Traffic Lights.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "eb7bc37c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import pulp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c44ed5a",
   "metadata": {},
   "source": [
    "# Compatibility graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3676c9af",
   "metadata": {},
   "outputs": [],
   "source": [
    "G=nx.Graph()\n",
    "\n",
    "G.add_edge('a','b')\n",
    "\n",
    "G.add_edge('b','f')\n",
    "G.add_edge('b','g')\n",
    "G.add_edge('b','j')\n",
    "\n",
    "G.add_edge('c','e')\n",
    "G.add_edge('c','g')\n",
    "G.add_edge('c','h')\n",
    "G.add_edge('c','i')\n",
    "G.add_edge('c','j')\n",
    "\n",
    "G.add_edge('d','e')\n",
    "G.add_edge('d','g')\n",
    "G.add_edge('d','j')\n",
    "G.add_edge('d','h')\n",
    "\n",
    "G.add_edge('e','i')\n",
    "\n",
    "G.add_edge('f','g')\n",
    "G.add_edge('f','j')\n",
    "\n",
    "G.add_edge('g','h')\n",
    "G.add_edge('g','i')\n",
    "\n",
    "G.add_edge('h','i')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3a3148e3",
   "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": "57a3b9c7",
   "metadata": {},
   "source": [
    "# Maximal cliques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "99e04755",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['g', 'h', 'd'],\n",
       " ['g', 'h', 'c', 'i'],\n",
       " ['g', 'b', 'f'],\n",
       " ['e', 'd'],\n",
       " ['e', 'c', 'i'],\n",
       " ['a', 'b'],\n",
       " ['j', 'd'],\n",
       " ['j', 'f', 'b'],\n",
       " ['j', 'c']]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.find_cliques(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bd12e7f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "K=list(k for k in nx.enumerate_all_cliques(G) if len(k)>1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "dc562f1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['a', 'b'],\n",
       " ['b', 'f'],\n",
       " ['b', 'g'],\n",
       " ['b', 'j'],\n",
       " ['f', 'g'],\n",
       " ['f', 'j'],\n",
       " ['g', 'c'],\n",
       " ['g', 'h'],\n",
       " ['g', 'i'],\n",
       " ['g', 'd'],\n",
       " ['j', 'c'],\n",
       " ['j', 'd'],\n",
       " ['c', 'e'],\n",
       " ['c', 'h'],\n",
       " ['c', 'i'],\n",
       " ['e', 'i'],\n",
       " ['e', 'd'],\n",
       " ['h', 'i'],\n",
       " ['h', 'd'],\n",
       " ['b', 'f', 'g'],\n",
       " ['b', 'f', 'j'],\n",
       " ['g', 'c', 'h'],\n",
       " ['g', 'c', 'i'],\n",
       " ['g', 'h', 'i'],\n",
       " ['g', 'h', 'd'],\n",
       " ['c', 'e', 'i'],\n",
       " ['c', 'h', 'i'],\n",
       " ['g', 'c', 'h', 'i']]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "6564c6d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "K=[['g','h','i'],['g','b','f'],['a','b'],['b','j'],['c','j'],['d','j'],['d','e'],['e','i']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e9240ddf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: ['a', 'b'],\n",
       " 2: ['b', 'f'],\n",
       " 3: ['b', 'g'],\n",
       " 4: ['b', 'j'],\n",
       " 5: ['f', 'g'],\n",
       " 6: ['f', 'j'],\n",
       " 7: ['g', 'c'],\n",
       " 8: ['g', 'h'],\n",
       " 9: ['g', 'i'],\n",
       " 10: ['g', 'd'],\n",
       " 11: ['j', 'c'],\n",
       " 12: ['j', 'd'],\n",
       " 13: ['c', 'e'],\n",
       " 14: ['c', 'h'],\n",
       " 15: ['c', 'i'],\n",
       " 16: ['e', 'i'],\n",
       " 17: ['e', 'd'],\n",
       " 18: ['h', 'i'],\n",
       " 19: ['h', 'd'],\n",
       " 20: ['b', 'f', 'g'],\n",
       " 21: ['b', 'f', 'j'],\n",
       " 22: ['g', 'c', 'h'],\n",
       " 23: ['g', 'c', 'i'],\n",
       " 24: ['g', 'h', 'i'],\n",
