{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4ed711c8",
   "metadata": {},
   "source": [
    "# The P-Dispersion (max-min-min) Problem\n",
    "\n",
    "*Authors:* [Erin Olson](https://github.com/erinrolson), [James Gaboardi](https://github.com/jGaboardi), [Levi J. Wolf](https://github.com/ljwolf), [Qunshan Zhao](https://github.com/qszhao)\n",
    "\n",
    "\n",
    "When locating some types of facilites a primary objective may be to limit the potential for cascading adverse effects damage should one facility be damaged. Therefore, maximally dispersed arrangement would be the most beneficial. For example, power plants are generally not near other power plants as a precaution against localized damage or disablement during a natural disaster. To address this kind of scenarios with a mixed-integer program, Kuby (1987) described the following problem: _Locate $p$ facilities so that the minimum distance between any pair of facilities is maximized._\n",
    "\n",
    "**P-Dispersion can be written as:**\n",
    "\n",
    "\\begin{equation*}\n",
    "\\textbf{Maximize } D \n",
    "\\end{equation*}\n",
    "\n",
    "___Subject to:___\n",
    "\\begin{equation*}\n",
    "\\sum_{i \\in I} Y_i = p \n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "D \\leq d_{ij} + M (2 - Y_{i} - Y_{j}), \\quad \\forall i \\in I \\quad \\forall j > i \n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "Y_i = \\{0,1\\}, \\quad \\forall i \\in I\n",
    "\\end{equation*}\n",
    "\n",
    "___Where:___\n",
    "\n",
    "\\begin{array}{lll}\n",
    "i,j & \\small = & \\textrm{index of potential facility sites} \\\\\n",
    "n & \\small = & \\textrm{number of potential facility sites} \\\\\n",
    "d_{ij} & \\small = & \\textrm{shortest path distance between sites } i \\textrm{ and } j \\\\\n",
    "M & \\small = & \\textrm{some large number; such that } M \\geq \\max_{ij}\\{d_{ij}\\} \\\\\n",
    "p & \\small = & \\textrm{number of facilities to be located} \\\\\n",
    "Y_i & \\small = & \\begin{cases} \n",
    "          1 \\quad \\text{if facility is located at node } i\\\\\n",
    "          0 \\quad \\text{if otherwise} \\\\\n",
    "       \\end{cases} \\end{array}\n",
    "\n",
    "_The above fomulation was adapted from Maliszewski et al (2012), the original formulation is from Kuby (1987)._ \n",
    "\n",
    "This tutorial generates synthetic facility sites near a 10x10 lattice representing a gridded urban core. Three $p$-Dispersion instances are solved while varying parameters:\n",
    "\n",
    "* `PDispersion.from_cost_matrix()` with network distance as the metric\n",
    "* `PDispersion.from_geodataframe()` with euclidean distance as the metric\n",
    "* `PDispersion.from_geodataframe()` with predefined facility locations and euclidean distance as the metric\n",
    "\n",
    "Unlike other facility location models available in `spopt.locate`, the $p$-Dispersion problem does not take demand/client locations into consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "67638055",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:30.469050Z",
     "start_time": "2023-01-10T18:23:30.433456Z"
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    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:14.371179Z",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: 2025-04-07T15:07:14.389023-04:00\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.12.9\n",
      "IPython version      : 9.0.2\n",
      "\n",
      "Compiler    : Clang 18.1.8 \n",
      "OS          : Darwin\n",
      "Release     : 24.4.0\n",
      "Machine     : arm64\n",
      "Processor   : arm\n",
      "CPU cores   : 8\n",
      "Architecture: 64bit\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "%load_ext watermark\n",
    "%watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dfd6bccc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.017045Z",
     "start_time": "2023-01-10T18:23:30.472931Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:14.400601Z",
     "iopub.status.busy": "2025-04-07T19:07:14.400377Z",
     "iopub.status.idle": "2025-04-07T19:07:15.572882Z",
     "shell.execute_reply": "2025-04-07T19:07:15.572613Z",
     "shell.execute_reply.started": "2025-04-07T19:07:14.400583Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Watermark: 2.5.0\n",
      "\n",
      "pulp      : 2.8.0\n",
      "spaghetti : 1.7.6\n",
      "shapely   : 2.1.0\n",
      "spopt     : 0.6.2.dev3+g13ca45e\n",
      "matplotlib: 3.10.1\n",
      "numpy     : 2.2.4\n",
      "geopandas : 1.0.1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "\n",
    "import geopandas\n",
    "import matplotlib.lines as mlines\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import pulp\n",
    "import shapely\n",
    "from matplotlib.patches import Patch\n",
    "\n",
    "import spopt\n",
    "from spopt.locate import PDispersion, simulated_geo_points\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    # ignore deprecation warning - GH pysal/spaghetti#649\n",
    "    import spaghetti\n",
    "\n",
    "%watermark -w\n",
    "%watermark -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e952f337",
   "metadata": {},
   "source": [
    "Since the model needs a cost matrix (distance, time, etc.) we should define some variables. First we will assign some the number of facility locations followed by the random seed in order to reproduce the results. Finally, the solver, assigned below as `pulp.COIN_CMD`, is an interface to optimization solver developed by [COIN-OR](https://github.com/coin-or/Cbc). If you want to use another optimization interface, such as Gurobi or CPLEX, see this [guide](https://coin-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6725bc44",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.028779Z",
     "start_time": "2023-01-10T18:23:33.022873Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.574034Z",
     "iopub.status.busy": "2025-04-07T19:07:15.573882Z",
     "iopub.status.idle": "2025-04-07T19:07:15.575882Z",
     "shell.execute_reply": "2025-04-07T19:07:15.575620Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.574027Z"
    }
   },
   "outputs": [],
   "source": [
    "# quantity supply points\n",
    "FACILITY_COUNT = 16\n",
    "\n",
    "# number of candidate facilities in optimal solution\n",
    "P_FACILITIES = 3\n",
    "\n",
    "# random seeds for reproducibility\n",
    "FACILITY_SEED = 6\n",
    "\n",
    "# set the solver\n",
    "solver = pulp.COIN_CMD(msg=False, warmStart=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e579217",
