notebooks/LP example 1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_feasible_space(x_star, y_star): \n",
    "    \"\"\"\n",
    "    x_star: optimum x\n",
    "    y_star: optimum y\n",
    "    \n",
    "    \"\"\"\n",
    "\n",
    "    # plot the feasible region\n",
    "    d = np.linspace(0,4,300)\n",
    "    x,y = np.meshgrid(d,d)\n",
    "    plt.imshow( ((y>=0) & (-x+2*y<=1) & (-x+y<=0) & (4*x+3*y<=12)).astype(int) , \n",
    "                    extent=(x.min(),x.max(),y.min(),y.max()),origin=\"lower\", cmap=\"Greys\", alpha = 0.3);\n",
    "\n",
    "\n",
    "    # plot the lines defining the constraints\n",
    "    x = np.linspace(0, 4, 2000)\n",
    "    y1 = (x*0)\n",
    "    y2 = 1/2 + x/2\n",
    "    y3 = x\n",
    "    y4 = 4-4/3*x\n",
    "\n",
    "    # Make plot\n",
    "    plt.plot(x, 0*np.ones_like(y1))\n",
    "    plt.plot(x, y2, label=r'$-x_1+2x_2 \\leq 1$')\n",
    "    plt.plot(x, y3, label=r'$-x_1+x_2 \\leq 0$')\n",
    "    plt.plot(x, y4, label=r'$4x_1+3x_2 \\leq 12$')\n",
    "    plt.xlim(0,4)\n",
    "    plt.ylim(0,2)\n",
    "    plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "    plt.xlabel(r'$x_1$')\n",
    "    plt.ylabel(r'$x_2$')\n",
    "    plt.scatter(x_star, y_star, lw=5, c='b')\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyomo.environ import *\n",
    "\n",
    "# Instantiate the problem\n",
    "model = ConcreteModel()\n",
    "\n",
    "# Create the variables\n",
    "model.x = Var([1, 2], domain=NonNegativeReals)\n",
    "\n",
    "# Create the constraints\n",
    "model.Constraint1 = Constraint(expr=-model.x[1] + 2 * model.x[2] <= 1)\n",
    "model.Constraint2 = Constraint(expr=-model.x[1] + model.x[2] <= 0)\n",
    "model.Constraint3 = Constraint(expr=4*model.x[1] + 3 * model.x[2] <= 12)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: Implicitly replacing the Component attribute OBJ (type=<class\n",
      "    'pyomo.core.base.objective.SimpleObjective'>) on block unknown with a new\n",
      "    Component (type=<class 'pyomo.core.base.objective.SimpleObjective'>). This\n",
      "    is usually indicative of a modelling error. To avoid this warning, use\n",
      "    block.del_component() and block.add_component().\n",
      "Objective = 0.90\n",
      "x[1] = 1.00\n",
      "x[2] = 1.00\n"
     ]
    }
   ],
   "source": [
    "# Create the objective\n",
    "model.OBJ = Objective(sense=maximize, expr=-1.1*model.x[1] + 2 * model.x[2]) \n",
    "\n",
    "# Solve the problem\n",
    "opt = SolverFactory('cplex')\n",
    "opt.solve(model)\n",
    "\n",
    "print(\"Objective = %.2f\" % model.OBJ.expr())\n",
    "\n",
    "# Get the solution\n",
    "print(\"x[1] = %.2f\" % model.x[1].value)\n",
    "print(\"x[2] = %.2f\" % model.x[2].value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_feasible_space(model.x[1].value, model.x[2].value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.4 64-bit ('mlec_simulator': virtualenv)",
   "language": "python",
   "name": "python37464bitmlecsimulatorvirtualenv1bfc1c4f9533419585bbf645213764b8"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}