BILP_Q_Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tCd1bMQaI2h8"
   },
   "source": [
    "## This notebook demonstrates the pipeline of solving the CSG problem using BILP-Q."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6aW6kIG6bV1D"
   },
   "source": [
    "**Note:** Make sure the scripts *Utils_Solvers.py* and *Utils_CSG.py* in the root directory of the repository is in the same location of this notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jNYLLUbWIk2p"
   },
   "source": [
    "#### Install and  Import Dependencies\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "24oELRTUYFyQ"
   },
   "outputs": [],
   "source": [
    "!pip install qiskit\n",
    "!pip install qiskit_optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZOHHJV_JmZEa"
   },
   "source": [
    "##### Important: Restart the runtime after installing *pylatexenc*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ChsByqlBahwR"
   },
   "outputs": [],
   "source": [
    "!pip install pylatexenc                             # for fetching the diagram of the Quantum circuit used to solve\n",
    "\n",
    "# Important: Restart the runtime after installing 'pylatexenc'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "GnSpknmjZLuA"
   },
   "outputs": [],
   "source": [
    "!pip install dimod                                   #for runninng Quantum Aneealing approach to solve the CSG problem, you need a D-Wave account\n",
    "!pip install dwave                                   #for runninng Quantum Aneealing approach to solve the CSG problem, you need a D-Wave account\n",
    "!pip install dwave-system                            #for runninng Quantum Aneealing approach to solve the CSG problem, you need a D-Wave account"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "fsE2jTvQIkBC"
   },
   "outputs": [],
   "source": [
    "from Utils_Solvers import *\n",
    "from Utils_CSG import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "v016HVvLFPCH"
   },
   "source": [
    "## Coalition Structure Generation(CSG) Problem Instance\n",
    "\n",
    "Consider a game consisiting of 3 agents. The value corresponding to each of the 7 possible coalitions are given as a dictionary where the key represents the coalition and the value the correspondent coalition value.\n",
    "\n",
    "The distribution of the following coalition values are taken from  *Rahwan, Talal, et al. \"Coalition structure generation: A survey.\" Artificial Intelligence 229 (2015): 139-174.*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "xhJQBqdPFLed",
    "outputId": "4afd2247-d246-435f-e451-bd110d32db83"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1': 30, '2': 40, '3': 25, '1,2': 70, '1,3': 60, '2,3': 65, '1,2,3': 90}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coalition_values={\n",
    "    '1':30,\n",
    "    '2':40,\n",
    "    '3':25,\n",
    "    '1,2':70,\n",
    "    '1,3':60,\n",
    "    '2,3':65,\n",
    "    '1,2,3':90\n",
    "}\n",
    "coalition_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually the CSGP solution are benchmarked using different probability distribution for coalition values. The code to generate several possible distributions for the coalition values is reported below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# distributions = [Agent_based_uniform, Agent_based_normal, Modified_uniform_distribution,\n",
    "#                  Normal_distribution, Weibull_distribution, Weighted_random_with_chisquare]\n",
    "# n_agents = [2,3]\n",
    "\n",
    "# n=3\n",
    "# penalty = 50\n",
    "# distribution = Agent_based_uniform\n",
    "\n",
    "# np.random.seed(seed=12)\n",
    "# coalition_values, linear, quadratic = get_linear_quads(distribution, n, penalty)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3c-CTot4Jp6Q"