   "metadata": {},
   "source": [
    "## Lattice 10x10\n",
    "\n",
    "Create a 10x10 lattice with 9 interior lines, both vertical and horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4371f5e5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.082856Z",
     "start_time": "2023-01-10T18:23:33.034844Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.576243Z",
     "iopub.status.busy": "2025-04-07T19:07:15.576164Z",
     "iopub.status.idle": "2025-04-07T19:07:15.587967Z",
     "shell.execute_reply": "2025-04-07T19:07:15.587732Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.576237Z"
    }
   },
   "outputs": [],
   "source": [
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    # ignore deprecation warning - GH pysal/libpysal#468\n",
    "    lattice = spaghetti.regular_lattice((0, 0, 10, 10), 9, exterior=True)\n",
    "ntw = spaghetti.Network(in_data=lattice)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf6e7748",
   "metadata": {},
   "source": [
    "Transform the `spaghetti` instance into a geodataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d767d1ad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.225733Z",
     "start_time": "2023-01-10T18:23:33.086985Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.588367Z",
     "iopub.status.busy": "2025-04-07T19:07:15.588298Z",
     "iopub.status.idle": "2025-04-07T19:07:15.627701Z",
     "shell.execute_reply": "2025-04-07T19:07:15.627487Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.588360Z"
    }
   },
   "outputs": [],
   "source": [
    "streets = spaghetti.element_as_gdf(ntw, arcs=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1f639684",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.263515Z",
     "start_time": "2023-01-10T18:23:33.228853Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.628099Z",
     "iopub.status.busy": "2025-04-07T19:07:15.628031Z",
     "iopub.status.idle": "2025-04-07T19:07:15.638682Z",
     "shell.execute_reply": "2025-04-07T19:07:15.638428Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.628090Z"
    }
   },
   "outputs": [],
   "source": [
    "streets_buffered = geopandas.GeoDataFrame(\n",
    "    geopandas.GeoSeries(streets[\"geometry\"].buffer(0.5).union_all()),\n",
    "    crs=streets.crs,\n",
    "    columns=[\"geometry\"],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ff2e134",
   "metadata": {},
   "source": [
    "Plotting the network created by `spaghetti` we can verify that it mimics a district with quarters and streets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d4b67cb3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.471286Z",
     "start_time": "2023-01-10T18:23:33.266165Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.639115Z",
     "iopub.status.busy": "2025-04-07T19:07:15.639028Z",
     "iopub.status.idle": "2025-04-07T19:07:15.700010Z",
     "shell.execute_reply": "2025-04-07T19:07:15.699789Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.639106Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 416
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "streets.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fcf8cfe",
   "metadata": {},
   "source": [
    "## Simulate points in a network\n",
    "\n",
    "The `simulated_geo_points` function simulates points near a network. In this case, it uses the 10x10 lattice network created using the `spaghetti` package. Below we use the function defined above and simulate the points near the lattice edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d5aad045",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.482666Z",
     "start_time": "2023-01-10T18:23:33.473980Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.700459Z",
     "iopub.status.busy": "2025-04-07T19:07:15.700386Z",
     "iopub.status.idle": "2025-04-07T19:07:15.703948Z",
     "shell.execute_reply": "2025-04-07T19:07:15.703732Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.700452Z"
    }
   },
   "outputs": [],
   "source": [
    "facility_points = simulated_geo_points(\n",
    "    streets_buffered, needed=FACILITY_COUNT, seed=FACILITY_SEED\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfb6aa6b",
   "metadata": {},
   "source": [
    "Plotting the facility points we can see that the function generates dummy points to an area of 10x10, which is the area created by our lattice created on previous cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "91d8cddf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.960755Z",
     "start_time": "2023-01-10T18:23:33.485494Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.704412Z",
     "iopub.status.busy": "2025-04-07T19:07:15.704294Z",
     "iopub.status.idle": "2025-04-07T19:07:15.829423Z",
     "shell.execute_reply": "2025-04-07T19:07:15.829190Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.704404Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 505,
       "width": 776
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "streets.plot(ax=ax, alpha=0.8, zorder=1, label=\"streets\")\n",
    "facility_points.plot(\n",
    "    ax=ax,\n",
    "    color=\"red\",\n",
    "    zorder=2,\n",
    "    label=f\"facility candidate sites ($n$={FACILITY_COUNT})\",\n",
    ")\n",
    "plt.legend(loc=\"upper left\", bbox_to_anchor=(1.05, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bb0cc9b",
   "metadata": {},
   "source": [
    "## Assign simulated points network locations\n",
    "\n",
    "The facility points do not adhere to network space. Calculating distances between them without restricting movement to the network results in a euclidean distances,'as the crow flies.' While this is acceptable for some applications, for others it is more realistic to consider network traversal (e.g. Does a mail carrier follow roads to deliver letters or fly from mailbox to mailbox?).\n",
    "\n",
    "In our first example we will consider distance along the 10x10 lattice network created above. Therefore, we must first snap the observation points to the network prior to calculating a cost matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1d447220",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:33.997317Z",
     "start_time": "2023-01-10T18:23:33.967233Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.829807Z",
     "iopub.status.busy": "2025-04-07T19:07:15.829734Z",
     "iopub.status.idle": "2025-04-07T19:07:15.838617Z",
     "shell.execute_reply": "2025-04-07T19:07:15.838414Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.829799Z"
    }
   },
   "outputs": [],
   "source": [
