deploy: 7c3d79b

_sources/notebooks/04/graph-coloring.ipynb

@@ -17,7 +17,7 @@
     "```{index} networkx\n",
     "```\n",
     "\n",
-    "# Scheduling as a graph coloring problem"
+    "# Exam room scheduling"
    ]
   },
   {

_sources/notebooks/05/markowitz_portfolio.ipynb

@@ -41,8 +41,7 @@
    },
    "outputs": [],
    "source": [
-    "import sys\n",
-    "import os\n",
+    "import sys, os\n",
     "\n",
     "if 'google.colab' in sys.modules:\n",
     "    !pip install idaes-pse --pre >/dev/null 2>/dev/null\n",
@@ -165,7 +164,7 @@
     }
    ],
    "source": [
-    "# Specify the initial capital, the risk threshold, and the guaranteed return rate. \n",
+    "# Specify the initial capital, the risk threshold, and the guaranteed return rate.\n",
     "C = 1\n",
     "gamma = 1\n",
     "R = 1.01\n",
@@ -179,14 +178,14 @@
     "assert np.all(np.linalg.eigvals(Sigma) >= 0)\n",
     "\n",
     "# If you want to change the covariance matrix Sigma, ensure you input a semi-definite positive one.\n",
-    "# The easiest way to generate a random covariance matrix is first generating a random m x m matrix A \n",
+    "# The easiest way to generate a random covariance matrix is first generating a random m x m matrix A\n",
     "# and then taking the matrix A^T A (which is always semi-definite positive)\n",
     "# m = 3\n",
     "# A = np.random.rand(m, m)\n",
     "# Sigma = A.T @ A\n",
     "\n",
+    "\n",
     "def markowitz(gamma, mu, Sigma):\n",
-    "    \n",
     "    model = pyo.ConcreteModel(\"Markowitz portfolio optimization\")\n",
     "\n",
     "    model.xtilde = pyo.Var(domain=pyo.NonNegativeReals)\n",
@@ -205,13 +204,22 @@
     "        return sum(m.x[i] for i in range(n)) + m.xtilde == C\n",
     "\n",
     "    result = pyo.SolverFactory(SOLVER).solve(model)\n",
-    "    \n",
+    "\n",
     "    return result, model\n",
     "\n",
+    "\n",
     "result, model = markowitz(gamma, mu, Sigma)\n",
     "\n",
-    "display(Markdown(f\"**Solver status:** *{result.solver.status}, {result.solver.termination_condition}*\"))\n",
-    "display(Markdown(f\"**Solution:** $\\\\tilde x = {model.xtilde.value:.3f}$, $x_1 = {model.x[0].value:.3f}$,  $x_2 = {model.x[1].value:.3f}$,  $x_3 = {model.x[2].value:.3f}$\"))\n",
+    "display(\n",
+    "    Markdown(\n",
+    "        f\"**Solver status:** *{result.solver.status}, {result.solver.termination_condition}*\"\n",
+    "    )\n",
+    ")\n",
+    "display(\n",
+    "    Markdown(\n",
+    "        f\"**Solution:** $\\\\tilde x = {model.xtilde.value:.3f}$, $x_1 = {model.x[0].value:.3f}$,  $x_2 = {model.x[1].value:.3f}$,  $x_3 = {model.x[2].value:.3f}$\"\n",
+    "    )\n",
+    ")\n",
     "display(Markdown(f\"**Maximizes objective value to:** ${model.objective():.2f}$\"))"
    ]
   },
@@ -241,17 +249,59 @@
     }
    ],
    "source": [
-    "gamma_values = [0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 4.75, 5, 5.25, 5.5]\n",
+    "gamma_values = [\n",
+    "    0.005,\n",
+    "    0.01,\n",
+    "    0.02,\n",
+    "    0.03,\n",
+    "    0.04,\n",
+    "    0.05,\n",
+    "    0.06,\n",
+    "    0.07,\n",
+    "    0.08,\n",
+    "    0.09,\n",
+    "    0.1,\n",
+    "    0.11,\n",
+    "    0.12,\n",
+    "    0.13,\n",
+    "    0.14,\n",
+    "    0.15,\n",
+    "    0.16,\n",
+    "    0.17,\n",
+    "    0.18,\n",
+    "    0.19,\n",
+    "    0.20,\n",
+    "    0.25,\n",
+    "    0.3,\n",
+    "    0.4,\n",
+    "    0.5,\n",
+    "    0.6,\n",
+    "    0.7,\n",
+    "    0.8,\n",
+    "    0.9,\n",
+    "    1,\n",
+    "    1.5,\n",
+    "    2,\n",
+    "    2.5,\n",
+    "    3,\n",
+    "    3.5,\n",
+    "    4,\n",
+    "    4.5,\n",
+    "    4.75,\n",
+    "    5,\n",
+    "    5.25,\n",
+    "    5.5,\n",
+    "]\n",
     "objective = []\n",
     "\n",
-    "plt.rcParams.update({'font.size': 14})\n",
+    "plt.rcParams.update({\"font.size\": 14})\n",
     "for gamma in gamma_values:\n",
     "    _, model = markowitz(gamma, mu, Sigma)\n",
-    "    objective.append(round(model.objective(),3))\n",
+    "    objective.append(round(model.objective(), 3))\n",
     "\n",
     "plt.plot(gamma_values, objective, color=plt.cm.tab20c(0))\n",
-    "plt.xlabel(r'Risk threshold $\\gamma$')\n",
-    "plt.ylabel('Optimal objective value')\n",
+    "plt.xlabel(r\"Risk threshold $\\gamma$\")\n",
+    "plt.ylabel(\"Optimal objective value\")\n",
     "plt.tight_layout()\n",
     "plt.show()"
    ]