: -139.0}, {(3, 0): 96.0, (3, 1): 96.0, (4, 0): 96.0, (4, 2): 96.0, (4, 3): 96.0, (5, 0): 96.0, (5, 1): 96.0, (5, 3): 192.0, (5, 4): 96.0, (6, 1): 96.0, (6, 2): 96.0, (6, 3): 96.0, (6, 4): 96.0, (6, 5): 96.0, (7, 0): 96.0, (7, 2): 96.0, (7, 3): 96.0, (7, 4): 192.0, (7, 5): 96.0, (7, 6): 96.0, (8, 0): 96.0, (8, 1): 96.0, (8, 2): 96.0, (8, 3): 192.0, (8, 4): 192.0, (8, 5): 192.0, (8, 6): 192.0, (8, 7): 192.0, (9, 0): 96.0, (9, 1): 96.0, (9, 2): 96.0, (9, 3): 192.0, (9, 4): 192.0, (9, 5): 192.0, (9, 6): 192.0, (9, 7): 192.0, (9, 8): 288.0, (10, 0): 96.0, (10, 1): 96.0, (10, 2): 96.0, (10, 3): 192.0, (10, 4): 192.0, (10, 5): 192.0, (10, 6): 192.0, (10, 7): 192.0, (10, 8): 288.0, (10, 9): 288.0}, 144.0, 'BINARY')\n"
     ]
    }
   ],
   "source": [
    "model = dimod.BinaryQuadraticModel.from_qubo(Q, offset=Beta)\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the problem is relatively small (11 variables, $2^{11}=2048$ combinations), we can afford to enumerate all the solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "exactSampler = dimod.reference.samplers.ExactSolver()\n",
    "exactSamples = exactSampler.sample(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some useful functions to get plots\n",
    "def plot_enumerate(results, title=None):\n",
    "\n",
    "    plt.figure()\n",
    "\n",
    "    energies = [datum.energy for datum in results.data(\n",
    "        ['energy'], sorted_by='energy')]\n",
    "    \n",
    "    if results.vartype == 'Vartype.BINARY':\n",
    "        samples = [''.join(c for c in str(datum.sample.values()).strip(\n",
    "            ', ') if c.isdigit()) for datum in results.data(['sample'], sorted_by=None)]\n",
    "        plt.xlabel('bitstring for solution')\n",
    "    else:\n",
    "        samples = np.arange(len(energies))\n",
    "        plt.xlabel('solution')\n",
    "\n",
    "    plt.bar(samples,energies)\n",
    "    plt.xticks(rotation=90)\n",
    "    plt.ylabel('Energy')\n",
    "    plt.title(str(title))\n",
    "    print(\"minimum energy:\", min(energies))\n",
    "\n",
    "def plot_samples(results, title=None):\n",
    "    plt.figure()\n",
    "    if results.vartype == 'Vartype.BINARY':\n",
    "        samples = [''.join(c for c in str(datum.sample.values()).strip(\n",
    "            ', ') if c.isdigit()) for datum in results.data(['sample'], sorted_by=None)]\n",
    "        plt.xlabel('bitstring for solution')\n",
    "    else:\n",
    "        samples = np.arange(len(energies))\n",
    "        plt.xlabel('solution')\n",
    "\n",
    "    counts = Counter(samples)\n",
    "    total = len(samples)\n",
    "    for key in counts:\n",
    "        counts[key] /= total\n",
    "    df = pd.DataFrame.from_dict(counts, orient='index').sort_index()\n",
    "    df.plot(kind='bar', legend=None)\n",
    "\n",
    "    plt.xticks(rotation=80)\n",
    "    plt.ylabel('Probabilities')\n",
    "    plt.title(str(title))\n",
    "    plt.show()\n",
    "    print(\"minimum energy:\", min(energies))\n",
    "\n",
    "\n",
    "def plot_energies(results, title=None, skip=1):\n",
    "    # skip parameter given to avoid putting all xlabels\n",
    "    energies = results.data_vectors['energy']\n",
    "    occurrences = results.data_vectors['num_occurrences']\n",
    "    counts = Counter(energies)\n",
    "    total = sum(occurrences)\n",
    "    counts = {}\n",
    "    for index, energy in enumerate(energies):\n",
    "        if energy in counts.keys():\n",
    "            counts[energy] += occurrences[index]\n",
    "        else:\n",
    "            counts[energy] = occurrences[index]\n",
    "    for key in counts:\n",
    "        counts[key] /= total\n",
    "    df = pd.DataFrame.from_dict(counts, orient='index').sort_index()\n",
    "    ax = df.plot(kind='bar', legend=None)\n",
    "\n",
    "    plt.xlabel('Energy')\n",
    "    plt.ylabel('Probabilities')\n",
    "    # Plot only a subset of xlabels (every skip steps)\n",
    "    ax.set_xticklabels([t if not i%skip else \"\" for i,t in enumerate(ax.get_xticklabels())])\n",
    "    plt.title(str(title))\n",
    "    plt.show()\n",
    "    print(\"minimum energy:\", min(energies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 5.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 5.0\n"
     ]
    }
   ],
   "source": [
    "plot_enumerate(exactSamples, title='Enumerate all solutions')\n",
    "plot_energies(exactSamples, title='Enumerate all solutions', skip=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now solve this QUBO via traditional Integer Programming."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 'QUBO example as an IP, 47-779/785 QuIPML'\n",
      "\n",
      "  Variables:\n",
      "    x : Size=11, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :  None :     1 : False :  True : Binary\n",
      "          1 :     0 :  None :     1 : False :  True : Binary\n",
      "          2 :     0 :  None :     1 : False :  True : Binary\n",
      "          3 :     0 :  None :     1 : False :  True : Binary\n",
      "          4 :     0 :  None :     1 : False :  True : Binary\n",
      "          5 :     0 :  None :     1 : False :  True : Binary\n",
      "          6 :     0 :  None :     1 : False :  True : Binary\n",
      "          7 :     0 :  None :     1 : False :  True : Binary\n",
      "          8 :     0 :  None :     1 : False :  True : Binary\n",
      "          9 :     0 :  None :     1 : False :  True : Binary\n",
      "         10 :     0 :  None :     1 : False :  True : Binary\n",
      "    y : Size=121, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}*{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key      : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (0, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (1, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (2, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (3, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (4, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (5, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (6, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (7, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (8, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (9, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "        (10, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "  Objectives:\n",
      "    objective : Size=1, Index=None, Active=True\n",
      "ERROR: evaluating object as numeric value: y[3,0]\n",
      "        (object: <class 'pyomo.core.base.var.VarData'>)\n",
      "    No value for uninitialized NumericValue object y[3,0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: evaluating object as numeric value: objective\n",
      "        (object: <class 'pyomo.core.base.objective.ScalarObjective'>)\n",
      "    No value for uninitialized NumericValue object y[3,0]\n",
      "        Key : Active : Value\n",
      "        None :   None :  None\n",
      "\n",
      "  Constraints:\n",
      "    c1 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : None :   0.0\n",
      "          2 :  None : None :   0.0\n",
      "          3 :  None : None :   0.0\n",
      "          4 :  None : None :   0.0\n",
