TSP.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8fe06e97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Delivery(22.8, 69.9)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct Delivery\n",
    "    x::Float64\n",
    "    y::Float64\n",
    "end;\n",
    "function random_delivery()\n",
    "    x = rand(0.0:0.1:100.0)\n",
    "    y = rand(0.0:0.1:100.0)\n",
    "    return Delivery(x, y)\n",
    "end;\n",
    "random_delivery()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8cb33b4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TSProblem(Delivery[Delivery(9.6, 95.9), Delivery(77.1, 3.6), Delivery(69.3, 69.0), Delivery(97.0, 31.5), Delivery(21.1, 66.2)])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "struct TSProblem\n",
    "    deliveries::Array{Delivery}\n",
    "end;\n",
    "\n",
    "function random_instance(n_deliveries)\n",
    "    deliveries = [random_delivery() for _=1:n_deliveries]\n",
    "    problem = TSProblem(deliveries)\n",
    "    return problem\n",
    "end;\n",
    "random_instance(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "675b5366",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "\n",
    "function display_problem(problem)\n",
    "    x_pos = [c.x for c in problem.deliveries]\n",
    "    y_pos = [c.y for c in problem.deliveries]\n",
    "    return scatter(x_pos, y_pos, shape = :circle, markersize = 6, label= \"Delivery\")\n",
    "end;\n",
    "\n",
    "problem = random_instance(20)\n",
    "display_problem(problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00198e9a",
   "metadata": {},
   "source": [
    "![problem](problem.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bafc9378",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20×20 Matrix{Float64}:\n",
       "   0.0     39.4069   108.809   33.0256   …  35.4572   28.1576   80.7059\n",
       "  39.4069   0.0       71.6874  31.8027       4.07063  27.9866   46.0541\n",
       " 108.809   71.6874     0.0     84.0967      74.9531   85.43     29.2961\n",
       "  33.0256  31.8027    84.0967   0.0         28.8402    5.79828  54.8063\n",
       "  37.4903  29.4391    78.2387   5.87963     27.052     9.33435  48.9449\n",
       "  55.6475  60.377     95.2148  29.5386   …  57.8744   34.9006   67.6757\n",
       "  89.6889  55.8659    23.4401  62.3039      58.3888   64.3525    9.90454\n",
       "  71.893   33.0946    50.6001  61.1616      37.1637   58.9196   37.4226\n",
       "  83.8468  63.8437    57.168   50.9652      64.1789   55.709    37.3872\n",
       "  42.3457  38.6163    81.3807   9.88989     36.2802   15.6541   52.3087\n",
       "  55.1994  24.7631    54.6466  30.0935   …  26.0204   30.8299   25.7109\n",
       "  59.7609  21.174     50.6077  42.8445      24.6854   41.5323   26.8745\n",
       "  74.1874  58.5844    65.3499  41.1643      58.2417   46.3159   41.701\n",
       "  83.3893  57.2943    43.8201  51.92        58.4607   55.6325   23.7474\n",
       "  38.3885  35.6867    82.4942   5.76975     33.1006   11.5486   53.2564\n",
       "  90.4498  69.8079    56.5043  57.5608   …  70.3034   62.3116   39.9204\n",
       "  51.9434  14.9459    57.312   34.5463      17.7553   33.0547   31.1082\n",
       "  35.4572   4.07063   74.9531  28.8402       0.0      24.6435   48.677\n",
       "  28.1576  27.9866    85.43     5.79828     24.6435    0.0      56.2854\n",
       "  80.7059  46.0541    29.2961  54.8063      48.677    56.2854    0.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function dist(del1::Delivery, del2::Delivery)\n",
    "    return sqrt((del1.x - del2.x)^2 + (del1.y - del2.y)^2)\n",
    "end\n",
    "function calc_travelmatrix(deliveries::Array{Delivery})\n",
    "    tm = zeros(Float64, length(deliveries), length(deliveries))\n",
    "    for i = 1:length(deliveries)\n",
    "        for j = 1:length(deliveries)\n",
    "            tm[i, j] = dist(deliveries[i], deliveries[j])\n",
    "        end\n",
    "    end\n",
    "    return tm\n",
    "end\n",
    "travelmatrix = calc_travelmatrix(problem.deliveries)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "363db71d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "termination_status(model) = MathOptInterface.OPTIMAL\n",
      "primal_status(model) = MathOptInterface.FEASIBLE_POINT\n",
      "dual_status(model) = MathOptInterface.NO_SOLUTION\n",
      "objective_value(model) = 352.23158274970643\n",
      "value.(route) = [0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "20×20 Matrix{Float64}:\n",
       " 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  …  0.0  0.0  0.0  0.0  0.0  1.0  0.0\n",
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      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using JuMP\n",
    "import GLPK\n",
    "\n",
    "model = Model(GLPK.Optimizer)\n",
    "# route is an adjence matrix representing a route traveled\n",
    "route=@variable(model, route[1:length(problem.deliveries), 1:length(problem.deliveries)], Bin)\n",
    "# mtzu is a helper variable to ensure no subtours are allowed (only one continous tour)\n",
    "# see MTZ constraint\n",
    "mtzu = @variable(model, mtzu[1:length(problem.deliveries)], Int)\n",
    "\n",
    "# ensure all events are planned\n",
    "@constraint(model, [i = 1:length(problem.deliveries)], sum(route[i, :]) == 1.0)\n",
    "# ensure there is just one route\n",
    "@constraint(model, [c = 1:length(problem.deliveries)], sum(route[:, c]) == 1.0)\n",
    "# disallow traveling to itself\n",
    "@constraint(model, [j = 1:length(problem.deliveries)], route[j, j] == 0)\n",
    "\n",
    "# MTZ constraints for removing subtours\n",
    "n = length(problem.deliveries)\n",
    "@constraint(model, [ui = 1:n, uj = 2:n], mtzu[ui] + route[ui, uj] <= mtzu[uj]+ (n - 1) * (1 - route[ui, uj]) )\n",
    "\n",
    "traveltime = travelmatrix.* route \n",
    "@objective(model, Min, sum(traveltime))\n",
    "optimize!(model)\n",
    "@show termination_status(model)\n",
    "@show primal_status(model)\n",
    "@show dual_status(model)\n",
    "@show objective_value(model)\n",
    "@show value.(route)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "50809ee7",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function display_solution(problem, route)\n",
    "    x_pos = [c.x for c in problem.deliveries]\n",
    "    y_pos = [c.y for c in problem.deliveries]\n",
    "    plot_result = scatter(x_pos, y_pos, shape = :circle, markersize = 6)\n",
    "    for i in 1:length(problem.deliveries)\n",
    "        for j in 1:length(problem.deliveries)\n",
    "            val = route[i, j]\n",
    "            if val > 0\n",
    "                del1 = problem.deliveries[i]\n",
    "                del2 = problem.deliveries[j]\n",
    "                plot!([del1.x, del2.x], [del1.y, del2.y], legend = false)\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return plot_result\n",
    "end;\n",
    "display_solution(problem, value.(route))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7b761015",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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