GPS's e Sudoku's.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Vehicle Routing Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from Numberjack import *\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as ntx\n",
    "import random\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Criação do Grafo\n",
    "a) Criação de uma rede de estradas (ou seja um grafo orientado e pesado) com caminhos aleatórios e atribuição de valores às variaveis:\n",
    "\n",
    "    i)Nodes: Podem ser considerados \"cidades\" pois se pode (ou não) encontrar os clientes\n",
    "    ii)Carros: Número de carros que a empresa tem disponiveis\n",
    "    iii)LCarga: Limite de carga que os carros podem levar\n",
    "    iv)NumClientes: Número máximo de Clientes\n",
    "\n",
    "As arestas do grafo serão bidirecionais, pois na geração de um grafo aleatório é muito provavel haver nodos que não sejam possiveis aceder.\n",
    "\n",
    "É feita a atribuição de um \"tempo\" aleatório a cada aresta com um valor entre (1,10).\n",
    "\n",
    "Qualquer uma destas variáveis pode ser alterada sem correr o risco de estragar o programa desde que esta alteração seja feita com bom senso (por exemplo nao ter mais nodos que clientes ou ter qualquer um deles negativo).\n",
    "\n",
    "Também é possivel alterar a frequência de ligações e para este teste consideramos (4,0.5) a melhor combinação."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mapa das cidades\n"
     ]
    },
    {
     "data": {
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/ITY2Fj179hS6JJPEsiyWLl2KI0eOIC4uDq6uroLUUV5ejoSEBM7rHouKihpa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\nAIcQwgAAOIQQBgDAIf8FCqZmJBqprAMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff8a05797f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Atribuições\n",
    "Nodes = 5\n",
    "Carros = 1\n",
    "LCarga = 14\n",
    "NumClientes = 2\n",
    "\n",
    "g = ntx.DiGraph()\n",
    "g = ntx.connected_watts_strogatz_graph(Nodes,4,0.5)\n",
    "\n",
    "for i, j in g.edges():\n",
    "    r = np.random.randint(1,10)\n",
    "    g.add_edge(i,j,weight = r)\n",
    "    g.add_edge(j,i,weight = r)\n",
    "\n",
    "print(\"Mapa das cidades\")\n",
    "ntx.draw_shell(g,arrows=False,node_size=900,node_color='y',with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assumimos o Nodo 0 como sendo a \"central\" da empresa de onde partem e retornam todos os veículos.\n",
    "\n",
    "Criação de um grafo completo apartir do grafo anterior em que cada aresta é o caminho mais curto entre cada nodo.\n",
    "\n",
    "Gera-se também um array \"Clientes\" que contém os clientes a ser atendidos.\n",
    "\n",
    "E finalmente retira-se do grafo anterior os nodos que não são clientes ou a central da empresa e as respetivas arestas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grafo completo\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZKIQfzSuvvII9e/bg3Xffxdtvv812OeRPUAjLSZUTAm3koBoikQgJCQk4efIk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\nVz8kj08AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff8a057a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grafo final\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff86d5334a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = ntx.DiGraph()\n",
    "\n",
    "G.add_nodes_from(g)\n",
    "EdgesP = []\n",
    "\n",
    "#inicializar a matriz\n",
    "for i in range(Nodes):\n",
    "    EdgesP.append([])\n",
    "    for j in range(Nodes):\n",
    "        EdgesP[i].append(-1)\n",
    "        \n",
    "#colocar os pesos ja calculados\n",
    "for i, j, p in g.edges(data = True):\n",
    "    w = p['weight']\n",
    "    EdgesP[j][i] = EdgesP[i][j] = w\n",
    "    G.add_edge(i, j, weight = w)\n",
    "    G.add_edge(j, i, weight = w)\n",
    "\n",
    "#calcular os caminhos mais curtos\n",
    "dic = ntx.shortest_path(G, weight = 'weight')\n",
    "\n",
    "#colocar os menores pesos\n",
    "for i in range(Nodes):\n",
    "    for j in range(Nodes):     \n",
    "        w = 0\n",
    "        for k in range(len(dic[i][j])-1):\n",
    "            i1 = dic[i][j][k]\n",
    "            i2 = dic[i][j][k+1]\n",