      "          5 :  None : None :   0.0\n",
      "          6 :  None : None :   0.0\n",
      "          7 :  None : None :   0.0\n",
      "          8 :  None : None :   0.0\n",
      "          9 :  None : None :   0.0\n",
      "         10 :  None : None :   0.0\n",
      "         11 :  None : None :   0.0\n",
      "         12 :  None : None :   0.0\n",
      "         13 :  None : None :   0.0\n",
      "         14 :  None : None :   0.0\n",
      "         15 :  None : None :   0.0\n",
      "         16 :  None : None :   0.0\n",
      "         17 :  None : None :   0.0\n",
      "         18 :  None : None :   0.0\n",
      "         19 :  None : None :   0.0\n",
      "         20 :  None : None :   0.0\n",
      "         21 :  None : None :   0.0\n",
      "         22 :  None : None :   0.0\n",
      "         23 :  None : None :   0.0\n",
      "         24 :  None : None :   0.0\n",
      "         25 :  None : None :   0.0\n",
      "         26 :  None : None :   0.0\n",
      "         27 :  None : None :   0.0\n",
      "         28 :  None : None :   0.0\n",
      "         29 :  None : None :   0.0\n",
      "         30 :  None : None :   0.0\n",
      "         31 :  None : None :   0.0\n",
      "         32 :  None : None :   0.0\n",
      "         33 :  None : None :   0.0\n",
      "         34 :  None : None :   0.0\n",
      "         35 :  None : None :   0.0\n",
      "         36 :  None : None :   0.0\n",
      "         37 :  None : None :   0.0\n",
      "         38 :  None : None :   0.0\n",
      "         39 :  None : None :   0.0\n",
      "         40 :  None : None :   0.0\n",
      "         41 :  None : None :   0.0\n",
      "         42 :  None : None :   0.0\n",
      "         43 :  None : None :   0.0\n",
      "         44 :  None : None :   0.0\n",
      "         45 :  None : None :   0.0\n",
      "         46 :  None : None :   0.0\n",
      "         47 :  None : None :   0.0\n",
      "    c2 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : None :   0.0\n",
      "          2 :  None : None :   0.0\n",
      "          3 :  None : None :   0.0\n",
      "          4 :  None : None :   0.0\n",
      "          5 :  None : None :   0.0\n",
      "          6 :  None : None :   0.0\n",
      "          7 :  None : None :   0.0\n",
      "          8 :  None : None :   0.0\n",
      "          9 :  None : None :   0.0\n",
      "         10 :  None : None :   0.0\n",
      "         11 :  None : None :   0.0\n",
      "         12 :  None : None :   0.0\n",
      "         13 :  None : None :   0.0\n",
      "         14 :  None : None :   0.0\n",
      "         15 :  None : None :   0.0\n",
      "         16 :  None : None :   0.0\n",
      "         17 :  None : None :   0.0\n",
      "         18 :  None : None :   0.0\n",
      "         19 :  None : None :   0.0\n",
      "         20 :  None : None :   0.0\n",
      "         21 :  None : None :   0.0\n",
      "         22 :  None : None :   0.0\n",
      "         23 :  None : None :   0.0\n",
      "         24 :  None : None :   0.0\n",
      "         25 :  None : None :   0.0\n",
      "         26 :  None : None :   0.0\n",
      "         27 :  None : None :   0.0\n",
      "         28 :  None : None :   0.0\n",
      "         29 :  None : None :   0.0\n",
      "         30 :  None : None :   0.0\n",
      "         31 :  None : None :   0.0\n",
      "         32 :  None : None :   0.0\n",
      "         33 :  None : None :   0.0\n",
      "         34 :  None : None :   0.0\n",
      "         35 :  None : None :   0.0\n",
      "         36 :  None : None :   0.0\n",
      "         37 :  None : None :   0.0\n",
      "         38 :  None : None :   0.0\n",
      "         39 :  None : None :   0.0\n",
      "         40 :  None : None :   0.0\n",
      "         41 :  None : None :   0.0\n",
      "         42 :  None : None :   0.0\n",
      "         43 :  None : None :   0.0\n",
      "         44 :  None : None :   0.0\n",
      "         45 :  None : None :   0.0\n",
      "         46 :  None : None :   0.0\n",
      "         47 :  None : None :   0.0\n",
      "    c3 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : None :   0.0\n",
      "          2 :  None : None :   0.0\n",
      "          3 :  None : None :   0.0\n",
      "          4 :  None : None :   0.0\n",
      "          5 :  None : None :   0.0\n",
      "          6 :  None : None :   0.0\n",
      "          7 :  None : None :   0.0\n",
      "          8 :  None : None :   0.0\n",
      "          9 :  None : None :   0.0\n",
      "         10 :  None : None :   0.0\n",
      "         11 :  None : None :   0.0\n",
      "         12 :  None : None :   0.0\n",
      "         13 :  None : None :   0.0\n",
      "         14 :  None : None :   0.0\n",
      "         15 :  None : None :   0.0\n",
      "         16 :  None : None :   0.0\n",
      "         17 :  None : None :   0.0\n",
      "         18 :  None : None :   0.0\n",
      "         19 :  None : None :   0.0\n",
      "         20 :  None : None :   0.0\n",
      "         21 :  None : None :   0.0\n",
      "         22 :  None : None :   0.0\n",
      "         23 :  None : None :   0.0\n",
      "         24 :  None : None :   0.0\n",
      "         25 :  None : None :   0.0\n",
      "         26 :  None : None :   0.0\n",
      "         27 :  None : None :   0.0\n",
      "         28 :  None : None :   0.0\n",
      "         29 :  None : None :   0.0\n",
      "         30 :  None : None :   0.0\n",
      "         31 :  None : None :   0.0\n",
      "         32 :  None : None :   0.0\n",
      "         33 :  None : None :   0.0\n",
      "         34 :  None : None :   0.0\n",
      "         35 :  None : None :   0.0\n",
      "         36 :  None : None :   0.0\n",
      "         37 :  None : None :   0.0\n",
      "         38 :  None : None :   0.0\n",
      "         39 :  None : None :   0.0\n",
      "         40 :  None : None :   0.0\n",
      "         41 :  None : None :   0.0\n",
      "         42 :  None : None :   0.0\n",
      "         43 :  None : None :   0.0\n",
      "         44 :  None : None :   0.0\n",
      "         45 :  None : None :   0.0\n",
      "         46 :  None : None :   0.0\n",
      "         47 :  None : None :   0.0\n"
     ]
    }
   ],
   "source": [
    "# We do not need to worry about the tranformation to QUBO since dimod takes care of it\n",
    "Q, c = model.to_qubo()\n",
    "\n",
    "# Define the model\n",
    "model_pyo = pyo.ConcreteModel(name='QUBO example as an IP, 47-779/785 QuIPML')\n",
    "\n",
    "I = range(len(model))\n",
    "J = range(len(model))\n",
    "#Define the original variables\n",
    "model_pyo.x = pyo.Var(I, domain=pyo.Binary)\n",
    "# Define the edges variables\n",
    "model_pyo.y = pyo.Var(I, J, domain=pyo.Binary)\n",
    "\n",
    "obj_expr = c\n",
    "\n",
    "# add model constraints\n",
    "model_pyo.c1 = pyo.ConstraintList()\n",
    "model_pyo.c2 = pyo.ConstraintList()\n",
    "model_pyo.c3 = pyo.ConstraintList()\n",
    "for (i,j) in Q.keys():\n",
    "    if i != j:\n",