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    # ignore deprecation warning - GH pysal/libpysal#468\n",
    "    ntw.snapobservations(facility_points, \"facilities\", attribute=True)\n",
    "facilities_snapped = spaghetti.element_as_gdf(ntw, pp_name=\"facilities\", snapped=True)\n",
    "facilities_snapped.drop(columns=[\"id\", \"comp_label\"], inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af1768f2",
   "metadata": {},
   "source": [
    "Now the plot seems more organized as the points occupy network space. The network is plotted below with the network locations of the facility points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "81fe5065",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.310140Z",
     "start_time": "2023-01-10T18:23:34.000540Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.839027Z",
     "iopub.status.busy": "2025-04-07T19:07:15.838950Z",
     "iopub.status.idle": "2025-04-07T19:07:15.928245Z",
     "shell.execute_reply": "2025-04-07T19:07:15.928042Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.839019Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 505,
       "width": 798
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "streets.plot(ax=ax, alpha=0.8, zorder=1, label=\"streets\")\n",
    "facilities_snapped.plot(\n",
    "    ax=ax,\n",
    "    color=\"red\",\n",
    "    zorder=2,\n",
    "    label=f\"facility candidate sites ($n$={FACILITY_COUNT})\",\n",
    ")\n",
    "plt.legend(loc=\"upper left\", bbox_to_anchor=(1.05, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5f02e47",
   "metadata": {},
   "source": [
    "## Calculating the (network distance) cost matrix\n",
    "Calculate the inter-facility network distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4fbb1d6d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.381679Z",
     "start_time": "2023-01-10T18:23:34.312980Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.930088Z",
     "iopub.status.busy": "2025-04-07T19:07:15.930005Z",
     "iopub.status.idle": "2025-04-07T19:07:15.950010Z",
     "shell.execute_reply": "2025-04-07T19:07:15.949805Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.930080Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16, 16)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_matrix = ntw.allneighbordistances(\n",
    "    sourcepattern=ntw.pointpatterns[\"facilities\"], fill_diagonal=0.0\n",
    ")\n",
    "cost_matrix.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a67562b",
   "metadata": {},
   "source": [
    "The expected result here is a network distance facilities points, in our case a 2D 16x16*** array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "98bf0abb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.390422Z",
     "start_time": "2023-01-10T18:23:34.384090Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.950372Z",
     "iopub.status.busy": "2025-04-07T19:07:15.950312Z",
     "iopub.status.idle": "2025-04-07T19:07:15.952551Z",
     "shell.execute_reply": "2025-04-07T19:07:15.952353Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.950365Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  3.78794131, 11.63723819,  4.99347068,  9.66917542],\n",
       "       [ 3.78794131,  0.        , 13.84929687,  7.20552937, 11.88123411],\n",
       "       [11.63723819, 13.84929687,  0.        ,  6.6437675 ,  2.66349027],\n",
       "       [ 4.99347068,  7.20552937,  6.6437675 ,  0.        ,  4.67570474],\n",
       "       [ 9.66917542, 11.88123411,  2.66349027,  4.67570474,  0.        ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_matrix[:5, :5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "41681306",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.397069Z",
     "start_time": "2023-01-10T18:23:34.392434Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.952871Z",
     "iopub.status.busy": "2025-04-07T19:07:15.952800Z",
     "iopub.status.idle": "2025-04-07T19:07:15.955156Z",
     "shell.execute_reply": "2025-04-07T19:07:15.954966Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.952863Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  3.15016768,  9.526461  ,  9.71401032,  3.00949261],\n",
       "       [ 3.15016768,  0.        , 10.67662868,  6.56384263,  4.93972891],\n",
       "       [ 9.526461  , 10.67662868,  0.        , 11.24047132,  6.51696839],\n",
       "       [ 9.71401032,  6.56384263, 11.24047132,  0.        , 11.50357155],\n",
       "       [ 3.00949261,  4.93972891,  6.51696839, 11.50357155,  0.        ]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_matrix[-5:, -5:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd231297",
   "metadata": {},
   "source": [
    "With ``PDispersion.from_cost_matrix`` we model the $p$-dispersion problem to maximize the minimum inter-facility \n",
    "cost (in this case network distance in generic units, as calculated above) while siting $p$ facilites."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "43393fcb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.515202Z",
     "start_time": "2023-01-10T18:23:34.399391Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.955598Z",
     "iopub.status.busy": "2025-04-07T19:07:15.955490Z",
     "iopub.status.idle": "2025-04-07T19:07:15.995219Z",
     "shell.execute_reply": "2025-04-07T19:07:15.994926Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.955586Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spopt.locate.p_dispersion.PDispersion at 0x152e3da90>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdispersion_from_cm = PDispersion.from_cost_matrix(\n",
    "    cost_matrix, P_FACILITIES, name=\"p-dispersion-network-distance\"\n",
    ")\n",
    "pdispersion_from_cm = pdispersion_from_cm.solve(solver)\n",
    "pdispersion_from_cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f0c9b8e8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.526089Z",
     "start_time": "2023-01-10T18:23:34.519658Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.995835Z",
     "iopub.status.busy": "2025-04-07T19:07:15.995739Z",
     "iopub.status.idle": "2025-04-07T19:07:15.998088Z",
     "shell.execute_reply": "2025-04-07T19:07:15.997888Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.995827Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A maximized minimum inter-facility distance between any two sited candiate facilities of 10.706 distance units is observed while siting facilities at 3 of the available 16 locations.\n"
     ]
    }
   ],
   "source": [
    "pdispersion_obj = round(pdispersion_from_cm.problem.objective.value(), 3)\n",