       " 25: ['g', 'h', 'd'],\n",
       " 26: ['c', 'e', 'i'],\n",
       " 27: ['c', 'h', 'i'],\n",
       " 28: ['g', 'c', 'h', 'i']}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cliques=dict(zip(\n",
    "    [k for k in range(1,len(K)+1)],\n",
    "    K\n",
    "))\n",
    "cliques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a1ddbf7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': [1],\n",
       " 'b': [1, 2, 3, 4, 20, 21],\n",
       " 'f': [2, 5, 6, 20, 21],\n",
       " 'g': [3, 5, 7, 8, 9, 10, 20, 22, 23, 24, 25, 28],\n",
       " 'j': [4, 6, 11, 12, 21],\n",
       " 'c': [7, 11, 13, 14, 15, 22, 23, 26, 27, 28],\n",
       " 'e': [13, 16, 17, 26],\n",
       " 'h': [8, 14, 18, 19, 22, 24, 25, 27, 28],\n",
       " 'i': [9, 15, 16, 18, 23, 24, 26, 27, 28],\n",
       " 'd': [10, 12, 17, 19, 25]}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H={}\n",
    "for m in G.nodes():\n",
    "    H[m]=[]\n",
    "    for k in cliques:\n",
    "        if m in cliques[k]:\n",
    "            H[m].append(k)\n",
    "H           "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6edc9a2f",
   "metadata": {},
   "source": [
    "# Circular layout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "70a11a13",
   "metadata": {},
   "outputs": [],
   "source": [
    "prob=pulp.LpProblem(\"circular_cliques\",pulp.LpMaximize)\n",
    "z=pulp.LpVariable.dicts(\"z\",(cliques,cliques),cat=pulp.LpBinary)\n",
    "y=pulp.LpVariable.dicts(\"y\",cliques,cat=pulp.LpBinary)\n",
    "u=pulp.LpVariable.dicts(\"u\",cliques,lowBound=1,upBound=len(cliques),cat=pulp.LpInteger)\n",
    "prob+=pulp.lpSum(len(cliques[k])*y[k] for k in y)\n",
    "for j in cliques:\n",
    "    prob+=pulp.lpSum(z[i][j] for i in z)==y[j]\n",
    "for i in cliques:\n",
    "    prob+=pulp.lpSum(z[i][j] for j in z[i])==y[i]\n",
    "    prob+=z[i][i]==0\n",
    "for m in G.nodes():\n",
    "    #prob+=pulp.lpSum(z[i][j] + z[j][i] for i in H[m] for j in H[m] if i<j)>= len(H[m])-1 \n",
    "    prob+=pulp.lpSum(z[i][j] + z[j][i] for i in H[m] for j in H[m] if i<j)>= pulp.lpSum(y[k] for k in cliques if m in cliques[k])-1\n",
    "    #prob+=pulp.lpSum(y[k] for k in cliques if m in cliques[k])>=1\n",
    "for i in cliques:\n",
    "    for j in cliques:\n",
    "        if j>1:\n",
    "            prob+= u[i]+1-u[j]<=len(cliques)*(1-z[i][j]) \n",
    "prob+=pulp.lpSum(y)==8\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "3f969881",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "682fc704",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Optimal'"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.solve()\n",
    "pulp.LpStatus[prob.status]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "40b0c079",
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 'b']\n",
      "['b', 'f', 'g']\n",
      "['b', 'f', 'j']\n",
      "['g', 'h', 'i']\n",
      "['g', 'h', 'd']\n",
      "['c', 'e', 'i']\n",
      "['c', 'h', 'i']\n",
      "['g', 'c', 'h', 'i']\n"
     ]
    }
   ],
   "source": [
    "for i in y:\n",
    "    val = pulp.value(y[i])\n",
    "    if val >0.9:\n",
    "        print(cliques[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "315a266b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 'b'] 1.0\n",
      "['b', 'f', 'g'] 3.0\n",
      "['b', 'f', 'j'] 2.0\n",
      "['g', 'h', 'i'] 5.0\n",
      "['g', 'h', 'd'] 4.0\n",
      "['c', 'e', 'i'] 8.0\n",
      "['c', 'h', 'i'] 7.0\n",
      "['g', 'c', 'h', 'i'] 6.0\n"
     ]
    }
   ],
   "source": [
    "for i in cliques:\n",
    "    val = pulp.value(y[i])\n",
    "    if val >0.9:\n",