    "        model_pyo.c1.add(model_pyo.y[i,j] >= model_pyo.x[i] + model_pyo.x[j] - 1)\n",
    "        model_pyo.c2.add(model_pyo.y[i,j] <= model_pyo.x[i])\n",
    "        model_pyo.c3.add(model_pyo.y[i,j] <= model_pyo.x[j])\n",
    "        obj_expr += Q[i,j]*model_pyo.y[i,j]\n",
    "    else:\n",
    "        obj_expr += Q[i,j]*model_pyo.x[i]\n",
    "\n",
    "# Define the objective function\n",
    "model_pyo.objective = pyo.Objective(expr = obj_expr, sense=pyo.minimize)\n",
    "# Print the model\n",
    "model_pyo.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's install the MIP solver GLPK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's install the LP/MIP solver GLPK\n",
    "if IN_COLAB:\n",
    "    !apt-get install -y -qq glpk-utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the solver GLPK\n",
    "if IN_COLAB:\n",
    "    opt_glpk = pyo.SolverFactory('glpk', executable='/usr/bin/glpsol')\n",
    "else:\n",
    "    opt_glpk = pyo.SolverFactory('glpk')\n",
    "# Here we could use another solver, e.g. gurobi or cplex\n",
    "# opt_gurobi = pyo.SolverFactory('gurobi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 'QUBO example as an IP, 47-779/785 QuIPML'\n",
      "\n",
      "  Variables:\n",
      "    x : Size=11, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          1 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          2 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          3 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          4 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          5 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          6 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          7 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          8 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          9 :     0 :   0.0 :     1 : False : False : Binary\n",
      "         10 :     0 :   1.0 :     1 : False : False : Binary\n",
      "    y : Size=121, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}*{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key      : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (0, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (1, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (2, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (3, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (3, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (3, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (4, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 2) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (4, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (4, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (4, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (5, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 2) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (6, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 2) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 6) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (7, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 2) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 6) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (8, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 2) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 6) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (9, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 2) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 6) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 9) :     0 :   0.0 :     1 : False : False : Binary\n",
      "        (10, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "  Objectives:\n",
      "    objective : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Value\n",
      "        None :   True :   5.0\n",
      "\n",
      "  Constraints:\n",
      "    c1 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : -1.0 :   0.0\n",
      "          2 :  None : -1.0 :   0.0\n",
      "          3 :  None : -1.0 :   0.0\n",
      "          4 :  None : -1.0 :   0.0\n",
      "          5 :  None : -1.0 :   0.0\n",
      "          6 :  None : -1.0 :   0.0\n",
      "          7 :  None : -1.0 :   0.0\n",
      "          8 :  None : -1.0 :   0.0\n",
      "          9 :  None : -1.0 :   0.0\n",
      "         10 :  None : -1.0 :   0.0\n",
      "         11 :  None : -1.0 :   0.0\n",
      "         12 :  None : -1.0 :   0.0\n",
      "         13 :  None : -1.0 :   0.0\n",
      "         14 :  None : -1.0 :   0.0\n",
      "         15 :  None : -1.0 :   0.0\n",
      "         16 :  None : -1.0 :   0.0\n",
      "         17 :  None : -1.0 :   0.0\n",
      "         18 :  None : -1.0 :   0.0\n",
      "         19 :  None : -1.0 :   0.0\n",
      "         20 :  None : -1.0 :   0.0\n",
      "         21 :  None : -1.0 :   0.0\n",
      "         22 :  None : -1.0 :   0.0\n",
      "         23 :  None : -1.0 :   0.0\n",
      "         24 :  None : -1.0 :   0.0\n",
      "         25 :  None : -1.0 :   0.0\n",
      "         26 :  None : -1.0 :   0.0\n",
      "         27 :  None : -1.0 :   0.0\n",
      "         28 :  None : -1.0 :   0.0\n",
      "         29 :  None : -1.0 :   0.0\n",
      "         30 :  None : -1.0 :   0.0\n",
      "         31 :  None : -1.0 :   0.0\n",
      "         32 :  None : -1.0 :   0.0\n",
      "         33 :  None : -1.0 :   0.0\n",
      "         34 :  None : -1.0 :   0.0\n",
      "         35 :  None : -1.0 :   0.0\n",
      "         36 :  None : -1.0 :   0.0\n",
      "         37 :  None : -1.0 :   0.0\n",
      "         38 :  None :  0.0 :   0.0\n",
      "         39 :  None :  0.0 :   0.0\n",
      "         40 :  None :  0.0 :   0.0\n",
      "         41 :  None :  0.0 :   0.0\n",
      "         42 :  None :  0.0 :   0.0\n",
      "         43 :  None :  0.0 :   0.0\n",
      "         44 :  None :  0.0 :   0.0\n",
      "         45 :  None :  0.0 :   0.0\n",
      "         46 :  None :  0.0 :   0.0\n",
      "         47 :  None :  0.0 :   0.0\n",
      "    c2 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None :  0.0 :   0.0\n",
      "          2 :  None :  0.0 :   0.0\n",
      "          3 :  None :  0.0 :   0.0\n",
      "          4 :  None :  0.0 :   0.0\n",
      "          5 :  None :  0.0 :   0.0\n",
      "          6 :  None :  0.0 :   0.0\n",
      "          7 :  None :  0.0 :   0.0\n",
      "          8 :  None :  0.0 :   0.0\n",
      "          9 :  None :  0.0 :   0.0\n",
      "         10 :  None :  0.0 :   0.0\n",
      "         11 :  None :  0.0 :   0.0\n",
      "         12 :  None :  0.0 :   0.0\n",
      "         13 :  None :  0.0 :   0.0\n",
      "         14 :  None :  0.0 :   0.0\n",
      "         15 :  None :  0.0 :   0.0\n",
      "         16 :  None :  0.0 :   0.0\n",
      "         17 :  None :  0.0 :   0.0\n",
      "         18 :  None :  0.0 :   0.0\n",
      "         19 :  None :  0.0 :   0.0\n",
      "         20 :  None :  0.0 :   0.0\n",
      "         21 :  None :  0.0 :   0.0\n",
      "         22 :  None :  0.0 :   0.0\n",
      "         23 :  None :  0.0 :   0.0\n",
      "         24 :  None :  0.0 :   0.0\n",
      "         25 :  None :  0.0 :   0.0\n",
