All-Paths Problem.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ca008404",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import pulp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f0e8a06",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "id": "8fa6407f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create graph\n",
    "G = nx.DiGraph()\n",
    "G.add_edge(0,1)\n",
    "G.add_edge(1,2)\n",
    "G.add_edge(1,4)\n",
    "G.add_edge(1,8)\n",
    "G.add_edge(2,6)\n",
    "G.add_edge(2,8)\n",
    "G.add_edge(3,3)\n",
    "G.add_edge(3,8)\n",
    "G.add_edge(3,9)\n",
    "G.add_edge(4,3)\n",
    "G.add_edge(4,4)\n",
    "G.add_edge(4,6)\n",
    "G.add_edge(4,7)\n",
    "G.add_edge(5,9)\n",
    "G.add_edge(6,5)\n",
    "G.add_edge(6,10)\n",
    "G.add_edge(7,1)\n",
    "G.add_edge(7,5)\n",
    "G.add_edge(8,3)\n",
    "G.add_edge(8,10)\n",
    "G.add_edge(9,1)\n",
    "G.add_edge(9,7)\n",
    "G.add_edge(9,10)\n",
    "\n",
    "# create line graph\n",
    "H = nx.line_graph(G)\n",
    "new_edges = []\n",
    "# add source and sink nodes\n",
    "for (u,v) in H.nodes():\n",
    "    if u==0:\n",
    "        new_edges.append(((\"s\",\"s\"),(u,v)))\n",
    "    if v==10:\n",
    "        new_edges.append(((u,v),(\"t\",\"t\")))\n",
    "H.add_edges_from(new_edges)\n",
    "\n",
    "# max number of arcs\n",
    "M = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "id": "fc7de306",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G,pos=nx.spring_layout(G),with_labels=True,node_size=800,alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "id": "0ff401a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 8, 10]"
      ]
     },
     "execution_count": 314,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(G,source=0,target=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "id": "7ce3a6ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('s', 's'), (0, 1), (1, 8), (8, 10), ('t', 't')]"
      ]
     },
     "execution_count": 315,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(H,source=(\"s\",\"s\"),target=(\"t\",\"t\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5078e782",
   "metadata": {},
   "source": [
    "# MIP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "id": "6c0a986e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create LP\n",
    "prob = pulp.LpProblem(\"AllPaths\", pulp.LpMinimize)\n",
    "\n",
    "# x[(i,j)] = 1 if (i,j) is used\n",
    "x = pulp.LpVariable.dicts(\"x\",\n",
    "                          H.edges(),\n",
    "                          cat=pulp.LpBinary)\n",
    "\n",
    "# objective function : minimize number of edges\n",
    "prob += pulp.lpSum(x)\n",
    "\n",
    "# flow conservation\n",
    "for (u, v) in H.nodes():\n",
    "    if (u, v) not in [(\"s\", \"s\"), (\"t\", \"t\")]:\n",
    "        inflow = pulp.lpSum(x[((a, b), (u, v))]\n",
    "                            for (a, b) in H.predecessors((u, v)))\n",
    "        outflow = pulp.lpSum(x[((u, v), (a, b))]\n",
    "                             for (a, b) in H.successors((u, v)))\n",
    "        prob += inflow == outflow\n",
    "prob += pulp.lpSum(x[((\"s\", \"s\"), (a, b))]\n",
    "                   for (a, b) in H.successors((\"s\", \"s\"))) == 1\n",
    "prob += pulp.lpSum(x[((a, b), (\"t\", \"t\"))]\n",
    "                   for (a, b) in H.predecessors((\"t\", \"t\"))) == 1\n",
    "\n",
    "# max arcs\n",
    "prob += pulp.lpSum(x) <= M+2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "id": "dcfeca44",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21 paths\n"
     ]
    }
   ],
   "source": [
    "# solve and add no good cuts\n",
    "k = 0\n",
    "while True:\n",
    "    # solve MIP\n",
    "    prob.solve()#pulp.CPLEX_CMD())\n",
    "\n",
    "    # if optimal solution is found, print the edges of the path\n",
    "    if pulp.LpStatus[prob.status] == \"Optimal\":\n",
    "        k += 1\n",
    "        P = nx.DiGraph()\n",
    "        for ((u, v), (a, b)) in H.edges():\n",
    "            if pulp.value(x[((u, v), (a, b))]) > 0.9:\n",
    "                P.add_edge((u, v), (a, b))\n",
    "        # print(k, i, nx.shortest_path(P, (\"s\", \"s\"), (\"t\", \"t\")))\n",
    "        # add no good cut\n",
    "        yes_vars = pulp.lpSum((1-x[((u, v), (a, b))])\n",
    "                              for ((u, v), (a, b)) in P.edges())\n",
    "        no_vars = pulp.lpSum(x[((u, v), (a, b))] for (\n",
    "            (u, v), (a, b)) in H.edges() if ((u, v), (a, b)) not in P.edges())\n",
    "        prob += yes_vars >= 1  \n",
    "        prob += no_vars >= 2\n",
    "    else:\n",
    "        break\n",
    "print(k, \"paths\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5e39a9e",
   "metadata": {},
   "source": [
    "# Ranking paths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "id": "e169dc2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import islice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "id": "7c049a7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create line graph\n",
    "H = nx.line_graph(G)\n",
    "new_edges = []\n",
    "# add source and sink nodes\n",
    "for (u,v) in H.nodes():\n",
    "    if u==0:\n",
    "        new_edges.append((\"source\",(u,v)))\n",
    "    if v==10:\n",
    "        new_edges.append(((u,v),\"sink\"))\n",
    "H.add_edges_from(new_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "id": "5d65f50f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['source', (0, 1), (1, 8), (8, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 2), (2, 8), (8, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 4), (4, 6), (6, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 2), (2, 6), (6, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 8), (8, 3), (3, 8), (8, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 4), (4, 3), (3, 8), (8, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 8), (8, 3), (3, 9), (9, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 4), (4, 4), (4, 6), (6, 10), 'sink'],\n",
       " ['source', (0, 1), (1, 4), (4, 3), (3, 9), (9, 10), 'sink']]"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 9 shortest paths\n",
    "list(islice(nx.shortest_simple_paths(H, source=\"source\", target=\"sink\"), 9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "id": "eadcaafd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "268\n"
     ]
    }
   ],
   "source": [
    "M=10\n",
    "count=0\n",
    "for p in list(islice(nx.shortest_simple_paths(H, source=\"source\", target=\"sink\"), 300)):\n",
    "    if len(p)<=M+3:\n",
    "        count+=1\n",
    "print(count)"
   ]
  }
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