spanning_tree.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cc499b9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pulp\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de2fba6a",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "072e1f8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "sommets = [v for v in range(1,9)]\n",
    "aretes = [(1, 2),(1, 3),(1, 7),(2, 3),(2, 4),(2, 5),(2, 7),(2, 8),(3, 4),(7, 6),(7, 8),(4, 5),(5, 6),(5, 8),(8, 6)]\n",
    "poids = [6,7,4,4,9,9,10,5,4,12,11,6,8,7,14]\n",
    "aretes = dict(zip(aretes,poids))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "851ae352",
   "metadata": {},
   "outputs": [],
   "source": [
    "G=nx.Graph()\n",
    "for (u,v) in aretes:\n",
    "    G.add_edge(u,v,cost=aretes[(u,v)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c97c4cfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EdgeDataView([(1, 2, {'cost': 6}), (1, 3, {'cost': 7}), (1, 7, {'cost': 4}), (2, 3, {'cost': 4}), (2, 4, {'cost': 9}), (2, 5, {'cost': 9}), (2, 7, {'cost': 10}), (2, 8, {'cost': 5}), (3, 4, {'cost': 4}), (7, 6, {'cost': 12}), (7, 8, {'cost': 11}), (4, 5, {'cost': 6}), (5, 6, {'cost': 8}), (5, 8, {'cost': 7}), (8, 6, {'cost': 14})])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.edges(data=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e517b914",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G,with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78549aa7",
   "metadata": {},
   "source": [
    "# Kruskal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "93dafe32",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = nx.minimum_spanning_tree(G,weight=\"cost\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9680b0a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, {'cost': 6}),\n",
       " (1, 7, {'cost': 4}),\n",
       " (2, 3, {'cost': 4}),\n",
       " (2, 8, {'cost': 5}),\n",
       " (3, 4, {'cost': 4}),\n",
       " (4, 5, {'cost': 6}),\n",
       " (5, 6, {'cost': 8})]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(T.edges(data=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "61dc295f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(G[u][v][\"cost\"] for (u,v) in sorted(T.edges()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c801fe8",
   "metadata": {},
   "source": [
    "# MIP1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "22194fd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# déclaration du problème\n",
    "prob=pulp.LpProblem(\"tree\",pulp.LpMinimize)\n",
    "\n",
    "# variables\n",
    "x=pulp.LpVariable.dicts(\"x\",G.edges(),cat=pulp.LpBinary)\n",
    "\n",
    "# objectif\n",
    "prob += pulp.lpSum(x[(i,j)]*G[i][j][\"cost\"] for (i,j) in x)\n",
    "\n",
    "# n-1 edges\n",
    "prob += pulp.lpSum(x)==len(G.nodes())-1\n",
    "\n",
    "# no cycles\n",
    "for S in pulp.allcombinations(list(G.nodes()),len(G.nodes())):\n",
    "    if len(S)>1:\n",
    "        prob += pulp.lpSum(x[(u,v)] for u in S for v in S if (u,v) in x) <= len(S)-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "97d291f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#for S in pulp.allcombinations(list(G.nodes()),len(G.nodes())):\n",
    "#    if len(S)>2:\n",
    "#        print(S,\":\",pulp.lpSum(x[(u,v)] for u in S for v in S if (u,v) in x),\"<=\", len(S)-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "307e5389",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "c4f244db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "72cf84ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37.0"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pulp.value(prob.objective)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8bf29549",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2) 6\n",
      "(1, 7) 4\n",
      "(2, 3) 4\n",
      "(2, 8) 5\n",
      "(3, 4) 4\n",
      "(4, 5) 6\n",
      "(5, 6) 8\n"
     ]
    }
   ],
   "source": [
    "for (i,j) in x:\n",
    "    if pulp.value(x[(i,j)])>0.9:\n",
    "        print((i,j),G[i][j][\"cost\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "949ce777",
   "metadata": {},
   "source": [
    "# MIP 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c90a6783",
   "metadata": {},
   "outputs": [],
   "source": [