      "         26 :  None :  0.0 :   0.0\n",
      "         27 :  None :  0.0 :   0.0\n",
      "         28 :  None :  0.0 :   0.0\n",
      "         29 :  None :  0.0 :   0.0\n",
      "         30 :  None :  0.0 :   0.0\n",
      "         31 :  None :  0.0 :   0.0\n",
      "         32 :  None :  0.0 :   0.0\n",
      "         33 :  None :  0.0 :   0.0\n",
      "         34 :  None :  0.0 :   0.0\n",
      "         35 :  None :  0.0 :   0.0\n",
      "         36 :  None :  0.0 :   0.0\n",
      "         37 :  None :  0.0 :   0.0\n",
      "         38 :  None : -1.0 :   0.0\n",
      "         39 :  None : -1.0 :   0.0\n",
      "         40 :  None : -1.0 :   0.0\n",
      "         41 :  None : -1.0 :   0.0\n",
      "         42 :  None : -1.0 :   0.0\n",
      "         43 :  None : -1.0 :   0.0\n",
      "         44 :  None : -1.0 :   0.0\n",
      "         45 :  None : -1.0 :   0.0\n",
      "         46 :  None : -1.0 :   0.0\n",
      "         47 :  None : -1.0 :   0.0\n",
      "    c3 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None :  0.0 :   0.0\n",
      "          2 :  None :  0.0 :   0.0\n",
      "          3 :  None :  0.0 :   0.0\n",
      "          4 :  None :  0.0 :   0.0\n",
      "          5 :  None :  0.0 :   0.0\n",
      "          6 :  None :  0.0 :   0.0\n",
      "          7 :  None :  0.0 :   0.0\n",
      "          8 :  None :  0.0 :   0.0\n",
      "          9 :  None :  0.0 :   0.0\n",
      "         10 :  None :  0.0 :   0.0\n",
      "         11 :  None :  0.0 :   0.0\n",
      "         12 :  None :  0.0 :   0.0\n",
      "         13 :  None :  0.0 :   0.0\n",
      "         14 :  None :  0.0 :   0.0\n",
      "         15 :  None :  0.0 :   0.0\n",
      "         16 :  None :  0.0 :   0.0\n",
      "         17 :  None :  0.0 :   0.0\n",
      "         18 :  None :  0.0 :   0.0\n",
      "         19 :  None :  0.0 :   0.0\n",
      "         20 :  None :  0.0 :   0.0\n",
      "         21 :  None :  0.0 :   0.0\n",
      "         22 :  None :  0.0 :   0.0\n",
      "         23 :  None :  0.0 :   0.0\n",
      "         24 :  None :  0.0 :   0.0\n",
      "         25 :  None :  0.0 :   0.0\n",
      "         26 :  None :  0.0 :   0.0\n",
      "         27 :  None :  0.0 :   0.0\n",
      "         28 :  None :  0.0 :   0.0\n",
      "         29 :  None :  0.0 :   0.0\n",
      "         30 :  None :  0.0 :   0.0\n",
      "         31 :  None :  0.0 :   0.0\n",
      "         32 :  None :  0.0 :   0.0\n",
      "         33 :  None :  0.0 :   0.0\n",
      "         34 :  None :  0.0 :   0.0\n",
      "         35 :  None :  0.0 :   0.0\n",
      "         36 :  None :  0.0 :   0.0\n",
      "         37 :  None :  0.0 :   0.0\n",
      "         38 :  None :  0.0 :   0.0\n",
      "         39 :  None :  0.0 :   0.0\n",
      "         40 :  None :  0.0 :   0.0\n",
      "         41 :  None :  0.0 :   0.0\n",
      "         42 :  None :  0.0 :   0.0\n",
      "         43 :  None :  0.0 :   0.0\n",
      "         44 :  None :  0.0 :   0.0\n",
      "         45 :  None :  0.0 :   0.0\n",
      "         46 :  None :  0.0 :   0.0\n",
      "         47 :  None :  0.0 :   0.0\n"
     ]
    }
   ],
   "source": [
    "# We obtain the solution with GLPK\n",
    "result_obj = opt_glpk.solve(model_pyo, tee=False)\n",
    "model_pyo.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that the optimal solution of this problem is $x_{8} = 1, 0$ otherwise, leading to an objective of $5$. Notice that this problem has a degenerate optimal solution given that $x_{10} = 1, 0$ otherwise also leads to the same solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ising model\n",
    "This notebook will explain the basics of the Ising model. In order to implement the different Ising Models we will use D-Wave's packages **[dimod](https://github.com/dwavesystems/dimod)** and **[neal](https://github.com/dwavesystems/dwave-neal)**, for defining the Ising model and solving it with simulated annealing, respectively. When posing the problems as Integer programs, we will model using **[Pyomo](http://www.pyomo.org/)**, an open-source Python package, which provides a flexible access to different solvers and a general modeling framework for linear and nonlinear integer programs.\n",
    "The examples solved here will make use of open-source solver **[GLPK](https://www.gnu.org/software/glpk/)** for mixed-integer linear programming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem statement\n",
    "We pose the Ising problem as the following optimization problem:\n",
    "$$\n",
    "\\min_{\\sigma \\in \\{ -1,+1 \\}^n} H(\\sigma) =\\min_{\\sigma \\in \\{ -1,+1 \\}^n} \\sum_{(ij) \\in E(G)} J_{ij}\\sigma_i\\sigma_j + \\sum_{i \\in V(G)}h_i\\sigma_i + c_I\n",
    "$$\n",
    "where we optimize over spins $\\sigma \\in \\{ -1,+1 \\}^n$, on a constrained graph $G(V,E)$, where the quadratic coefficients are $J_{ij}$ and the linear coefficients are $h_i$. We also include an arbitrary offset of the Ising model $c_I$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "\n",
    "Suppose we have an Ising model defined from\n",
    "\n",
    "$$\n",
    "h = \\begin{bmatrix}\n",
    "145.0 \\\\ 122.0 \\\\ 122.0 \\\\ 266.0 \\\\ 266.0 \\\\ 266.0 \\\\ 242.5 \\\\ 266.0 \\\\ 386.5 \\\\ 387.0 \\\\ 386.5\n",
    "\\end{bmatrix},\n",
    "J = \\begin{bmatrix}\n",
    "0 & 0 & 0 & 24 & 24 & 24 & 24 & 24 & 24 & 24 & 24\\\\\n",
    "0 & 0 & 0 & 24 & 0 & 24 & 24 & 24 & 24 & 24 & 24\\\\\n",
    "0 & 0 & 0 & 0 & 24 & 0 & 24 & 24 & 24 & 24 & 24\\\\\n",
    "0 & 0 & 0 & 0 & 24 & 48 & 24 & 24 & 48 & 48 & 48\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 24 & 24 & 48 & 48 & 48 & 48\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 24 & 24 & 48 & 48 & 48\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 24 & 48 & 48 & 48\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 48 & 48 & 48\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 72 & 72\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 72\\\\\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n",
    "\\end{bmatrix} \\text{ and }\n",
    "\\beta = 1319.5\n",
    "$$\n",
    "Let's solve this problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# These could also be simple lists and numpy matrices\n",
    "h = {0: 145.0, 1: 122.0, 2: 122.0, 3: 266.0, 4: 266.0, 5: 266.0, 6: 242.5, 7: 266.0, 8: 386.5, 9: 387.0, 10: 386.5}\n",
    "J = {(0, 3): 24.0, (0, 4): 24.0, (0, 5): 24.0, (0, 7): 24.0, (0, 8): 24.0, (0, 9): 24.0, (0, 10): 24.0, (1, 3): 24.0, (1, 5): 24.0, (1, 6): 24.0, (1, 8): 24.0, (1, 9): 24.0, (1, 10): 24.0, (2, 4): 24.0, (2, 6): 24.0, (2, 7): 24.0, (2, 8): 24.0, (2, 9): 24.0, (2, 10): 24.0, (3, 4): 24.0, (3, 5): 48.0, (3, 6): 24.0, (3, 7): 24.0, (3, 8): 48.0, (3, 9): 48.0, (3, 10): 48.0, (4, 5): 24.0, (4, 6): 24.0, (4, 7): 48.0, (4, 8): 48.0, (4, 9): 48.0, (4, 10): 48.0, (5, 6): 24.0, (5, 7): 24.0, (5, 8): 48.0, (5, 9): 48.0, (5, 10): 48.0, (6, 7): 24.0, (6, 8): 48.0, (6, 9): 48.0, (6, 10): 48.0, (7, 8): 48.0, (7, 9): 48.0, (7, 10): 48.0, (8, 9): 72.0, (8, 10): 72.0, (9, 10): 72.0}\n",
    "cI = 1319.5\n",
    "\n",