    "        print(cliques[i],pulp.value(u[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "338fbe8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 'b'] ['b', 'f', 'j']\n",
      "['b', 'f', 'g'] ['g', 'h', 'd']\n",
      "['b', 'f', 'j'] ['b', 'f', 'g']\n",
      "['g', 'h', 'i'] ['g', 'c', 'h', 'i']\n",
      "['g', 'h', 'd'] ['g', 'h', 'i']\n",
      "['c', 'e', 'i'] ['a', 'b']\n",
      "['c', 'h', 'i'] ['c', 'e', 'i']\n",
      "['g', 'c', 'h', 'i'] ['c', 'h', 'i']\n"
     ]
    }
   ],
   "source": [
    "for i in cliques:\n",
    "    for j in cliques:\n",
    "        if pulp.value(z[i][j])>0.9:\n",
    "            print(cliques[i],cliques[j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "5e67eacd",
   "metadata": {},
   "outputs": [],
   "source": [
    "selected_cliques=[k for k in cliques if pulp.value(y[k])>0.9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "33873d3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 20, 21, 24, 25, 26, 27, 28]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selected_cliques"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dca28ceb",
   "metadata": {},
   "source": [
    "# Circular layout II"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "81b6fa5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "k=[_ for _ in range(1,9)]\n",
    "prob=pulp.LpProblem(\"circular_cliques\",pulp.LpMaximize)\n",
    "z=pulp.LpVariable.dicts(\"z\",(k,k),cat=pulp.LpBinary)\n",
    "y=pulp.LpVariable.dicts(\"y\",k,cat=pulp.LpBinary)\n",
    "u=pulp.LpVariable.dicts(\"u\",k,lowBound=1,upBound=len(k),cat=pulp.LpInteger)\n",
    "x=pulp.LpVariable.dicts(\"x\",(G.nodes(),k),cat=pulp.LpBinary)\n",
    "w=pulp.LpVariable.dicts(\"w\",(k,k,G.nodes()),cat=pulp.LpBinary)\n",
    "prob+=pulp.lpSum(x)\n",
    "for m in G.nodes():\n",
    "    prob+=pulp.lpSum(x[m][i] for i in k)>=1\n",
    "for i in k:\n",
    "    for m in G.nodes():\n",
    "        for n in G.nodes():\n",
    "            if m!=n:\n",
    "                if (m,n) not in G.edges() and (n,m) not in G.edges():\n",
    "                    prob+=x[m][i]+x[n][i]<=y[i]\n",
    "for i in k:\n",
    "    if i>1:\n",
    "        prob+=y[i]<=y[i-1]\n",
    "    prob+=2*y[i]<=pulp.lpSum(x[m][i] for m in G.nodes())\n",
    "    prob+=pulp.lpSum(x[m][i] for m in G.nodes())<=3*y[i]\n",
    "\n",
    "for j in k:\n",
    "    prob+=pulp.lpSum(z[i][j] for i in z)==y[j]\n",
    "for i in k:\n",
    "    prob+=pulp.lpSum(z[i][j] for j in z[i])==y[i]\n",
    "    prob+=z[i][i]==0\n",
    "for m in G.nodes():\n",
    "    prob+=pulp.lpSum(w[i][j][m] for i in k for j in k if i<j)>=pulp.lpSum(x[m][i] for i in k)-1\n",
    "for i in k:\n",
    "    for j in k:\n",
    "        for m in G.nodes():\n",
    "            prob+=w[i][j][m]<=z[i][j]+z[j][i]\n",
    "            prob+=w[i][j][m]<=x[m][i]\n",
    "            prob+=w[i][j][m]<=x[m][j]\n",
    "for i in k:\n",
    "    for j in k:\n",
    "        if j>1:\n",
    "            prob+= u[i]+1-u[j]<=len(k)*(1-z[i][j])\n",
    "            \n",
    "prob+=x[\"g\"][1]==1\n",
    "prob+=x[\"h\"][1]==1\n",
    "prob+=x[\"i\"][1]==1\n",
    "prob+=x[\"f\"][2]==1\n",
    "prob+=x[\"b\"][2]==1\n",
    "prob+=x[\"g\"][2]==1\n",
    "prob+=x[\"a\"][3]==1\n",
    "prob+=x[\"b\"][3]==1\n",
    "prob+=x[\"j\"][4]==1\n",
    "prob+=x[\"b\"][4]==1\n",
    "prob+=x[\"j\"][5]==1\n",
    "prob+=x[\"c\"][5]==1\n",
    "prob+=x[\"j\"][6]==1\n",
    "prob+=x[\"d\"][6]==1\n",
    "#prob+=x[\"e\"][7]==1\n",
    "#prob+=x[\"d\"][7]==1\n",
    "#prob+=x[\"e\"][8]==1\n",
    "#prob+=x[\"i\"][8]==1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "8c9f6b09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Optimal'"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.solve()\n",