    "H=G.to_directed()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c1ee3efd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OutEdgeDataView([(1, 2, {'cost': 6}), (1, 3, {'cost': 7}), (1, 7, {'cost': 4}), (2, 1, {'cost': 6}), (2, 3, {'cost': 4}), (2, 4, {'cost': 9}), (2, 5, {'cost': 9}), (2, 7, {'cost': 10}), (2, 8, {'cost': 5}), (3, 1, {'cost': 7}), (3, 2, {'cost': 4}), (3, 4, {'cost': 4}), (7, 1, {'cost': 4}), (7, 2, {'cost': 10}), (7, 6, {'cost': 12}), (7, 8, {'cost': 11}), (4, 2, {'cost': 9}), (4, 3, {'cost': 4}), (4, 5, {'cost': 6}), (5, 2, {'cost': 9}), (5, 4, {'cost': 6}), (5, 6, {'cost': 8}), (5, 8, {'cost': 7}), (8, 2, {'cost': 5}), (8, 7, {'cost': 11}), (8, 5, {'cost': 7}), (8, 6, {'cost': 14}), (6, 7, {'cost': 12}), (6, 5, {'cost': 8}), (6, 8, {'cost': 14})])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.edges(data=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f7e9c1f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "L=[]\n",
    "for (u,v) in H.edges():\n",
    "    if v==1:\n",
    "        L.append((u,v))\n",
    "H.remove_edges_from(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "88f63e9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# déclaration du problème\n",
    "prob=pulp.LpProblem(\"tree\",pulp.LpMinimize)\n",
    "\n",
    "# variables\n",
    "x=pulp.LpVariable.dicts(\"x\",H.edges(),cat=pulp.LpBinary)\n",
    "u=pulp.LpVariable.dicts(\"u\",H.nodes(),lowBound=0,upBound=len(H.nodes())-1,cat=pulp.LpInteger)\n",
    "\n",
    "# objectif\n",
    "prob += pulp.lpSum(x[(i,j)]*H[i][j][\"cost\"] for (i,j) in x)\n",
    "\n",
    "prob += pulp.lpSum(x[(1,j)] for j in H.nodes() if (1,j) in x)>=1\n",
    "for j in H.nodes():\n",
    "    if j>1:\n",
    "        prob += pulp.lpSum(x[(i,j)] for i in H.nodes() if (i,j) in x)==1\n",
    "for (i,j) in H.edges():\n",
    "    if j>1:\n",
    "        prob += u[i]+1-u[j]<=len(H.nodes())*(1-x[(i,j)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f5708284",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b3c1c9b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "74e752f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pulp.value(prob.objective)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f05edda6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2) 6\n",
      "(1, 7) 4\n",
      "(2, 3) 4\n",
      "(2, 8) 5\n",
      "(3, 4) 4\n",
      "(4, 5) 6\n",
      "(5, 6) 8\n"
     ]
    }
   ],
   "source": [
    "for (i,j) in x:\n",
    "    if pulp.value(x[(i,j)])>0.9:\n",
    "        print((i,j),H[i][j][\"cost\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c3117db",
   "metadata": {},
   "source": [
    "# MIP 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1759770a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# déclaration du problème\n",
    "prob=pulp.LpProblem(\"tree\",pulp.LpMinimize)\n",
    "\n",
    "# variables\n",
    "x=pulp.LpVariable.dicts(\"x\",H.edges(),cat=pulp.LpBinary)\n",
    "f=pulp.LpVariable.dicts(\"f\",H.edges(),lowBound=0,upBound=None,cat=pulp.LpContinuous)\n",
    "\n",
    "# objectif\n",
    "prob += pulp.lpSum(x[(i,j)]*H[i][j][\"cost\"] for (i,j) in x)\n",
    "\n",
    "# optional\n",
    "#prob += pulp.lpSum(x)==len(H.nodes())-1\n",
    "\n",
    "prob += pulp.lpSum(f[(1,j)] for j in H.nodes() if (1,j) in f)==len(H.nodes())-1\n",
    "for j in H.nodes():\n",
    "    if j>1:\n",
    "        prob += pulp.lpSum(f[(i,j)] for i in H.nodes() if (i,j) in f)==pulp.lpSum(f[(j,i)] for i in H.nodes() if (j,i) in f)+1\n",
    "for (i,j) in H.edges():\n",
    "    prob +=f[(i,j)]<=(len(H.nodes())-1)*(x[(i,j)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a2153482",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "fd78184a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0714230a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pulp.value(prob.objective)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "46e4bb2c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2) 6\n",
      "(1, 7) 4\n",
      "(2, 3) 4\n",
      "(2, 8) 5\n",
      "(3, 4) 4\n",
      "(4, 5) 6\n",
      "(5, 6) 8\n"
     ]
    }
   ],
   "source": [
    "for (i,j) in x:\n",
    "    if pulp.value(x[(i,j)])>0.9:\n",
    "        print((i,j),H[i][j][\"cost\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93cdbc40",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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