    "print(\n",
    "    \"A maximized minimum inter-facility distance between any two sited candiate \"\n",
    "    f\"facilities of {pdispersion_obj} distance units is observed while siting \"\n",
    "    f\"facilities at {P_FACILITIES} of the available {FACILITY_COUNT} locations.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad67dbb2",
   "metadata": {},
   "source": [
    "Define the decision variable names used for mapping later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0883d494",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.547112Z",
     "start_time": "2023-01-10T18:23:34.529055Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:15.998420Z",
     "iopub.status.busy": "2025-04-07T19:07:15.998359Z",
     "iopub.status.idle": "2025-04-07T19:07:16.004969Z",
     "shell.execute_reply": "2025-04-07T19:07:16.004742Z",
     "shell.execute_reply.started": "2025-04-07T19:07:15.998413Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>geometry</th>\n",
       "      <th>dv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>POINT (9.32146 3.15178)</td>\n",
       "      <td>y0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>POINT (8.53352 -0.04134)</td>\n",
       "      <td>y1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>POINT (0.68422 6.04557)</td>\n",
       "      <td>y2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>POINT (5.32799 4.10688)</td>\n",
       "      <td>y3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>POINT (3.18949 6.34771)</td>\n",
       "      <td>y4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>POINT (4.31956 7.5947)</td>\n",
       "      <td>y5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>POINT (5.1984 5.86744)</td>\n",
       "      <td>y6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>POINT (6.59891 10.39247)</td>\n",
       "      <td>y7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>POINT (8.51844 4.04521)</td>\n",
       "      <td>y8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>POINT (9.13894 8.56135)</td>\n",
       "      <td>y9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>POINT (0.09922 7.40501)</td>\n",
       "      <td>y10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>POINT (8.32388 7.60047)</td>\n",
       "      <td>y11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>POINT (7.30045 5.45031)</td>\n",
       "      <td>y12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>POINT (0.87307 10.03412)</td>\n",
       "      <td>y13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>POINT (3.93582 1.88646)</td>\n",
       "      <td>y14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>POINT (7.39003 10.43628)</td>\n",
       "      <td>y15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    geometry   dv\n",
       "0    POINT (9.32146 3.15178)   y0\n",
       "1   POINT (8.53352 -0.04134)   y1\n",
       "2    POINT (0.68422 6.04557)   y2\n",
       "3    POINT (5.32799 4.10688)   y3\n",
       "4    POINT (3.18949 6.34771)   y4\n",
       "5     POINT (4.31956 7.5947)   y5\n",
       "6     POINT (5.1984 5.86744)   y6\n",
       "7   POINT (6.59891 10.39247)   y7\n",
       "8    POINT (8.51844 4.04521)   y8\n",
       "9    POINT (9.13894 8.56135)   y9\n",
       "10   POINT (0.09922 7.40501)  y10\n",
       "11   POINT (8.32388 7.60047)  y11\n",
       "12   POINT (7.30045 5.45031)  y12\n",
       "13  POINT (0.87307 10.03412)  y13\n",
       "14   POINT (3.93582 1.88646)  y14\n",
       "15  POINT (7.39003 10.43628)  y15"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "facility_points[\"dv\"] = pdispersion_from_cm.fac_vars\n",
    "facility_points[\"dv\"] = facility_points[\"dv\"].map(lambda x: x.name.replace(\"_\", \"\"))\n",
    "facilities_snapped[\"dv\"] = facility_points[\"dv\"]\n",
    "facility_points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f4b31a0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-10-22T14:40:39.366530Z",
     "start_time": "2022-10-22T14:40:39.366518Z"
    }
   },
   "source": [
    "## Calculating euclidean distance from a `GeoDataFrame`\n",
    "\n",
    "With ``PDispersion.from_cost_matrix`` we model the $p$-dispersion problem to maximize the minimum inter-facility \n",
    "cost (in this case euclidean distance in generic units) while siting $p$ facilites.\n",
    "\n",
    "Next we will solve the $p$-dispersion problem considering all candidate locations for potential selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3ae768c1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.653494Z",
     "start_time": "2023-01-10T18:23:34.549901Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.005418Z",
     "iopub.status.busy": "2025-04-07T19:07:16.005350Z",
     "iopub.status.idle": "2025-04-07T19:07:16.042123Z",
     "shell.execute_reply": "2025-04-07T19:07:16.041865Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.005411Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spopt.locate.p_dispersion.PDispersion at 0x152e3ce60>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_metric = \"euclidean\"\n",
    "pdispersion_from_gdf = PDispersion.from_geodataframe(\n",
    "    facilities_snapped,\n",
    "    \"geometry\",\n",
    "    P_FACILITIES,\n",
    "    distance_metric=distance_metric,\n",
    "    name=f\"p-dispersion-{distance_metric}-distance\",\n",
    ")\n",
    "pdispersion_from_gdf = pdispersion_from_gdf.solve(solver)\n",
    "pdispersion_from_gdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0aa3cec1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.661088Z",
     "start_time": "2023-01-10T18:23:34.657115Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.042621Z",
     "iopub.status.busy": "2025-04-07T19:07:16.042550Z",
     "iopub.status.idle": "2025-04-07T19:07:16.044703Z",
     "shell.execute_reply": "2025-04-07T19:07:16.044469Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.042613Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A maximized minimum inter-facility distance between any two sited candiate facilities of 8.574 distance units is observed while siting facilities at 3 of the available 16 locations.\n"
     ]
    }
   ],
   "source": [
    "pdispersion_obj = round(pdispersion_from_gdf.problem.objective.value(), 3)\n",
    "print(\n",
    "    \"A maximized minimum inter-facility distance between any two sited candiate \"\n",
    "    f\"facilities of {pdispersion_obj} distance units is observed while siting \"\n",
    "    f\"facilities at {P_FACILITIES} of the available {FACILITY_COUNT} locations.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d53d6bfe",