   },
   "source": [
    "## Reduce the CSG problem to a Binary Integer Linaer Programming(BILP) Problem\n",
    "\n",
    "The BILP problem is described as a cost vector $\\boldsymbol{C}$, a binary vector $\\boldsymbol{b}$ and a $(n \\times (2^n-1))$ binary matrix $\\boldsymbol{S}$, with  ~$n$~ agents ~$A=\\{a_1,a_2,....a_n\\}$~ as rows and ~$\\mathcal{P}(A)$~ coalitions as columns (null set excluded).\n",
    "$S_{i,j}$ is $1$ if $a_i \\in C_j$. The solution $x=\\{x_1,x_2,..,x_{2^n-1}\\}$ is a $(2^n-1)$ binary string,  which represents a $1$ if a coalition is selected in the solution.\\\n",
    "\\\n",
    "The Binary Integer Linear Programming problem is a constraint optimization problem.\n",
    "The cost function to maximize and the constraint to be satisfied can be defined using the following formulae:\n",
    "\\begin{equation}\n",
    " \\text{Maximize}\\ \\sum_{j=1}^{2^n-1} v(C_j).x_j\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\text{subject to}\\ \\sum_{j=1}^{2^n-1} S_{i,j}.x_j=1\\ \\text{for}\\ i=1,2,....,n\\\\\n",
    "x_j \\in \\{0,1\\}\\ \\ \\text{for}\\ j=1,2,.....,(2^n-1)\n",
    "\\end{split}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "PtKcdUAAJqYS",
    "outputId": "6c6c4e31-8e6f-4353-ecd9-5100aae420db"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c = [30, 40, 25, 70, 60, 65, 90]\n",
      "S = [[1, 0, 0, 1, 1, 0, 1], [0, 1, 0, 1, 0, 1, 1], [0, 0, 1, 0, 1, 1, 1]]\n",
      "b = [1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "c,S,b = convert_to_BILP(coalition_values)       # A function in Utils_CSG.py\n",
    "print(f'c = {c}\\nS = {S}\\nb = {b}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dNuqB-OxLuDW"
   },
   "source": [
    "## Convert the BILP problem to a Quadratic Unconsrained Binary Optimization(QUBO) problem.\n",
    "\n",
    "QUBO model is expressed as following\n",
    "$$\n",
    "\\begin{split}\n",
    "    QUBO: min/max\\ f(\\boldsymbol{x}) = \\boldsymbol{x}^T \\boldsymbol{Q} \\boldsymbol{x}\\\\\n",
    "    \\boldsymbol{x} \\in \\mathbb{R}^{n \\times 1}\\ and\\ \\boldsymbol{Q} \\in \\mathbb{R}^{n \\times n}\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "where x is again the vector of binary decision variables and $\\boldsymbol{Q}$ is a square matrix of constants. We can assume that $\\boldsymbol{Q}$ is symmetric or upper-triangular matrix, with out any loss of generality.\n",
    "\n",
    "Symmetric: for all $i,j \\in \\{1,2,...,n\\}$, except $i=j$ replace $q_{ij}$ with $\\frac{(q_{ij}+q_{ji})}{2}$\n",
    "\n",
    "Upper-Triangular matrix: for all $i,j \\in \\{1,2,...,n\\}$, when $j > i$ replace $q_{ij}$ with $q_{ij}+q_{ji}$ and when $j<i$ replace $q_{ij}$ with $0$.\n",
    "\n",
    "\n",
    "The CSG problem is a maximization problem. \n",
    "The converted BILP to QUBO will be a minimization problem.\n",
    "The constraints in the BILP formulation of the CSG problem will be subtracted from the cost function with penalty coefficients. These penalty coefficients are vital and has to be of high magnitude as the size of the problem increases.\n",
    "\n",
    "Specific to this tutorial, the chosen penalty coefficient is $50$, which allows to retrieve the right solution of the QUBO problem. The value $50$ is then multiplied by $-1$ and added to the cost function (for more details see the paper).\n",
    "\n",
    "The below function generates the linear and quadratic coefficients as dictionaries which constitute the $\\boldsymbol{Q}$ matrix of the QUBO problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Woaj1fF5PU6q",
    "outputId": "47b9e58f-4e7a-4f06-ed5d-7d5b170a8b81"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear Coefficients = {'x_6': -240.0, 'x_3': -170.0, 'x_4': -160.0, 'x_5': -165.0, 'x_0': -80.0, 'x_1': -90.0, 'x_2': -75.0} \n",