    "            w += EdgesP[i1][i2]\n",
    "        EdgesP[i][j] = w\n",
    "        G.add_edge(i,j,weight = w)\n",
    "        \n",
    "#criar clientes\n",
    "Clientes = np.unique(np.random.choice(range(1,Nodes), NumClientes)).tolist()\n",
    "NumClientes = len(Clientes)\n",
    "CargasC = np.random.randint(1,high = 5, size = NumClientes).tolist()\n",
    "CargasC = dict(zip(Clientes,CargasC))\n",
    "CargasC[0] = 0\n",
    "\n",
    "#Grafo completo\n",
    "print(\"Grafo completo\")\n",
    "ntx.draw_shell(G,arrows=False,node_size=900,node_color='y',with_labels=True)\n",
    "plt.show()\n",
    "\n",
    "G_clientes = G.copy()\n",
    "\n",
    "for i in range(Nodes):\n",
    "    if(i not in Clientes and i != 0 ):\n",
    "        G_clientes.remove_node(i)\n",
    "\n",
    "#Grafo final\n",
    "print(\"Grafo final\")\n",
    "ntx.draw_shell(G_clientes,arrows=False,node_size=900,node_color='y',with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Restrições\n",
    "\n",
    "Para a resolução deste problema criamos uma matriz binária de carros por arestas em que:\n",
    "\n",
    "    0)Significa que o carro não utiliza aquela aresta (rua)\n",
    "    1)Significa que o carro utiliza aquela aresta (rua)\n",
    "\n",
    "###### Obrigar a ir apenas aos clientes: \n",
    "\n",
    "$\\forall_{c\\leq Carros}\\forall_{i\\leq Nodes}\\big(i \\in Clientes \\land i \\neq 0 \\Rightarrow \\sum_{j\\leq Nodes} Mat[c][i*Nodes+j]+Mat[c][j*Nodes+i]= 0 \\big)$\n",
    "\n",
    "###### Obrigar a que as arestas do tipo (i,i) tenham peso 0 :\n",
    "\n",
    "$\\forall_{c\\leq Carros}\\forall_{n\\leq Nodes}\\big(Mat[c][n*Nodes+n]= 0 \\big)$\n",
    "\n",
    "###### Obrigar os clientes a serem atendidos uma unica vez:\n",
    "\n",
    "$\\forall_{c\\leq Clientes}\\big(\\sum_{i\\leq Carros, j\\leq Nodes}Mat[i][c*Nodes+j]= 1 \\big)$\n",
    "$\\forall_{c\\leq Clientes}\\big(\\sum_{i\\leq Carros, j\\leq Nodes}Mat[i][j*Nodes+c]= 1 \\big)$\n",
    "\n",
    "###### Obrigar a começar e acabar no 0:\n",
    "\n",
    "$\\forall_{c\\leq Carros}\\big(\\sum_{i\\leq Nodes}Mat[c][0*Nodes+i]= \\big(\\big(\\sum_{e\\leq Nodes²} Mat[c][e]\\big)>0\\big) \\big)$       \n",
    "$\\forall_{c\\leq Carros}\\big(\\sum_{i\\leq Nodes}Mat[c][i*Nodes+0]= \\big(\\big(\\sum_{e\\leq Nodes²} Mat[c][e]\\big)>0\\big) \\big)$\n",
    "\n",
    "###### Minimizar os carros:\n",
    "\n",
    "$minimize\\big(\\sum_{c\\leq Carros}\\big(\\sum_{e\\leq Nodes²}Mat[c][e]\\big)>0\\big)$\n",
    "\n",
    "###### Minimizar o custo (tempo):\n",
    "\n",
    "$\\forall_{c\\leq Carros}minimize\\big(\\sum_{i\\leq Nodes,j\\leq Nodes}EdgesP[i][j]*Mat[c][i*Nodes + j]\\big)$\n",
    "\n",
    "###### Verificar que o caminho faz sentido:\n",
    "\n",
    "$\\forall_{c\\leq Carros}\\forall_{i\\leq Clientes}\\big(\\sum_{j\\leq Nodes}Mat[c][i*Nodes+j]-Mat[c][j*Nodes+i]=0\\big)$\n",
    "\n",
    "###### Verificar que nao excede a carga maxima:\n",
    "\n",
    "$\\forall_{c\\leq Carros}\\big(\\sum_{e\\leq Nodes²}Mat[c][e]*CargasC[e\\mod Nodes] \\leq LCarga \\big)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "in method 'new_MipWrapper_and', argument 2 of type 'MipWrapper_Expression *'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-a8fe644c126c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     85\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m \u001b[0;31m#print(model)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'SCIP'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(self, solvername, X, encoding)\u001b[0m\n\u001b[1;32m    909\u001b[0m             \u001b[0msolverstring\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"%s.%s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0msolverspkg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolvername\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    910\u001b[0m             \u001b[0mlib\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m__import__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolverstring\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfromlist\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msolverspkg\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 911\u001b[0;31m             \u001b[0msolver\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSolver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mencoding\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    912\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    913\u001b[0m             raise ImportError(\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/solvers/SCIP.