   "metadata": {},
   "source": [
    "However, in many real world applications there may already be existing facility locations with the goal being to add one or more new facilities. Here we will define facilites $y_{11}$ and $y_{12}$ as already existing (they must be present in the model solution). This will lead to a sub-optimal solution.\n",
    "\n",
    "***Important:*** The facilities in `\"predefined_loc\"` are a binary array where `1` means the associated location must appear in the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7ca5aa68",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.679228Z",
     "start_time": "2023-01-10T18:23:34.664344Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.045079Z",
     "iopub.status.busy": "2025-04-07T19:07:16.044984Z",
     "iopub.status.idle": "2025-04-07T19:07:16.051167Z",
     "shell.execute_reply": "2025-04-07T19:07:16.050929Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.045072Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>geometry</th>\n",
       "      <th>dv</th>\n",
       "      <th>predefined_loc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>POINT (9.32146 3.15178)</td>\n",
       "      <td>y0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>POINT (8.53352 -0.04134)</td>\n",
       "      <td>y1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>POINT (0.68422 6.04557)</td>\n",
       "      <td>y2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>POINT (5.32799 4.10688)</td>\n",
       "      <td>y3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>POINT (3.18949 6.34771)</td>\n",
       "      <td>y4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>POINT (4.31956 7.5947)</td>\n",
       "      <td>y5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>POINT (5.1984 5.86744)</td>\n",
       "      <td>y6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>POINT (6.59891 10.39247)</td>\n",
       "      <td>y7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>POINT (8.51844 4.04521)</td>\n",
       "      <td>y8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>POINT (9.13894 8.56135)</td>\n",
       "      <td>y9</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>POINT (0.09922 7.40501)</td>\n",
       "      <td>y10</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>POINT (8.32388 7.60047)</td>\n",
       "      <td>y11</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>POINT (7.30045 5.45031)</td>\n",
       "      <td>y12</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>POINT (0.87307 10.03412)</td>\n",
       "      <td>y13</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>POINT (3.93582 1.88646)</td>\n",
       "      <td>y14</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>POINT (7.39003 10.43628)</td>\n",
       "      <td>y15</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    geometry   dv  predefined_loc\n",
       "0    POINT (9.32146 3.15178)   y0               0\n",
       "1   POINT (8.53352 -0.04134)   y1               0\n",
       "2    POINT (0.68422 6.04557)   y2               0\n",
       "3    POINT (5.32799 4.10688)   y3               0\n",
       "4    POINT (3.18949 6.34771)   y4               0\n",
       "5     POINT (4.31956 7.5947)   y5               0\n",
       "6     POINT (5.1984 5.86744)   y6               0\n",
       "7   POINT (6.59891 10.39247)   y7               0\n",
       "8    POINT (8.51844 4.04521)   y8               0\n",
       "9    POINT (9.13894 8.56135)   y9               0\n",
       "10   POINT (0.09922 7.40501)  y10               0\n",
       "11   POINT (8.32388 7.60047)  y11               1\n",
       "12   POINT (7.30045 5.45031)  y12               1\n",
       "13  POINT (0.87307 10.03412)  y13               0\n",
       "14   POINT (3.93582 1.88646)  y14               0\n",
       "15  POINT (7.39003 10.43628)  y15               0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "facility_points[\"predefined_loc\"] = 0\n",
    "facility_points.loc[(11, 12), \"predefined_loc\"] = 1\n",
    "facilities_snapped[\"predefined_loc\"] = facility_points[\"predefined_loc\"]\n",
    "facility_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a8a4e8cf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.741687Z",
     "start_time": "2023-01-10T18:23:34.682497Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.051539Z",
     "iopub.status.busy": "2025-04-07T19:07:16.051465Z",
     "iopub.status.idle": "2025-04-07T19:07:16.075527Z",
     "shell.execute_reply": "2025-04-07T19:07:16.075264Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.051532Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<spopt.locate.p_dispersion.PDispersion at 0x152e3fb90>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdispersion_from_gdf_pre = PDispersion.from_geodataframe(\n",
    "    facilities_snapped,\n",
    "    \"geometry\",\n",
    "    P_FACILITIES,\n",
    "    predefined_facility_col=\"predefined_loc\",\n",
    "    distance_metric=distance_metric,\n",
    "    name=f\"p-dispersion-{distance_metric}-distance-predefined\",\n",
    ")\n",
    "pdispersion_from_gdf_pre = pdispersion_from_gdf_pre.solve(solver)\n",
    "pdispersion_from_gdf_pre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3f0db1d5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.748694Z",
     "start_time": "2023-01-10T18:23:34.744627Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.076053Z",
     "iopub.status.busy": "2025-04-07T19:07:16.075980Z",
     "iopub.status.idle": "2025-04-07T19:07:16.078126Z",
     "shell.execute_reply": "2025-04-07T19:07:16.077930Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.076045Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A maximized minimum inter-facility distance between any two sited candiate facilities of 2.371 distance units is observed while siting facilities at 3 of the available 16 locations.\n"
     ]
    }
   ],
   "source": [
    "pdispersion_obj = round(pdispersion_from_gdf_pre.problem.objective.value(), 3)\n",
    "print(\n",
    "    \"A maximized minimum inter-facility distance between any two sited candiate \"\n",
    "    f\"facilities of {pdispersion_obj} distance units is observed while siting \"\n",
    "    f\"facilities at {P_FACILITIES} of the available {FACILITY_COUNT} locations.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "837d517a",
   "metadata": {},
   "source": [
    "## Plotting the results\n",
    "\n",
