kCPP.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "230bc302",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import pulp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc53f7f1",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dd24ed3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "G=nx.DiGraph()\n",
    "G.add_edge(\"A\",\"B\",cost=120)\n",
    "G.add_edge(\"B\",\"D\",cost=150)\n",
    "G.add_edge(\"D\",\"C\",cost=120)\n",
    "G.add_edge(\"C\",\"D\",cost=120)\n",
    "G.add_edge(\"I\",\"C\",cost=250)\n",
    "G.add_edge(\"D\",\"I\",cost=300)\n",
    "G.add_edge(\"C\",\"A\",cost=150)\n",
    "G.add_edge(\"D\",\"E\",cost=150)\n",
    "G.add_edge(\"E\",\"K\",cost=250)\n",
    "G.add_edge(\"K\",\"J\",cost=80)\n",
    "G.add_edge(\"J\",\"D\",cost=250)\n",
    "G.add_edge(\"J\",\"I\",cost=120)\n",
    "G.add_edge(\"I\",\"J\",cost=120)\n",
    "G.add_edge(\"K\",\"L\",cost=150)\n",
    "G.add_edge(\"L\",\"K\",cost=150)\n",
    "G.add_edge(\"L\",\"M\",cost=100)\n",
    "G.add_edge(\"M\",\"G\",cost=250)\n",
    "G.add_edge(\"G\",\"N\",cost=180)\n",
    "G.add_edge(\"N\",\"E\",cost=260)\n",
    "G.add_edge(\"E\",\"F\",cost=80)\n",
    "G.add_edge(\"F\",\"L\",cost=250)\n",
    "G.add_edge(\"F\",\"G\",cost=100)\n",
    "G.add_edge(\"G\",\"F\",cost=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c84f7e3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = {\"A\": (0, 0), \"B\": (1, 0), \"D\": (1, 1), \"C\": (0, 1), \"I\": (0, 3), \"E\": (2, 1), \"K\": (\n",
    "    2, 3), \"J\": (1, 3), \"L\": (3, 3), \"M\": (4, 3), \"N\": (4, 0), \"G\": (4, 1), \"F\": (3, 1)}\n",
    "nx.draw(G,\n",
    "        with_labels=True,\n",
    "        pos=pos,\n",
    "        connectionstyle='arc3, rad = 0.1',\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8d8e551",
   "metadata": {},
   "source": [
    "# Compute cycles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "8563031d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['M', 'G', 'F', 'L']\n",
      "['M', 'G', 'N', 'E', 'F', 'L']\n",
      "['M', 'G', 'N', 'E', 'K', 'L']\n",
      "['K', 'L']\n",
      "['K', 'J', 'I', 'C', 'A', 'B', 'D', 'E', 'F', 'L']\n",
      "['K', 'J', 'I', 'C', 'A', 'B', 'D', 'E']\n",
      "['K', 'J', 'I', 'C', 'D', 'E', 'F', 'L']\n",
      "['K', 'J', 'I', 'C', 'D', 'E']\n",
      "['K', 'J', 'D', 'E', 'F', 'L']\n",
      "['K', 'J', 'D', 'E']\n",
      "['D', 'I', 'J']\n",
      "['D', 'I', 'C', 'A', 'B']\n",
      "['D', 'I', 'C']\n",
      "['D', 'C', 'A', 'B']\n",
      "['D', 'C']\n",
      "['I', 'J']\n",
      "['E', 'F', 'G', 'N']\n",
      "['G', 'F']\n"
     ]
    }
   ],
   "source": [
    "for c in nx.simple_cycles(G):\n",
    "    print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ca1ad79",
   "metadata": {},
   "source": [
    "The following code could definitely be optimized (many cycles are defined multiple times)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "664d7096",
   "metadata": {},
   "outputs": [],
   "source": [
    "cycles = list(nx.simple_cycles(G))\n",
    "G_cycles = {}\n",
    "i = 1\n",
    "# simple cycles\n",
    "cycles_1 = []\n",
    "for c in list(cycles):\n",
    "    H = nx.DiGraph()\n",
    "    nx.add_path(H, c)\n",
    "    H.add_edge(c[-1], c[0])\n",
    "    cost = sum(G[u][v][\"cost\"] for (u, v) in H.edges())\n",
    "    H.graph[\"cost\"] = cost\n",
    "    G_cycles[i] = H\n",
    "    cycles_1.append(H)\n",
    "    i += 1\n",
    "# 2-cycles\n",
    "cycles_2 = []\n",
    "for c1 in cycles:\n",
    "    for c2 in cycles:\n",