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, model, X, FD, clause_limit, encoding)\u001b[0m\n\u001b[1;32m    167\u001b[0m \u001b[0;32mclass\u001b[0m \u001b[0mSolver\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mNumberjack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNBJ_STD_Solver\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    168\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFD\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclause_limit\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m         \u001b[0mNumberjack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNBJ_STD_Solver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"SCIP\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"MipWrapper\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFD\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclause_limit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    170\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, Library, Wrapper, model, X, FD, clause_limit, encoding)\u001b[0m\n\u001b[1;32m   3173\u001b[0m             \u001b[0mloadstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdatetime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdatetime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3174\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mexpr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_exprs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3175\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3176\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_time\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtotal_seconds\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdatetime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdatetime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mloadstart\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3177\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload_expr\u001b[0;34m(self, expr)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload_expr\u001b[0;34m(self, expr)\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3289\u001b[0m                     \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3290\u001b[0;31m                         \u001b[0mmyarg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3291\u001b[0m                         \u001b[0mvar_array\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmyarg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3292\u001b[0m                         \u001b[0mkeep_alive\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmyarg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload_expr\u001b[0;34m(self, expr)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload_expr\u001b[0;34m(self, expr)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload_expr\u001b[0;34m(self, expr)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m   3284\u001b[0m                 \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3285\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3286\u001b[0;31m                     \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchild\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchild\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_children\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3287\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3288\u001b[0m                     \u001b[0mvar_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExpArray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/__init__.py\u001b[0m in \u001b[0;36mload_expr\u001b[0;34m(self, expr)\u001b[0m\n\u001b[1;32m   3313\u001b[0m                             \u001b[0marguments\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparam\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3314\u001b[0m                 \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3315\u001b[0;31m                     \u001b[0mvar\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfactory\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0marguments\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3316\u001b[0m                 \u001b[0;32mexcept\u001b[0m \u001b[0mNotImplementedError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3317\u001b[0m                     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Error the solver does not support this expression:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstderr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/Numberjack/solvers/MipWrapper.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, var1, var2)\u001b[0m\n\u001b[1;32m    655\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    656\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 657\u001b[0;31m         \u001b[0mthis\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_MipWrapper\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_MipWrapper_and\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    658\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    659\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: in method 'new_MipWrapper_and', argument 2 of type 'MipWrapper_Expression *'"
     ]
    }
   ],
   "source": [
    "Mat = Matrix(Carros,Nodes,NumClientes)\n",
    "model = Model()\n",
    "\n",
    "X = [[[ ((Mat[c][i]>0)*(Mat[c][j]>0)*(Mat[c][i]+1 == Mat[c][j]))+(i==0 & Mat[c][j]==1)>0 for j in range(Nodes)] \\\n",
    "                                                                                         for i in range(Nodes)] \\\n",
    "                                                                                         for c in range(Carros)]\n",
    "\n",
    "#obrigar a ir apenas aos clientes\n",
    "\n",
    "for c in range(Carros):\n",
    "    for i in range(Nodes):\n",
    "        if(i not in Clientes and i != 0 ):\n",
    "            model.add( Mat[c][i] == 0 )\n",
    "\n",
    "#Obrigar a que as arestas do tipo (i,i) sejam 0\n",
    "'''\n",
    "for c in range(Carros):\n",
    "    for n in range(Nodes):\n",
    "        model.add(Mat[c][n*Nodes+n]==0)\n",
    "'''        \n",
    "        \n",
    "#Obrigar os clientes a serem atendidos uma unica vez\n",
    "\n",
    "for cl in Clientes:\n",
    "    model.add( Sum([ X[ca][cl][i] for ca in range(Carros) for i in range(Nodes)]) == 1)\n",
    "    model.add( Sum([ X[ca][i][cl] for ca in range(Carros) for i in range(Nodes)]) == 1)\n",
    "\n",
    "    \n",
    "'''\n",
    "for c in Clientes:\n",
    "    A = [ Mat[i][c*Nodes+j] for i in range(Carros) for j in range(Nodes) ]\n",
    "    B = [ Mat[i][j*Nodes+c] for i in range(Carros) for j in range(Nodes) ]\n",
    "    model.add( Sum(A) == 1 )\n",
    "    model.add( Sum(B) == 1 )\n",
    "'''\n",
    "#Obrigar a começar e acabar no 0\n",
    "\n",
    "for c in range(Carros):\n",
    "    model.add( Sum([ X[c][i][0] for i in range(Nodes)]) == (Mat[c][0]>1) )\n",
    "'''   \n",
    "    # p = 1 se o carro esta, p = 0 se o carro nao esta\n",
    "    p = (Sum([ Mat[c][e] for e in range(Nodes**2)]) > 0)\n",
    "    model.add( Sum([ Mat[c][0*Nodes + i] for i in range(Nodes)]) == p )\n",
    "    model.add( Sum([ Mat[c][i*Nodes + 0] for i in range(Nodes)]) == p )\n",
    "'''\n",
    "    \n",
    "#Minimizar os carros\n",
    "model += Minimise(Sum([ (Mat[c][0]>1) for c in range(Carros)]))\n",
    "'''model += Minimise(Sum([ (Sum(Mat[c]) > 1) for c in range(Carros)]))'''\n",
    "\n",
    "#Minimizar o custo\n",
    "\n",
    "for c in range(Carros):\n",
    "    model += Minimise(Sum([ EdgesP[i][j]*(X[c][i][j]) for i in range(Nodes)\\\n",
    "                                                      for j in range(Nodes)]))\n",
    "#Verificar que o caminho faz sentido\n",
    "\n",
    "'''\n",
    "for c in range(Carros):\n",
    "    model.add( AllDiff([  for i in range(Nodes) for j in range(Nodes)]) )\n",
    "\n",
    "for c in range(Carros):\n",
    "    for i in range(Nodes):  \n",