    "The two cells below describe the plotting of the results. For each method from the `PDispersion` class (`.from_cost_matrix()`, `.from_geodataframe()`) there is a plot displaying the facility site that was selected with a colored star."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "250da306",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.755858Z",
     "start_time": "2023-01-10T18:23:34.750701Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.078539Z",
     "iopub.status.busy": "2025-04-07T19:07:16.078480Z",
     "iopub.status.idle": "2025-04-07T19:07:16.081129Z",
     "shell.execute_reply": "2025-04-07T19:07:16.080936Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.078533Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'y0': 'darkcyan',\n",
       " 'y1': 'mediumseagreen',\n",
       " 'y2': 'saddlebrown',\n",
       " 'y3': 'darkslategray',\n",
       " 'y4': 'lightskyblue',\n",
       " 'y5': 'thistle',\n",
       " 'y6': 'lavender',\n",
       " 'y7': 'darkgoldenrod',\n",
       " 'y8': 'peachpuff',\n",
       " 'y9': 'coral',\n",
       " 'y10': 'mediumvioletred',\n",
       " 'y11': 'blueviolet',\n",
       " 'y12': 'fuchsia',\n",
       " 'y13': 'cyan',\n",
       " 'y14': 'limegreen',\n",
       " 'y15': 'mediumorchid'}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dv_colors_arr = [\n",
    "    \"darkcyan\",\n",
    "    \"mediumseagreen\",\n",
    "    \"saddlebrown\",\n",
    "    \"darkslategray\",\n",
    "    \"lightskyblue\",\n",
    "    \"thistle\",\n",
    "    \"lavender\",\n",
    "    \"darkgoldenrod\",\n",
    "    \"peachpuff\",\n",
    "    \"coral\",\n",
    "    \"mediumvioletred\",\n",
    "    \"blueviolet\",\n",
    "    \"fuchsia\",\n",
    "    \"cyan\",\n",
    "    \"limegreen\",\n",
    "    \"mediumorchid\",\n",
    "]\n",
    "dv_colors = {f\"y{i}\": dv_colors_arr[i] for i in range(len(dv_colors_arr))}\n",
    "dv_colors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "99b1906a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:34.770679Z",
     "start_time": "2023-01-10T18:23:34.758414Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.081527Z",
     "iopub.status.busy": "2025-04-07T19:07:16.081463Z",
     "iopub.status.idle": "2025-04-07T19:07:16.133136Z",
     "shell.execute_reply": "2025-04-07T19:07:16.132890Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.081521Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_results(model, p, facs, clis=None, ax=None):\n",
    "    \"\"\"Visualize optimal solution sets and context.\"\"\"\n",
    "    if not ax:\n",
    "        multi_plot = False\n",
    "        fig, ax = plt.subplots(figsize=(6, 6))\n",
    "        markersize, markersize_factor = 4, 4\n",
    "    else:\n",
    "        ax.axis(\"off\")\n",
    "        multi_plot = True\n",
    "        markersize, markersize_factor = 2, 2\n",
    "\n",
    "    ax.set_title(model.name, fontsize=15)\n",
    "    facility_count = len(model.fac_vars)\n",
    "    fac_sites = {}\n",
    "\n",
    "    plot_clis = isinstance(clis, geopandas.GeoDataFrame)\n",
    "    if plot_clis:\n",
    "        cli_points = {}\n",
    "\n",
    "    for i, dv in enumerate(model.fac_vars):\n",
    "        if dv.varValue:\n",
    "            dv, predef = facs.loc[i, [\"dv\", \"predefined_loc\"]]\n",
    "            fac_sites[dv] = [i, predef]\n",
    "            if plot_clis:\n",
    "                geom = clis.iloc[model.fac2cli[i]][\"geometry\"]\n",
    "                cli_points[dv] = geom\n",
    "\n",
    "    # study area and legend entries initialization\n",
    "    streets.plot(ax=ax, alpha=1, color=\"black\", zorder=1)\n",
    "    legend_elements = [mlines.Line2D([], [], color=\"black\", label=\"streets\")]\n",
    "\n",
    "    if plot_clis and model.name.startswith(\"mclp\"):\n",
    "        # any clients that not asscociated with a facility\n",
    "        c = \"k\"\n",
    "        if model.n_cli_uncov:\n",
    "            idx = [i for i, v in enumerate(model.cli2fac) if len(v) == 0]\n",
    "            pnt_kws = {\n",
    "                \"ax\": ax,\n",
    "                \"fc\": c,\n",
    "                \"ec\": c,\n",
    "                \"marker\": \"s\",\n",
    "                \"markersize\": 7,\n",
    "                \"zorder\": 2,\n",
    "            }\n",
    "            clis.iloc[idx].plot(**pnt_kws)\n",
    "        _label = f\"Demand sites not covered ($n$={model.n_cli_uncov})\"\n",
    "        _mkws = {\n",
    "            \"marker\": \"s\",\n",
    "            \"markerfacecolor\": c,\n",
    "            \"markeredgecolor\": c,\n",
    "            \"linewidth\": 0,\n",
    "        }\n",
    "        legend_elements.append(mlines.Line2D([], [], ms=3, label=_label, **_mkws))\n",
    "\n",
    "    # all candidate facilities\n",
    "    facs.plot(ax=ax, fc=\"brown\", marker=\"*\", markersize=80, zorder=8)\n",
    "    _label = f\"Facility sites ($n$={facility_count})\"\n",
    "    _mkws = {\"marker\": \"*\", \"markerfacecolor\": \"brown\", \"markeredgecolor\": \"brown\"}\n",
    "    legend_elements.append(mlines.Line2D([], [], ms=7, lw=0, label=_label, **_mkws))\n",
    "\n",
    "    # client-facility symbology and legend entries\n",
    "    zorder = 4\n",
    "    for fname, (fac, predef) in fac_sites.items():\n",
    "        cset = dv_colors[fname]\n",
    "\n",
    "        if plot_clis:\n",
    "            # clients\n",
    "            geoms = cli_points[fname]\n",
    "            gdf = geopandas.GeoDataFrame(geoms)\n",
    "            gdf.plot(ax=ax, zorder=zorder, ec=\"k\", fc=cset, markersize=100 * markersize)\n",
    "            _label = f\"Demand sites covered by {fname}\"\n",
    "            _mkws = {\n",
    "                \"markerfacecolor\": cset,\n",
    "                \"markeredgecolor\": \"k\",\n",
    "                \"ms\": markersize + 7,\n",
    "            }\n",
    "            legend_elements.append(\n",
    "                mlines.Line2D([], [], marker=\"o\", lw=0, label=_label, **_mkws)\n",
    "            )\n",
    "        # facilities\n",
    "        ec = \"k\"\n",
    "        lw = 2\n",
    "        predef_label = \"predefined\"\n",
    "        if model.name.endswith(predef_label) and predef:\n",
    "            ec = \"r\"\n",
    "            lw = 3\n",
    "            fname += f\" ({predef_label})\"\n",
    "        facs.iloc[[fac]].plot(\n",
    "            ax=ax, marker=\"*\", markersize=1000, zorder=9, fc=cset, ec=ec, lw=lw\n",
    "        )\n",
    "        _mkws = {\"markerfacecolor\": cset, \"markeredgecolor\": ec, \"markeredgewidth\": lw}\n",