    "model_ising = dimod.BinaryQuadraticModel.from_ising(h, J, offset=cI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the problem is relatively small (11 variables, $2^{11}=2048$ combinations), we can afford to enumerate all the solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "exactSamples = exactSampler.sample(model_ising)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 5.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 5.0\n"
     ]
    }
   ],
   "source": [
    "plot_enumerate(exactSamples, title='Enumerate all solutions')\n",
    "plot_energies(exactSamples, title='Enumerate all solutions')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now solve this Ising Model via traditional Integer Programming."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 'Ising example as an IP, 47-779/785 QuIPML'\n",
      "\n",
      "  Variables:\n",
      "    x : Size=11, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :  None :     1 : False :  True : Binary\n",
      "          1 :     0 :  None :     1 : False :  True : Binary\n",
      "          2 :     0 :  None :     1 : False :  True : Binary\n",
      "          3 :     0 :  None :     1 : False :  True : Binary\n",
      "          4 :     0 :  None :     1 : False :  True : Binary\n",
      "          5 :     0 :  None :     1 : False :  True : Binary\n",
      "          6 :     0 :  None :     1 : False :  True : Binary\n",
      "          7 :     0 :  None :     1 : False :  True : Binary\n",
      "          8 :     0 :  None :     1 : False :  True : Binary\n",
      "          9 :     0 :  None :     1 : False :  True : Binary\n",
      "         10 :     0 :  None :     1 : False :  True : Binary\n",
      "    y : Size=121, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}*{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key      : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (0, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (1, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (2, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (3, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (4, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (5, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (6, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (7, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (8, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (9, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "        (10, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "  Objectives:\n",
      "    objective : Size=1, Index=None, Active=True\n",
      "ERROR: evaluating object as numeric value: y[3,0]\n",
      "        (object: <class 'pyomo.core.base.var.VarData'>)\n",
      "    No value for uninitialized NumericValue object y[3,0]\n",
      "ERROR: evaluating object as numeric value: objective\n",
      "        (object: <class 'pyomo.core.base.objective.ScalarObjective'>)\n",
      "    No value for uninitialized NumericValue object y[3,0]\n",
      "        Key : Active : Value\n",
      "        None :   None :  None\n",
      "\n",
      "  Constraints:\n",
      "    c1 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : None :   0.0\n",
      "          2 :  None : None :   0.0\n",
      "          3 :  None : None :   0.0\n",
      "          4 :  None : None :   0.0\n",
      "          5 :  None : None :   0.0\n",
      "          6 :  None : None :   0.0\n",
      "          7 :  None : None :   0.0\n",
      "          8 :  None : None :   0.0\n",
      "          9 :  None : None :   0.0\n",
      "         10 :  None : None :   0.0\n",
      "         11 :  None : None :   0.0\n",
      "         12 :  None : None :   0.0\n",
      "         13 :  None : None :   0.0\n",
      "         14 :  None : None :   0.0\n",
      "         15 :  None : None :   0.0\n",
      "         16 :  None : None :   0.0\n",
      "         17 :  None : None :   0.0\n",
      "         18 :  None : None :   0.0\n",
      "         19 :  None : None :   0.0\n",
      "         20 :  None : None :   0.0\n",
      "         21 :  None : None :   0.0\n",
      "         22 :  None : None :   0.0\n",
      "         23 :  None : None :   0.0\n",
      "         24 :  None : None :   0.0\n",
      "         25 :  None : None :   0.0\n",
      "         26 :  None : None :   0.0\n",
      "         27 :  None : None :   0.0\n",
      "         28 :  None : None :   0.0\n",
      "         29 :  None : None :   0.0\n",
      "         30 :  None : None :   0.0\n",
      "         31 :  None : None :   0.0\n",
      "         32 :  None : None :   0.0\n",
      "         33 :  None : None :   0.0\n",
      "         34 :  None : None :   0.0\n",
      "         35 :  None : None :   0.0\n",
      "         36 :  None : None :   0.0\n",
      "         37 :  None : None :   0.0\n",
      "         38 :  None : None :   0.0\n",
      "         39 :  None : None :   0.0\n",
      "         40 :  None : None :   0.0\n",
      "         41 :  None : None :   0.0\n",
      "         42 :  None : None :   0.0\n",
      "         43 :  None : None :   0.0\n",
      "         44 :  None : None :   0.0\n",
      "         45 :  None : None :   0.0\n",
      "         46 :  None : None :   0.0\n",
      "         47 :  None : None :   0.0\n",
      "    c2 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : None :   0.0\n",
      "          2 :  None : None :   0.0\n",
      "          3 :  None : None :   0.0\n",
      "          4 :  None : None :   0.0\n",
      "          5 :  None : None :   0.0\n",
      "          6 :  None : None :   0.0\n",
      "          7 :  None : None :   0.0\n",
      "          8 :  None : None :   0.0\n",
      "          9 :  None : None :   0.0\n",
      "         10 :  None : None :   0.0\n",
      "         11 :  None : None :   0.0\n",
      "         12 :  None : None :   0.0\n",
      "         13 :  None : None :   0.0\n",
      "         14 :  None : None :   0.0\n",
      "         15 :  None : None :   0.0\n",
      "         16 :  None : None :   0.0\n",
      "         17 :  None : None :   0.0\n",
      "         18 :  None : None :   0.0\n",
      "         19 :  None : None :   0.0\n",
      "         20 :  None : None :   0.0\n",
      "         21 :  None : None :   0.0\n",
      "         22 :  None : None :   0.0\n",
      "         23 :  None : None :   0.0\n",
      "         24 :  None : None :   0.0\n",
      "         25 :  None : None :   0.0\n",
      "         26 :  None : None :   0.0\n",
      "         27 :  None : None :   0.0\n",
      "         28 :  None : None :   0.0\n",
      "         29 :  None : None :   0.0\n",
      "         30 :  None : None :   0.0\n",
      "         31 :  None : None :   0.0\n",
      "         32 :  None : None :   0.0\n",
      "         33 :  None : None :   0.0\n",
      "         34 :  None : None :   0.0\n",
      "         35 :  None : None :   0.0\n",
      "         36 :  None : None :   0.0\n",
      "         37 :  None : None :   0.0\n",
      "         38 :  None : None :   0.0\n",
      "         39 :  None : None :   0.0\n",
      "         40 :  None : None :   0.0\n",
      "         41 :  None : None :   0.0\n",