    "        if c1 != c2:\n",
    "            H1 = nx.DiGraph()\n",
    "            nx.add_path(H1, c1)\n",
    "            H1.add_edge(c1[-1], c1[0])\n",
    "            H2 = nx.DiGraph()\n",
    "            nx.add_path(H2, c2)\n",
    "            H2.add_edge(c2[-1], c2[0])\n",
    "            if len(nx.intersection(H1, H2).nodes()) > 0:\n",
    "                H = nx.compose(H1, H2)\n",
    "                cost = sum(G[u][v][\"cost\"] for (u, v) in H.edges())\n",
    "                H.graph[\"cost\"] = cost\n",
    "                G_cycles[i] = H\n",
    "                cycles_2.append(H)\n",
    "                i += 1\n",
    "# 3-cycles\n",
    "cycles_3 = []\n",
    "for H1 in cycles_1:\n",
    "    for H2 in cycles_2:\n",
    "        if len(nx.intersection(H1, H2).nodes()) > 0:\n",
    "            H = nx.compose(H1, H2)\n",
    "            cost = sum(G[u][v][\"cost\"] for (u, v) in H.edges())\n",
    "            H.graph[\"cost\"] = cost\n",
    "            G_cycles[i] = H\n",
    "            cycles_3.append(H)\n",
    "            i += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6167812d",
   "metadata": {},
   "source": [
    "# MIP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ec3d7cf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define problem\n",
    "prob = pulp.LpProblem(\"cycles\", pulp.LpMinimize)\n",
    "\n",
    "# define variables\n",
    "x = pulp.LpVariable.dicts(\"x\", G_cycles.keys(), cat=pulp.LpBinary)\n",
    "z = pulp.LpVariable(\"z\", cat=pulp.LpContinuous, lowBound=0)\n",
    "\n",
    "# objective function\n",
    "prob += z\n",
    "\n",
    "# cover each edge exactly once\n",
    "for (i, j) in G.edges():\n",
    "    prob += pulp.lpSum(x[g]\n",
    "                       for g in x if (i, j) in G_cycles[g].edges()) == 1\n",
    "# use exactly 3 cycles\n",
    "prob += pulp.lpSum(x) == 3\n",
    "\n",
    "# minimize z\n",
    "for g in x:\n",
    "    prob += G_cycles[g].graph[\"cost\"]*x[g] <= z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c330e84a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# print problem for debug\n",
    "#prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c8b0efe8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve with default CBC solver\n",
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f253843d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1320.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.objective.value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fcef70bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# save solution\n",
    "k = 1\n",
    "for g in G_cycles:\n",
    "    val = pulp.value(x[g])\n",
    "    if val > 0.9:\n",
    "        for (i, j) in G.edges():\n",
    "            if (i, j) in G_cycles[g].edges():\n",
    "                G[i][j][\"cycle\"] = k\n",
    "        k += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "77b63d07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot solution\n",
    "color = dict(zip([1,2,3],[\"blue\",\"red\",\"green\"]))\n",
    "nx.draw(G,\n",
    "        with_labels=True,\n",
    "        pos=pos,\n",
    "        connectionstyle='arc3, rad = 0.3',\n",
    "        edge_color=[color[G[u][v][\"cycle\"]] for (u, v) in G.edges()]\n",
    "        )"
   ]
  }
 ],
 "metadata": {
  "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": "3.10.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "166.333px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}