    "        legend_elements.append(\n",
    "            mlines.Line2D([], [], marker=\"*\", ms=20, lw=0, label=fname, **_mkws)\n",
    "        )\n",
    "        # increment zorder up and markersize down for stacked client symbology\n",
    "        zorder += 1\n",
    "        if plot_clis:\n",
    "            markersize -= markersize_factor / p\n",
    "\n",
    "    if not multi_plot:\n",
    "        # legend\n",
    "        kws = {\"loc\": \"upper left\", \"bbox_to_anchor\": (1.05, 0.7)}\n",
    "        plt.legend(handles=legend_elements, **kws)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb124be7",
   "metadata": {},
   "source": [
    "### P-Dispersion built from cost matrix (network distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "05504b98",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:35.264726Z",
     "start_time": "2023-01-10T18:23:34.773148Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.133596Z",
     "iopub.status.busy": "2025-04-07T19:07:16.133505Z",
     "iopub.status.idle": "2025-04-07T19:07:16.265142Z",
     "shell.execute_reply": "2025-04-07T19:07:16.264874Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.133589Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 529,
       "width": 706
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(pdispersion_from_cm, P_FACILITIES, facility_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f774853",
   "metadata": {},
   "source": [
    "### P-Dispersion built from geodataframe (euclidean distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "39baa5ed",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:35.681008Z",
     "start_time": "2023-01-10T18:23:35.267574Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.265548Z",
     "iopub.status.busy": "2025-04-07T19:07:16.265465Z",
     "iopub.status.idle": "2025-04-07T19:07:16.392320Z",
     "shell.execute_reply": "2025-04-07T19:07:16.392072Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.265539Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 529,
       "width": 706
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(pdispersion_from_gdf, P_FACILITIES, facility_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da6e7401",
   "metadata": {},
   "source": [
    "### P-Dispersion with preselected facilities (euclidean distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1a5e68dd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:36.142414Z",
     "start_time": "2023-01-10T18:23:35.683575Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.392750Z",
     "iopub.status.busy": "2025-04-07T19:07:16.392677Z",
     "iopub.status.idle": "2025-04-07T19:07:16.526008Z",
     "shell.execute_reply": "2025-04-07T19:07:16.525759Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.392742Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 529,
       "width": 706
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(pdispersion_from_gdf_pre, P_FACILITIES, facility_points)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d82bea6b",
   "metadata": {},
   "source": [
    "-----------------------------------\n",
    "\n",
    "## Comparing solution from varied metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "47c49823",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-01-10T18:23:37.136128Z",
     "start_time": "2023-01-10T18:23:36.148889Z"
    },
    "execution": {
     "iopub.execute_input": "2025-04-07T19:07:16.526471Z",
     "iopub.status.busy": "2025-04-07T19:07:16.526383Z",
     "iopub.status.idle": "2025-04-07T19:07:16.896917Z",
     "shell.execute_reply": "2025-04-07T19:07:16.896687Z",
     "shell.execute_reply.started": "2025-04-07T19:07:16.526462Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LlixJ6/WorK8mTZpU45dNtj569eqV8TjU3/72t6R9+/YZP690jpe/+tWvklatWqW9zry8vOT73/9+UlpamtFzALYf8sbq+6I68kZ5Y7oPeeOnD3lj1eSN8sZtyRsrf8gba3405byxsmKIW265Je3rv/322y+t17Sy8+3ChQuT4cOHV7v+yr7L1BCf70+fPj3p3bt3Wuvu2rVr8tJLL9W6GKK+n09jKYYoLi5OLrroorS3/61vfSuj/X3p0qVpX69vfXTr1i15/vnn095GQ5wXqF/1ez89oF5t2rQpTjzxxJg+fXpEROTn58d+++0X/fv3j82bN8ebb74Zb7/9dln7LVu2xDe/+c3Iy8uLCy64IGtxXXfddfHDH/6wwvy99947dtlll4iIeOedd2LmzJkREfHMM8/E6NGjo1u3blmJZ86cOXHSSSfFhg0bUuZvvRVcly5dIiJi9erVMXfu3JgzZ05s2bKlVtsaPXp0PPPMM2XTe+21V9ktMLd9zhERSZLEL37xiygpKYlrr722xnUvXbo0jjvuuHj11VdT5rdp0yb22Wef6N27dxQUFMSHH34YU6ZMKXsO69evj9NPPz3+9re/xVe/+tWMns9ll10Wt912W9n04MGDY9CgQdGuXbtYtGhRTJkyJaV9Q/Z1TZ544ok45ZRTYuPGjSnz+/TpE3vvvXd07NgxFi1aFBMnToxNmzaV/f/hhx+Oww8/PMaNG5fR7fFKS0vjrLPOiocffjgiIgoKCmK//faLHXfcMQoKCuKdd96JadOmRZIkZctcfvnlseeee8bxxx9fx2ebvvvuuy/OP//8sjj69esXn/nMZ6JTp06xdOnSmDhxYqxZs6as/fjx4+OCCy6Ie++9t8Z1b9iwIU4++eR46qmnUuYXFhbG0KFDo2/fvtGqVauyW+WtX78+Ij65fe53v/vdWLlyZVx99dX192S3scMOO8RnPvOZeP311yMiYuzYsZEkSZW35lu4cGG88cYbFeY//fTT8Y1vfKPK7Tz99NMpr/ExxxxTZdt58+bF4YcfHvPmzUuZ36FDhzjwwAOjR48esWLFipg6dWosX7687P+zZ8+Ogw8+OJ555pnYe++9q1x/ZTJ9T2dq0aJF8dnPfjZeeeWVsnn7779/PPzww9GrV686rbsqzfmck6nytzgsKCiIXXfdNXbeeefo2LFj5OXlxfLly+O1116Ljz76qKzd8uXL48QTT4znn38+hg8fnvE2s3lsfO655+Lkk0+Ojz/+OGV+ixYtYp999ok+ffpE27ZtY9WqVTF79ux47733UrZVnUceeSTOOOOMsmPVVr169Yq99947unbtGuvWrYtZs2bFnDlzyv4/ffr0GDZsWEycODH69u2b1rYAaL7k9emR18vrt9Uc8/rJkyfHiSeeGMuWLUuZ361bt9hnn32ie/fusWnTppgzZ05Z3hsR8f7778chhxwSzz33XAwdOjSrMWYim9fx2VJaWhpf+MIX4tFHH02ZX1hYGMOGDYs+ffrE2rVrY+bMmfHhhx9GxCfH0u7du2e8rYY4VpTPD9u2bRtDhgyJXr16RceOHWPz5s3x0UcfxYwZM1LGiWbMmBFHHHFETJs2Lbp27Zrx8/rqV78ac+fOjYiIdu3axYEHHhg9e/aMTZs2xYwZM+K9994ra79mzZo47bTT4vXXX4/evXtntK1MrFu3Lo455piYOnVqyvy2bduW3cp+5cqV8eqrr8aSJUuitLQ0LrrooujRo0fWYrr22mvjxhtvTJnXokWL2GuvvaJfv37Rrl272LBhQ6xcuTLeeuutWLhwYdZiKa/8vtOxY8fYfffdo0ePHtGhQ4fYuHFjzJ8/P2bOnJlyLnn22WfjuOOOi5dffjlatWqV0TbffvvtGD16dKxYsSIiIrp06RL7779/dO/ePdatWxdTp05N6YNFixbFKaecEjNnzox27drVuP7vfve7ccMNN1SY37Vr1xg6dGgUFRVFSUlJLF26NGbOnBkrV65MK+7S0tL46le/GnfeeWfK/Pz8/Nhzzz2jf//+0a5du1i6dGlMnjy57JiYJElcf/31sWTJkrjjjjvS2hawfZM3pkfeKG/clrzxU/LGhiNv/IS8Ud4ob9x+88b77rsvLrroorLjbY8ePWLfffeNzp07x+LFi2PixIkpr+krr7wSRxxxRLz44otl1wfp2LRpU5xyyikxadKkiEg930ZEfPDBBynfSdmqIT7fnzVrVhx11FEp3+GJiOjZs2fss88+FfpixYoVcdJJJ8X111+f9vNvyOeTK9/5znfilltuiYiIvLy82GuvvWLAgAHRqlWrmDdvXkyZMiWKi4vL2t9yyy2xxx57xDe/+c0a1/3OO+/EqFGjUs4XEZ98F2u//faLnj17RklJSbz//vvx6quvlh2zli9fHsccc0w8/PDDMWrUqGq30RjPC6Sh4esvgKqUrxLs0qVL2d+jR4+utKpv8uTJyX777ZeyXMuWLdOq7q+NiRMnVrgN1qhRoyr9FfM333wzOfLIIyt9PhH190sgZ555ZkrbI488ssJt37a1cePG5Mknn0y+8Y1vJLvttluV7cpXLm4b/9FHH5289dZbFZZ56623Kq08rOkXt0tKSpKjjjoqZZnevXsnf//735ONGzdWaL9y5crkiiuuSKnGbd26dbXPO0lSqw87dOhQ9veJJ56YzJo1q0L71atXJ0uXLi2bzlZfl4+tpsrIDz/8MOnatWvKMjvvvHPy6KOPVqgU/fjjj5Mf/ehHFW6redZZZ1W7jfL74NZb1RUUFCQ//OEPk2XLllVY5q233qpwF4CBAwdmtVp728r3du3ald0e87DDDksmT55cof369euTH/7whxX20