      "         42 :  None : None :   0.0\n",
      "         43 :  None : None :   0.0\n",
      "         44 :  None : None :   0.0\n",
      "         45 :  None : None :   0.0\n",
      "         46 :  None : None :   0.0\n",
      "         47 :  None : None :   0.0\n",
      "    c3 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : None :   0.0\n",
      "          2 :  None : None :   0.0\n",
      "          3 :  None : None :   0.0\n",
      "          4 :  None : None :   0.0\n",
      "          5 :  None : None :   0.0\n",
      "          6 :  None : None :   0.0\n",
      "          7 :  None : None :   0.0\n",
      "          8 :  None : None :   0.0\n",
      "          9 :  None : None :   0.0\n",
      "         10 :  None : None :   0.0\n",
      "         11 :  None : None :   0.0\n",
      "         12 :  None : None :   0.0\n",
      "         13 :  None : None :   0.0\n",
      "         14 :  None : None :   0.0\n",
      "         15 :  None : None :   0.0\n",
      "         16 :  None : None :   0.0\n",
      "         17 :  None : None :   0.0\n",
      "         18 :  None : None :   0.0\n",
      "         19 :  None : None :   0.0\n",
      "         20 :  None : None :   0.0\n",
      "         21 :  None : None :   0.0\n",
      "         22 :  None : None :   0.0\n",
      "         23 :  None : None :   0.0\n",
      "         24 :  None : None :   0.0\n",
      "         25 :  None : None :   0.0\n",
      "         26 :  None : None :   0.0\n",
      "         27 :  None : None :   0.0\n",
      "         28 :  None : None :   0.0\n",
      "         29 :  None : None :   0.0\n",
      "         30 :  None : None :   0.0\n",
      "         31 :  None : None :   0.0\n",
      "         32 :  None : None :   0.0\n",
      "         33 :  None : None :   0.0\n",
      "         34 :  None : None :   0.0\n",
      "         35 :  None : None :   0.0\n",
      "         36 :  None : None :   0.0\n",
      "         37 :  None : None :   0.0\n",
      "         38 :  None : None :   0.0\n",
      "         39 :  None : None :   0.0\n",
      "         40 :  None : None :   0.0\n",
      "         41 :  None : None :   0.0\n",
      "         42 :  None : None :   0.0\n",
      "         43 :  None : None :   0.0\n",
      "         44 :  None : None :   0.0\n",
      "         45 :  None : None :   0.0\n",
      "         46 :  None : None :   0.0\n",
      "         47 :  None : None :   0.0\n"
     ]
    }
   ],
   "source": [
    "# We do not need to worry about the tranformation from Ising to QUBO since dimod takes care of it\n",
    "Q, c = model_ising.to_qubo()\n",
    "\n",
    "# Define the model\n",
    "model_ising_pyo = pyo.ConcreteModel(name='Ising example as an IP, 47-779/785 QuIPML')\n",
    "\n",
    "I = range(len(h))\n",
    "J = range(len(h))\n",
    "#Define the original variables\n",
    "model_ising_pyo.x = pyo.Var(I, domain=pyo.Binary)\n",
    "# Define the edges variables\n",
    "model_ising_pyo.y = pyo.Var(I, J, domain=pyo.Binary)\n",
    "\n",
    "obj_expr = c\n",
    "\n",
    "# add model constraints\n",
    "model_ising_pyo.c1 = pyo.ConstraintList()\n",
    "model_ising_pyo.c2 = pyo.ConstraintList()\n",
    "model_ising_pyo.c3 = pyo.ConstraintList()\n",
    "for (i,j) in Q.keys():\n",
    "    if i != j:\n",
    "        model_ising_pyo.c1.add(model_ising_pyo.y[i,j] >= model_ising_pyo.x[i] + model_ising_pyo.x[j] - 1)\n",
    "        model_ising_pyo.c2.add(model_ising_pyo.y[i,j] <= model_ising_pyo.x[i])\n",
    "        model_ising_pyo.c3.add(model_ising_pyo.y[i,j] <= model_ising_pyo.x[j])\n",
    "        obj_expr += Q[i,j]*model_ising_pyo.y[i,j]\n",
    "    else:\n",
    "        obj_expr += Q[i,j]*model_ising_pyo.x[i]\n",
    "\n",
    "# Define the objective function\n",
    "model_ising_pyo.objective = pyo.Objective(expr = obj_expr, sense=pyo.minimize)\n",
    "# Print the model\n",
    "model_ising_pyo.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 'Ising example as an IP, 47-779/785 QuIPML'\n",
      "\n",
      "  Variables:\n",
      "    x : Size=11, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          0 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          1 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          2 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          3 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          4 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          5 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          6 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          7 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          8 :     0 :   0.0 :     1 : False : False : Binary\n",
      "          9 :     0 :   0.0 :     1 : False : False : Binary\n",
      "         10 :     0 :   1.0 :     1 : False : False : Binary\n",
      "    y : Size=121, Index={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}*{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n",
      "        Key      : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "          (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (0, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (0, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (1, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (1, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (1, 9) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (1, 10) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (2, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (2, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (2, 6) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (2, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (2, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (2, 9) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (2, 10) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (3, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (3, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (3, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (3, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (4, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (4, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (4, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (4, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (5, 5) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (5, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (5, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 1) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (6, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (6, 9) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (6, 10) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (7, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 7) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (7, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (7, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (8, 8) :     0 :  None :     1 : False :  True : Binary\n",
      "          (8, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (8, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "          (9, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "          (9, 9) :     0 :  None :     1 : False :  True : Binary\n",