    "        model.add( Sum([ Mat[c][i*Nodes+j]-Mat[c][j*Nodes+i] for j in range(Nodes)]) == 0 )\n",
    "        \n",
    "    #obrigar a que nao haja ciclos distintos\n",
    "    #for i in range(1, Nodes):\n",
    "     #   for j in range(1, Nodes):\n",
    "      #      model.add( Mat[c][i*Nodes+j]+Mat[c][j*Nodes+i] <= 1 )\n",
    "    \n",
    "    u=[0]*Nodes\n",
    "    u[0]=1\n",
    "    for i in range(NumClientes):\n",
    "        for j in range(NumClientes):\n",
    "            u[j]+= (u[i] > 0)*Mat[c][i*Nodes+j]*(u[j] == 0)\n",
    "    #model.add(Sum([Mat[c][e] for e in range(Nodes**2)]) == Sum(u))\n",
    "    for i in range(1,Nodes):\n",
    "        for j in range(1,Nodes):\n",
    "            #model.add(u[i]-u[j]+Nodes*Mat[c][i*Nodes+j] <= Nodes-1)\n",
    "            model.add( (u[i]>u[j]) >= Mat[c][i*Nodes+j] )\n",
    "'''\n",
    "    \n",
    "#Verificar que nao excede a carga maxima\n",
    "\n",
    "for c in range(Carros):\n",
    "    model.add( Sum( [ CargasC.get(j, 0)*X[c][i][j] for i in range(Nodes) for j in range(Nodes) ] ) <= LCarga )\n",
    "\n",
    "print()\n",
    "#print(model)\n",
    "model.load('SCIP').solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resultado Final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print(\"Lista de Clientes:\")\n",
    "print(Clientes)\n",
    "\n",
    "for c in range(Carros):\n",
    "    print(\"\\nCarro\",c+1)\n",
    "    \n",
    "    Gaux = ntx.DiGraph()\n",
    "\n",
    "    Gaux.add_nodes_from(g)\n",
    "\n",
    "    for i in range(Nodes):\n",
    "        for j in range(Nodes):\n",
    "            if(Mat[c][i*Nodes+j].get_value()==1):\n",
    "                Gaux.add_edge(i,j)\n",
    "\n",
    "    ntx.draw_shell(Gaux,arrows=True,node_size=500,node_color='y',with_labels=True)\n",
    "    plt.show()\n",
    "    \n",
    "    atual = 0\n",
    "    caminho = []\n",
    "    c2 = []\n",
    "    \n",
    "    for i in range(Nodes):\n",
    "        if(Mat[c][atual*Nodes + i].get_value() == 1):\n",
    "            caminho = caminho + dic[atual][i]\n",
    "            caminho.pop()\n",
    "            atual = i\n",
    "            c2.append(atual)\n",
    "            break\n",
    "    while(atual != 0):\n",
    "        for i in range(Nodes):\n",
    "            if(Mat[c][atual*Nodes + i].get_value() == 1):\n",
    "                caminho = caminho + dic[atual][i]\n",
    "                caminho.pop()\n",
    "                atual = i\n",
    "                c2.append(atual)\n",
    "                break\n",
    "    caminho.append(0)\n",
    "    print(\"Percurso:\",caminho)\n",
    "    carga = 0\n",
    "    for c in c2:\n",
    "        carga = carga + CargasC.get(c, 0)\n",
    "    print(\"Carga:\",carga)\n",
    "                "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Sudoku"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Criação do sudoku"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 3\n",
    "NS = N*N\n",
    "Gre = Matrix(NS,NS,1,NS)\n",
    "model = Model()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Restrições\n",
    "Preencher a Grelha\n",
    "\n",
    "###### Todos os pequenos quadrados têm diferentes números\n",
    "\n",
    "$\\forall_{i< N²}\\forall_{j< N²}\\forall_{i<i2\\leq N²}\n",
    "\\forall_{j<j2\\leq N²}\\big(M[i,j] =M[i2,j2] \\Rightarrow \\big(i/N \\neq i2/N\\big) \\vee \\big(j/N \\neq j2/N\\big)  \\big)$\n",
    "        \n",
    "###### Todas as linhas têm diferentes números\n",
    "\n",
    "$\\forall_{i\\leq N²}\\forall_{j< N²}\\forall_{j<j2\\leq N²}\\big(M[i,j] \\neq M[i,j2] \\big)$\n",
    "\n",
    "###### Todas as colunas têm diferentes números\n",
    "\n",
    "$\\forall_{i< N²}\\forall_{i<i2\\leq N²}\\forall_{j\\leq N²}\\big(M[i,j] \\neq M[i2,j] \\big)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        model.add(AllDiff(Gre[i*N:(i+1)*N,j*N:(j+1)*N].flat))\n",
    "        model.add(AllDiff(Gre[i*N+j]))\n",
    "        model.add(AllDiff(Gre.col[i*N+j]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resolução"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model.load('SCIP').solve()\n",
    "\n",
    "print(Gre)"
   ]
  }
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