      " Quadratic Coefficients = {('x_3', 'x_6'): 200.0, ('x_4', 'x_6'): 200.0, ('x_5', 'x_6'): 200.0, ('x_0', 'x_3'): 100.0, ('x_0', 'x_4'): 100.0, ('x_0', 'x_6'): 100.0, ('x_1', 'x_3'): 100.0, ('x_1', 'x_5'): 100.0, ('x_1', 'x_6'): 100.0, ('x_2', 'x_4'): 100.0, ('x_2', 'x_5'): 100.0, ('x_2', 'x_6'): 100.0, ('x_3', 'x_4'): 100.0, ('x_3', 'x_5'): 100.0, ('x_4', 'x_5'): 100.0}\n"
     ]
    }
   ],
   "source": [
    "qubo_penalty = 50 * -1\n",
    "\n",
    "linear,quadratic = get_QUBO_coeffs(c,S,b,qubo_penalty)        # A function in Utils_CSG.py\n",
    "\n",
    "print(f\"Linear Coefficients = {linear} \\n Quadratic Coefficients = {quadratic}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "N94SP5TYUywg"
   },
   "source": [
    "### Explicit display of **Q** matrix of the QUBO problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Z2yYiETedJ38",
    "outputId": "f255d16b-38a6-4f9f-86a5-09028eafe13e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -80.,    0.,    0.,   50.,   50.,    0.,   50.],\n",
       "       [   0.,  -90.,    0.,   50.,    0.,   50.,   50.],\n",
       "       [   0.,    0.,  -75.,    0.,   50.,   50.,   50.],\n",
       "       [  50.,   50.,    0., -170.,   50.,   50.,  100.],\n",
       "       [  50.,    0.,   50.,   50., -160.,   50.,  100.],\n",
       "       [   0.,   50.,   50.,   50.,   50., -165.,  100.],\n",
       "       [  50.,   50.,   50.,  100.,  100.,  100., -240.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q = np.zeros([len(linear),len(linear)])\n",
    "\n",
    "#diagonal elements\n",
    "for key,value in linear.items():\n",
    "    Q[int(key.split('_')[1]),int(key.split('_')[1])] = value\n",
    "\n",
    "#non diagonal elements\n",
    "for key,value in quadratic.items():\n",
    "    Q[int(key[0].split('_')[1]),int(key[1].split('_')[1])] = value/2\n",
    "    Q[int(key[1].split('_')[1]),int(key[0].split('_')[1])] = value/2\n",
    "\n",
    "Q.round(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mW4DfiqgYkpk"
   },
   "source": [
    "## Solving QUBO using QAOA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cellView": "code",
    "id": "crd8vOMjocav"
   },
   "outputs": [],
   "source": [
    "#@title Default title text\n",
    "backend = BasicAer.get_backend('qasm_simulator') \n",
    "optimizer = COBYLA(maxiter=100, rhobeg=2, tol=1.5)\n",
    "qubo = create_QUBO(linear, quadratic)\n",
    "\n",
    "p=1\n",
    "init = [0.,0.]\n",
    "\n",
    "qaoa_mes = QAOA(optimizer=optimizer, reps=p, quantum_instance=backend, initial_point=init)\n",
    "qaoa = MinimumEigenOptimizer(qaoa_mes)  # using QAOA\n",
    "qaoa_result = qaoa.solve(qubo)\n",
    "\n",
    "solution = qaoa_result.x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the quantum circuit of QAOA for solving the CSGP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1591.6x1408.68 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoa_mes.get_optimal_circuit().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IZjP8f4VaTw1"
   },
   "source": [
    "## Decode the solution\n",
    "\n",
    "The solution from the QAOA is an array of binary digiits.\n",
    "The following piece of code converts the solution of QUBO to the solution of the original CSG problem, i.e., the Optimal Coaliton Structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "UHqpaOa3aRZ8",
    "outputId": "39fa0699-19c6-45db-c855-dcfa78959755"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'2'}, {'1', '3'}]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decode(solution, coalition_values) # A function in Utils_CSG.py"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "BILP-Q_Tutorial.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}