      "         (9, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 0) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 3) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 4) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 5) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 6) :     0 :  None :     1 : False :  True : Binary\n",
      "         (10, 7) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 8) :     0 :   0.0 :     1 : False : False : Binary\n",
      "         (10, 9) :     0 :   0.0 :     1 : False : False : Binary\n",
      "        (10, 10) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "  Objectives:\n",
      "    objective : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Value\n",
      "        None :   True :   5.0\n",
      "\n",
      "  Constraints:\n",
      "    c1 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None : -1.0 :   0.0\n",
      "          2 :  None : -1.0 :   0.0\n",
      "          3 :  None : -1.0 :   0.0\n",
      "          4 :  None : -1.0 :   0.0\n",
      "          5 :  None : -1.0 :   0.0\n",
      "          6 :  None : -1.0 :   0.0\n",
      "          7 :  None : -1.0 :   0.0\n",
      "          8 :  None : -1.0 :   0.0\n",
      "          9 :  None : -1.0 :   0.0\n",
      "         10 :  None : -1.0 :   0.0\n",
      "         11 :  None : -1.0 :   0.0\n",
      "         12 :  None : -1.0 :   0.0\n",
      "         13 :  None : -1.0 :   0.0\n",
      "         14 :  None : -1.0 :   0.0\n",
      "         15 :  None : -1.0 :   0.0\n",
      "         16 :  None : -1.0 :   0.0\n",
      "         17 :  None : -1.0 :   0.0\n",
      "         18 :  None : -1.0 :   0.0\n",
      "         19 :  None : -1.0 :   0.0\n",
      "         20 :  None : -1.0 :   0.0\n",
      "         21 :  None : -1.0 :   0.0\n",
      "         22 :  None :  0.0 :   0.0\n",
      "         23 :  None :  0.0 :   0.0\n",
      "         24 :  None :  0.0 :   0.0\n",
      "         25 :  None :  0.0 :   0.0\n",
      "         26 :  None :  0.0 :   0.0\n",
      "         27 :  None :  0.0 :   0.0\n",
      "         28 :  None :  0.0 :   0.0\n",
      "         29 :  None : -1.0 :   0.0\n",
      "         30 :  None : -1.0 :   0.0\n",
      "         31 :  None : -1.0 :   0.0\n",
      "         32 :  None : -1.0 :   0.0\n",
      "         33 :  None :  0.0 :   0.0\n",
      "         34 :  None : -1.0 :   0.0\n",
      "         35 :  None : -1.0 :   0.0\n",
      "         36 :  None : -1.0 :   0.0\n",
      "         37 :  None : -1.0 :   0.0\n",
      "         38 :  None : -1.0 :   0.0\n",
      "         39 :  None : -1.0 :   0.0\n",
      "         40 :  None :  0.0 :   0.0\n",
      "         41 :  None : -1.0 :   0.0\n",
      "         42 :  None : -1.0 :   0.0\n",
      "         43 :  None : -1.0 :   0.0\n",
      "         44 :  None : -1.0 :   0.0\n",
      "         45 :  None : -1.0 :   0.0\n",
      "         46 :  None :  0.0 :   0.0\n",
      "         47 :  None : -1.0 :   0.0\n",
      "    c2 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None :  0.0 :   0.0\n",
      "          2 :  None :  0.0 :   0.0\n",
      "          3 :  None :  0.0 :   0.0\n",
      "          4 :  None :  0.0 :   0.0\n",
      "          5 :  None :  0.0 :   0.0\n",
      "          6 :  None :  0.0 :   0.0\n",
      "          7 :  None :  0.0 :   0.0\n",
      "          8 :  None :  0.0 :   0.0\n",
      "          9 :  None :  0.0 :   0.0\n",
      "         10 :  None :  0.0 :   0.0\n",
      "         11 :  None :  0.0 :   0.0\n",
      "         12 :  None :  0.0 :   0.0\n",
      "         13 :  None :  0.0 :   0.0\n",
      "         14 :  None :  0.0 :   0.0\n",
      "         15 :  None :  0.0 :   0.0\n",
      "         16 :  None :  0.0 :   0.0\n",
      "         17 :  None :  0.0 :   0.0\n",
      "         18 :  None :  0.0 :   0.0\n",
      "         19 :  None :  0.0 :   0.0\n",
      "         20 :  None :  0.0 :   0.0\n",
      "         21 :  None :  0.0 :   0.0\n",
      "         22 :  None : -1.0 :   0.0\n",
      "         23 :  None : -1.0 :   0.0\n",
      "         24 :  None : -1.0 :   0.0\n",
      "         25 :  None : -1.0 :   0.0\n",
      "         26 :  None : -1.0 :   0.0\n",
      "         27 :  None : -1.0 :   0.0\n",
      "         28 :  None : -1.0 :   0.0\n",
      "         29 :  None :  0.0 :   0.0\n",
      "         30 :  None :  0.0 :   0.0\n",
      "         31 :  None :  0.0 :   0.0\n",
      "         32 :  None :  0.0 :   0.0\n",
      "         33 :  None :  0.0 :   0.0\n",
      "         34 :  None :  0.0 :   0.0\n",
      "         35 :  None :  0.0 :   0.0\n",
      "         36 :  None :  0.0 :   0.0\n",
      "         37 :  None :  0.0 :   0.0\n",
      "         38 :  None :  0.0 :   0.0\n",
      "         39 :  None :  0.0 :   0.0\n",
      "         40 :  None :  0.0 :   0.0\n",
      "         41 :  None :  0.0 :   0.0\n",
      "         42 :  None :  0.0 :   0.0\n",
      "         43 :  None :  0.0 :   0.0\n",
      "         44 :  None :  0.0 :   0.0\n",
      "         45 :  None :  0.0 :   0.0\n",
      "         46 :  None :  0.0 :   0.0\n",
      "         47 :  None :  0.0 :   0.0\n",
      "    c3 : Size=47\n",
      "        Key : Lower : Body : Upper\n",
      "          1 :  None :  0.0 :   0.0\n",
      "          2 :  None :  0.0 :   0.0\n",
      "          3 :  None :  0.0 :   0.0\n",
      "          4 :  None :  0.0 :   0.0\n",
      "          5 :  None :  0.0 :   0.0\n",
      "          6 :  None :  0.0 :   0.0\n",
      "          7 :  None :  0.0 :   0.0\n",
      "          8 :  None :  0.0 :   0.0\n",
      "          9 :  None :  0.0 :   0.0\n",
      "         10 :  None :  0.0 :   0.0\n",
      "         11 :  None :  0.0 :   0.0\n",
      "         12 :  None :  0.0 :   0.0\n",
      "         13 :  None :  0.0 :   0.0\n",
      "         14 :  None :  0.0 :   0.0\n",
      "         15 :  None :  0.0 :   0.0\n",
      "         16 :  None :  0.0 :   0.0\n",
      "         17 :  None :  0.0 :   0.0\n",
      "         18 :  None :  0.0 :   0.0\n",
      "         19 :  None :  0.0 :   0.0\n",
      "         20 :  None :  0.0 :   0.0\n",
      "         21 :  None :  0.0 :   0.0\n",
      "         22 :  None :  0.0 :   0.0\n",
      "         23 :  None :  0.0 :   0.0\n",
      "         24 :  None :  0.0 :   0.0\n",
      "         25 :  None :  0.0 :   0.0\n",
      "         26 :  None :  0.0 :   0.0\n",
      "         27 :  None :  0.0 :   0.0\n",
      "         28 :  None :  0.0 :   0.0\n",
      "         29 :  None :  0.0 :   0.0\n",
      "         30 :  None :  0.0 :   0.0\n",
      "         31 :  None :  0.0 :   0.0\n",
      "         32 :  None :  0.0 :   0.0\n",
      "         33 :  None : -1.0 :   0.0\n",
      "         34 :  None :  0.0 :   0.0\n",
      "         35 :  None :  0.0 :   0.0\n",
      "         36 :  None :  0.0 :   0.0\n",
      "         37 :  None :  0.0 :   0.0\n",
      "         38 :  None :  0.0 :   0.0\n",
      "         39 :  None :  0.0 :   0.0\n",
      "         40 :  None : -1.0 :   0.0\n",