    "pulp.LpStatus[prob.status]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "a7e3c68b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "clique 1\n",
      "=========\n",
      "g\n",
      "h\n",
      "i\n",
      "clique 2\n",
      "=========\n",
      "b\n",
      "f\n",
      "g\n",
      "clique 3\n",
      "=========\n",
      "a\n",
      "b\n",
      "clique 4\n",
      "=========\n",
      "b\n",
      "j\n",
      "clique 5\n",
      "=========\n",
      "j\n",
      "c\n",
      "clique 6\n",
      "=========\n",
      "j\n",
      "d\n",
      "clique 7\n",
      "=========\n",
      "c\n",
      "e\n",
      "i\n",
      "clique 8\n",
      "=========\n",
      "g\n",
      "h\n",
      "i\n"
     ]
    }
   ],
   "source": [
    "for i in k:\n",
    "    print(\"clique\",i)\n",
    "    print(\"=========\")\n",
    "    for m in G.nodes():\n",
    "        val=pulp.value(x[m][i])\n",
    "        if val>0.9:\n",
    "            print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "afb1b130",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "clique 1 ['g', 'h', 'i'] in position 1.0\n",
      "clique 2 ['b', 'f', 'g'] in position 8.0\n",
      "clique 3 ['a', 'b'] in position 7.0\n",
      "clique 4 ['b', 'j'] in position 6.0\n",
      "clique 5 ['j', 'c'] in position 5.0\n",
      "clique 6 ['j', 'd'] in position 4.0\n",
      "clique 7 ['e', 'd'] in position 3.0\n",
      "clique 8 ['e', 'i'] in position 2.0\n"
     ]
    }
   ],
   "source": [
    "for i in u:\n",
    "    print(\"clique\",i,[v for v in G.nodes() if pulp.value(x[v][i])>0.9],\"in position\",pulp.value(u[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "05b70e18",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prob"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3559fbec",
   "metadata": {},
   "source": [
    "# Maximize green light time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "31f7ce14",
   "metadata": {},
   "outputs": [],
   "source": [
    "prob=pulp.LpProblem(\"green\",pulp.LpMaximize)\n",
    "t=pulp.LpVariable.dicts(\"t\",selected_cliques,lowBound=0,cat=pulp.LpContinuous)\n",
    "prob+=pulp.lpSum(t[i] for m in G.nodes() for i in selected_cliques if i in H[m])\n",
    "prob+=pulp.lpSum(t[i] for i in selected_cliques)==60\n",
    "for m in G.nodes():\n",
    "    prob+=pulp.lpSum(t[i] for i in selected_cliques if i in H[m])>=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "56c38e4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Optimal'"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.solve()\n",
    "pulp.LpStatus[prob.status]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "1553f3d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 10.0\n",
      "20 0.0\n",
      "21 10.0\n",
      "24 0.0\n",
      "25 10.0\n",
      "26 10.0\n",
      "27 0.0\n",
      "28 20.0\n"
     ]
    }
   ],
   "source": [
    "for i in selected_cliques:\n",
    "    print(i,pulp.value(t[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "462eb6c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a 10.0\n",
      "b 20.0\n",
      "f 10.0\n",
      "g 30.0\n",
      "j 10.0\n",
      "c 30.0\n",
      "e 10.0\n",
      "h 30.0\n",
      "i 30.0\n",
      "d 10.0\n"
     ]
    }
   ],
   "source": [
    "for m in G.nodes():\n",
    "    print(m,pulp.lpSum(pulp.value(t[i]) for i in selected_cliques if i in H[m]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "aa9d4146",
   "metadata": {},
   "outputs": [],
   "source": [
    "#prob"
   ]
  }
 ],
 "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": "3.11.2"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}