      "         41 :  None :  0.0 :   0.0\n",
      "         42 :  None :  0.0 :   0.0\n",
      "         43 :  None :  0.0 :   0.0\n",
      "         44 :  None :  0.0 :   0.0\n",
      "         45 :  None :  0.0 :   0.0\n",
      "         46 :  None : -1.0 :   0.0\n",
      "         47 :  None :  0.0 :   0.0\n"
     ]
    }
   ],
   "source": [
    "# We obtain the solution with GLPK\n",
    "result_obj = opt_glpk.solve(model_ising_pyo, tee=False)\n",
    "model_ising_pyo.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that the optimal solution of this problem is $x_{10} = 1, 0$ otherwise, leading to an objective of $5$. Notice that this problem has a degenerate optimal solution given that $x_8 = 1, 0$ otherwise also leads to the same solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also solve this problem using Simulated Annealing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "simAnnSampler = neal.SimulatedAnnealingSampler()\n",
    "simAnnSamples = simAnnSampler.sample(model_ising, num_reads=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 5.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 5.0\n"
     ]
    }
   ],
   "source": [
    "plot_enumerate(simAnnSamples, title='Simulated annealing in default parameters')\n",
    "plot_energies(simAnnSamples, title='Simulated annealing in default parameters')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'beta_range': [np.float64(0.00041111932417553103),\n",
       "  np.float64(0.1458971970580513)],\n",
       " 'beta_schedule_type': 'geometric',\n",
       " 'timing': {'preprocessing_ns': 2912880,\n",
       "  'sampling_ns': 289277811,\n",
       "  'postprocessing_ns': 292034}}"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simAnnSamples.info"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's solve the graph coloring problem using QUBO.\n",
    "\n",
    "#### Vertex $k$-coloring of graphs\n",
    "\n",
    "Given a graph $G(V, E)$, where $V$ is the set of vertices and $E$ is the set of edges of $G$, and a positive integer $k$, we ask if it is possible to assign a color to every vertex from $V$, such that adjacent vertices have different colors assigned.\n",
    "\n",
    "$G(V, E)$ has $12$ vertices and $23$ edges.\n",
    "We ask if the graph is $3$–colorable.\n",
    "Let’s first encode $V$ and $E$ using Julia’s built–in data structures:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** This tutorial is heavily inspired in D-Wave's Map coloring of Canada found **[here](https://docs.ocean.dwavesys.com/en/stable/examples/map_coloring.html)**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's install with dimod and neal\n",
    "if IN_COLAB:\n",
    "    !pip install dwavebinarycsp\n",
    "    !pip install dwavebinarycsp[maxgap]\n",
    "    !pip install dwavebinarycsp[mip]\n",
    "\n",
    "import dwavebinarycsp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V = range(1, 12+1)\n",
    "E = [(1,2),(2,3),(1,4),(1,6),(1,12),(2,5),(2,7),(3,8),(3,10),(4,11),(4,9),(5,6),(6,7),(7,8),(8,9),(9,10),(10,11),(11,12),(5,12),(5,9),(6,10),(7,11),(8,12)]\n",
    "layout = {i: [np.cos((2*i+1)*np.pi/8),np.sin((2*i+1)*np.pi/8)] for i in np.arange(5,13)}\n",
    "layout[1] = [-1.5,1.5]\n",
    "layout[2] = [1.5,1.5]\n",
    "layout[3] = [1.5,-1.5]\n",
    "layout[4] = [-1.5,-1.5]\n",
    "G = nx.Graph()\n",
    "G.add_edges_from(E)\n",
    "nx.draw(G, with_labels=True, pos=layout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function for the constraint that two nodes with a shared edge not both select\n",
    "# one color\n",
    "def not_both_1(v, u):\n",
    "    return not (v and u)\n",
    "\n",
    "# Valid configurations for the constraint that each node select a single color, in this case we want to use 3 colors\n",
    "one_color_configurations = {(0, 0, 1), (0, 1, 0), (1, 0, 0)}\n",
    "colors = len(one_color_configurations)\n",
    "\n",
    "# Create a binary constraint satisfaction problem\n",
    "csp = dwavebinarycsp.ConstraintSatisfactionProblem(dwavebinarycsp.BINARY)\n",
    "\n",
    "# Add constraint that each node select a single color\n",
    "for node in V:\n",
    "    variables = ['x'+str(node)+','+str(i) for i in range(colors)]\n",
    "    csp.add_constraint(one_color_configurations, variables)\n",
    "\n",
    "# Add constraint that each pair of nodes with a shared edge not both select one color\n",
    "for edge in E:\n",
    "    v, u = edge\n",
    "    for i in range(colors):\n",
    "        variables = ['x'+str(v)+','+str(i), 'x'+str(u)+','+str(i)]\n",
    "        csp.add_constraint(not_both_1, variables)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining the Binary Quandratic model (QUBO) using the CSP library we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "bqm = dwavebinarycsp.stitch(csp)\n",
    "simAnnSamples = simAnnSampler.sample(bqm, num_reads=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum energy: 0.0\n"
     ]
    }
   ],
   "source": [
    "plot_enumerate(simAnnSamples, title='Simulated annealing in default parameters')\n",
    "plot_energies(simAnnSamples, title='Simulated annealing in default parameters')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of precision issues in the translation to BQM, we *may* obtain very tiny coefficeints that should be zero. In any case, since this is a constraint satisfaction problem, any of the solutions with energy ~0 is a valid coloring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'x1,0': np.int8(1), 'x1,1': np.int8(0), 'x1,2': np.int8(0), 'x10,0': np.int8(1), 'x10,1': np.int8(0), 'x10,2': np.int8(0), 'x11,0': np.int8(0), 'x11,1': np.int8(1), 'x11,2': np.int8(0), 'x12,0': np.int8(0), 'x12,1': np.int8(0), 'x12,2': np.int8(1), 'x2,0': np.int8(0), 'x2,1': np.int8(1), 'x2,2': np.int8(0), 'x3,0': np.int8(0), 'x3,1': np.int8(0), 'x3,2': np.int8(1), 'x4,0': np.int8(0), 'x4,1': np.int8(0), 'x4,2': np.int8(1), 'x5,0': np.int8(1), 'x5,1': np.int8(0), 'x5,2': np.int8(0), 'x6,0': np.int8(0), 'x6,1': np.int8(1), 'x6,2': np.int8(0), 'x7,0': np.int8(0), 'x7,1': np.int8(0), 'x7,2': np.int8(1), 'x8,0': np.int8(1), 'x8,1': np.int8(0), 'x8,2': np.int8(0), 'x9,0': np.int8(0), 'x9,1': np.int8(1), 'x9,2': np.int8(0)}\n"
     ]
    }
   ],
   "source": [
    "# Check that a good solution was found\n",
    "sample = simAnnSamples.first.sample     # doctest: +SKIP\n",
    "if not csp.check(sample):           # doctest: +SKIP\n",
    "        print(\"Failed to color map. Try sampling again.\")\n",
    "else:\n",
    "        print(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function that plots a returned sample\n",
    "def plot_map(sample):\n",
    "    # Translate from binary to integer color representation\n",
    "    color_map = {}\n",
    "    for node in V:\n",
    "          for i in range(colors):\n",
    "            if sample['x'+str(node)+','+str(i)]:\n",
    "                color_map[node] = i\n",
    "    # Plot the sample with color-coded nodes\n",
    "    node_colors = [color_map.get(node) for node in G.nodes()]\n",
    "    nx.draw(G, with_labels=True, pos=layout, node_color=node_colors)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_map(sample)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}