RdeeKHGbX3lK19JWaZTp07J73//+2T16tWVbuc3v/lN0rp167L2eXl5yWOPPVah7cqVK5O5c+cmc+fOTYYNG1bhOFHVY9GiRSnr+d73vpey7NSpU6t8LnfccUel1bqdO3eu9vaM5513Xkr79957r9J2W7ZsqVDF3r59++SGG26ocOvQLVu2JP/85z8r3A5x0KBBNf5qTV3f00mS/i+RTJs2Lenbt2/KNr/whS8k69atqzbGumgO55xFixaV7dPbrnfYsGHV7v+V/QrCfffdl3Tu3Dm56KKLkieffLLa29S+/PLLyRFHHJGyzZ122inZtGlTlctU1lfZPDa+++67FV7Hbt26Jb/73e+Sjz/+uNJlli5dmvzlL39JDjrooGp/GeiNN95I2rVrl7Lu4447Lpk0aVKl7V999dVkxIgRKe0PPfTQjG7nCkDzIK//lLxeXl8def2nFi1alPTq1atCPvDUU09Vut05c+YkJ598ckr7XXfdtdLcfKuG/IXPbF7HZ/MXPn/961+ntM/Ly0u++93vVrh9emlpafLEE0+U/WJby5YtU3KLmuJqqGPFt771rWSXXXZJrrnmmmTq1KlJSUlJpe02b96c/Oc//6nwC3Tp3HGz/H619T3WrVu35C9/+Uul+eUTTzyRFBUVpSz31a9+tcZt1cWFF16Ysr1WrVolv/zlL5O1a9emtCsuLk7uvvvupEePHklEVDhG1dcvfK5atSplvKygoCC5+uqrq71z68KFC5O///3vyciRIyv88vSWLVvKxgquv/76lBiuv/76ascWtmzZUmFbJ554YrL33nsn119/ffLGG29UGdO6deuSv/71r2X9tfWx9ZdvM+mrrftOv379kvvuu69Crl1aWpr861//qnAn3J/97Gc1but3v/tdhXP68OHDk7Fjx1b5vpg+fXpy5ZVXJkVFRdUeL6+++uoK+9ZVV11V6a9ibtmyJfn73/9e4fh466231vgcgO2PvPFT8kZ5Y3XkjZ+SN8ob5Y3yRnmjvDEbyt8ZYuu2e/bsmdx7770V+nnt2rXJz372s6Rly5Ypy5199tnVbqf8+Xbr9Ul+fn5y6aWXVnq+/eCDD1L2v4b4fH/z5s0V7tbWq1ev5D//+U+FfWHNmjXJ1VdfnRQWFqb03dZHTXeGyNbz2fb9Pnfu3OQ73/lOyjJ33313pe/18t9NqsudIbb97tPXvva15MMPP6ywzPz585MTTjghZbmOHTtWOO6Wt27duuQzn/lMynKDBw9O7r///kpf24ULFyb/93//VyG+mu4U0lDnBeqXYghoRMqf/Lc+Lr300mqXW7duXaUnvGwof7u60aNHV3nxlySfHPS/8IUvVPq86mPwq7S0NOXiYNCgQZUmgFVZv359lf+r6tZRp59+eo3P+Ytf/GLKMv379680SdiqfOK87777VnqxV959992X5OXllS13xBFHVNu+sudzwQUXpDU4k82+Lh9bTRcD5W89udtuuyWLFy+udpl77rmnwq3cHnnkkSrbV/Z+LCgoSP73v/9Vu52PP/442XHHHVOWe+aZZ6pdpi4quw3gWWedVe3+liRJhQveL33pS9W2/89//pPSvl+/ftW+h7caP358SqI+cODAat8/ld2GL12PP/54yrLXXnttlW3POuuslIRi233j5ZdfrnK5Pn36pDyXqtxwww0psbRr167a9SZJksyaNatCQcRll11W7TJ1eU9vlc6g4MMPP1zhlpANcVvG5nTOSZK63y5vyZIlGRWnlJaWVihyqmmgtyGPjQcffHCFY/3777+f9vMrXzC1VUlJSYUE+eqrr65xfVu2bKmwf915551pxwNA8yCv/1RjuMaS16dqTNez8vpPlf/Q5/zzz0+r6Pbb3/52ynLXXHNNlW0b8kst2bqOT5Lsfall/vz5KWMXEZH86U9/qnb9ixcvTgYNGlRhH6sproY6VsybN6/a41x5K1asSPmwNz8/P3n33XerXab8fhXxyQfE77zzTrXLTZkyJeXLlW3btq32S1l1MWXKlJR+a9GiRY3HgLfeeqvCFzXSOa6l+6WWe++9N63zY1WqOxZn+mWuyqQz3retefPmpRwzO3bsWOUX2LYq31cRkeyxxx6VfhlkWw8++GDKMjvttFO157833nijwhciv/Wtb6X93li/fn2yatWqSv83ceLElHNSly5dkldffbXGdc6ePTvp1q1b2XKdOnXK2v4PNF7yxk/JG+WN1ZE3fkremEreWDl5Y+3IG2/PaN1JIm/cVlPPG8t/Pycikh122CGZM2dOtcs9+OCDFQpnqzsPVnX9++9//zutOBvq8/3f/va3FY5XNR3n7r///grXHjW9bxvy+wq1Pb/XpRhi6+OPf/xjjc+nfMH33/72t2qXKV+kcPzxx9d4/ZkkFV/br3zlK1W2bcjzAvVLMQQ0IpWd/Pfbb7+0LrI+/PDDCl9UfeWVV+o1vrFjx1a4aEznS5erV69OevfuXeG51cfg15IlS1La1TRQmInKTtZ9+/at8Zfak+STCtBtvzQdEcmYMWMqbbt+/fqUyvZOnTolCxcuTDvO8if66l738s9nyJAhNf4K+FbZ7OvysVV3MfDOO++kXEgWFBQk06ZNS2sbF110Ucp2qhsAqOz9eOWVV6a1nZtvvrlWy9VG+WKIgQMHpnWht3z58pRq7d69e1fZtrS0NOVCvEWLFsmMGTPSjrH8gE1V74UkqVsxxPr165NWrVrV+PqWlpamXITefvvtyQEHHFA2XdVA4BtvvJES2ze/+c1K25WUlCQ777xzStubbropredw//33pyzXsWPHahPburynt6ppUPD3v/99ynuusLCwxgSkPjS3c06S1L0YojbWrVuX8n44+uijq23fUMfGp556KqVt+/btaxx0Sdd9992Xsu7TTz897WXXrFmT0l977rlnvcQEwPZDXv+pxnCNJa9P1ViuZ+X1n5oyZUrKdoYPH572h63FxcUpX1IrKiqq8ktKDfWllmxexydJ9r7U8pOf/CSl7amnnppWPJMnT67wYWd1cTXksaI2pk6dmrL+X/ziF9W2r+xLLTX9GvJWp512Wq2Wy9SXv/zlWh33yo/PpJOnp/ullvLjZK+99lqGz6pq9fGlltoo31//+te/qm1fvq9atGhR6a9UV2b//fdPWbayXyjfatsfQ4n45APy+vphjxNPPDFl3ZXdDbcq5X905re//W29xAQ0HfLGT8kb5Y1VkTd+St6YGXmjvDFT8sbb623d1ZE3Ns68sbJiiP/+979pLVu+4O6zn/1slW0rO99mcseXhvh8v6SkJOnfv3/Kdmr6AvxW5a89IqovhmjI7yvkqhiiprtzbfXII4+kvdyCBQtSvufWv3//jH4sdNvi0pYtW1ZZXNmQ5wXqV34AjdrVV18d+fk1v1X79u0bX//611Pm3XHHHfUayz/+8Y+U6csvvzzatm1b43IdOnSIH/zgB/UaS1WWLFmS1fVffvnl0b59+xrbtW/fPi6//PKUeVW9HnfffXcsXbq0bPq73/1u9OrVK+2YLr300pTphx9+OO1lv/e970XLli3Tbr+tbPd1Vf75z39GaWlp2fTpp58eQ4cOTWvZa665Jlq1alU2PW7cuJg3b15ay7Zp06ZCX1flpJNOSpmeNm1aWsvVh0svvTTatGlTY7uuXbvGwQcfXDa9cOHCKl/TcePGxeuvv142ffbZZ8dee+2Vdkzf+ta3onXr1mXTmeyjmWjTpk0ccsghZdPjx4+PdevWVWg3c+bMlOd6zDHHxLHHHls2/dRTT1W6/qeffjpl+phjjqm03QsvvBBz584tm+7bt29ceOGFaT2HU089Nfbff/+y6dWrV8eDDz6Y1rIRdXtPl1dcXBzf/OY345JLLil7z3Xu3DmeeOKJOP/88+tlG9VxzmkYbdu2jeOPP75setKkSSnH2Jpk69j4pz/9KWX60ksvjYEDB6YdV3VuvPHGsr/z8vLiV7/6VdrLtm/fPi644IKy6ddeey3ef//9eokLgO2XvD4z8np5fXW2t7x+22vTiIhrr702reNFRERBQUF85zvfKZteunRpTJgwoV7jy1Q2r+Ozqfyx8ZprrklruQMOOCA+97nPpb2dXB4r0rHffvtFv379yqZffvnljJYfNmxYlWMl5TXEe2zjxo1x3333lU23atUqrrzyyrSWPfXUU9M+LtXV9jC28NnPfjblXJTpvnPqqafGkCFD0mqb7r6zYsWKuPfee8um8/Pz46abboq8vLyMYqvMu+++G48++mjZ9OGHH54ytlKT0047LeW9lq2xUqBpkTdmRt4ob6yOvPFT8sb6I2/8hLzxU/LGzMgbm0beuN9++8XnP//5tNr+9Kc/TXlNH3300ZTjV01++MMfpt22IT7ff+GFF1LmH3DAARX2par89Kc/jcLCwrRjag7fV/jJT36SVrtjjz02ZT+q7lh/6623xubNm8umr7rqqrTylK22PUdu3rw5nnjiiQptmsp5gcophoBGrEuXLnHcccel3f6ss85KmX7ppZfqNZ5t15eXlxdnnHFG2sueddZZ9XLBWF737t2je/fuZdP3339/vPjii/W+nYhPnvOZZ56ZdvvRo0enPOfx48dHkiQV2pX/gnUm/RoRMWDAgNhpp53KpjN5/ulexEY0bF9Xp/x+/aUvfSntZbt27Ronnnhiyrzx48entezw4cOja9euabXt169fygVXQyan5Z9fdconi1XFWdd9tG3btnHggQeWTWdzv9m2qGHz5s3x/PPPV2izbbHD7rvvHn369ElZbtKkSbF69epqlysoKIgjjjii0hjK76OjR49Oe1AyIuKcc86pdn3VyeQ9XZ2PP/44TjzxxLj11lvL5u2yyy4xYcKEOPLII+tlGzVp7uec+rZx48ZYunRpzJs3L95///2UR4cOHcrarVmzJubPn5/2erNxbCwtLY3nnnsuZd62CX1drFu3LiZOnFg2fcABB8TOO++c0TrKv/ebyj4AQG7I62smr5fXN+e8/plnnin7e4cddojDDz88o+Ub07VpNq/js2n+/PkpX4zaa6+9Yo899kh7+bPPPjvttrk8VmyVJEmsXbs2Fi1aVCE3fP/996OoqKis7ZtvvpnRurMxJlUXU6dOjY0bN5ZNjxo1Ku1jQERmr20mdtttt5TpH/3oR7F27dqsbKs+lZaWxpo1a2LhwoUV9puFCxem9G1j2Heef/75KCkpKZs+5phjYpdddskorqpse+yOyPy9nJeXl3K8nzRpUsqH+UDzI2+smbxR3ihv/IS8MTfkjfLGqsgbU8kbP9VU88by15nV6datW8r3bEpLS9MuuNtjjz1i1113TattQ32+X9n3fNJVVFSU0hfVaQ7fVxgwYECF41hVCgsLU9531R3rtz1HFhQUxGmnnZZRXIceemi0aNGibLqyfmus5wXS06LmJkCu7LfffikH4Zrsvffe0bp167KD8syZM2Pz5s1lFXSrVq2KVatWpbWuzp07R+fOncumV61aFe+++27Z9MCBA6Nbt25px1ZUVBQ777xzvPfee2kvk46tA1I333xzRERs2LAhjjjiiDjttNPizDPPjKOPPjqtX+5Ixy677JIy+FOT7t27x4ABA8r6bcWKFfHee+9VuHje9oKqZcuW0apVq4yrNrt27RoffPBBRETK61Sdvn37piSqNWnIvq7O1KlTU6aHDx+e0fIHH3xwPPDAA2XTU6ZMSeuCfvfdd89oO507d47169dHxCdfLK/MsmXL0k5au3fvXmP/tm/fPnbccce0Y+zSpUvKdFVxlr/o79q1a8b7aMeOHcv+fv/996O0tDSjAoF0HXPMMSkV5E8//XSccMIJKW22vUDempAMHz482rdvH2vXro3i4uIYN25cyuDwli1bUgorDjzwwJRj5LbK76Pb3oEjHeXbT5kyJa3lMn1PV2Xu3Llx0kknxaxZs8rmHXroofHggw9mdAx0zsmtSZMmxX333RcTJkyIN954o8r3d2VWrlyZMlBanWwcG998881YuXJl2fTgwYMz+tWb6kycODG2bNlSNj1gwICMj2fl75yR7nkXgOZJXl8zef0n5PXp217y+nfffTcWLVpUNj1w4MC0f610q/Ifguby2jSb1/HZVH5/HDZsWEbLZ9I+F8eKzZs3x1NPPRUPPPBAvPrqq/HWW2/Fpk2b0trWtq9nOjJ5j6U7JjV//vwoLi5Oa519+/ZNOec25GubiaOOOip69OhR9uHuxIkTY9ddd43zzz8/TjnllNhnn32yMmaWqXXr1sUjjzwSDz30UEyfPj3mzJmT9mvRGPad8r8yOnLkyIxiqk75sdIePXpk/F7e9ouTGzdujIULF0b//v3rITqgKZI31kze+Al5Y/rkjZ+SN9advLFqjeHaX96YO/LGqjVE3liXa76q1OY98Mgjj5RNT5kyJa274eyzzz5pb6OhPt+vj+PBtncDqUpz+L5CptdT275nq3q/bty4MV555ZWy6R133DGWLVsWy5Yty2hbnTt3LlsmW/sBuaMYAhqxQYMGZdS+RYsW0b9//3jrrbciIqKkpCSWL19elkD+4Q9/SPt2fVdddVVcffXVZdOLFy9O+X+6FZrbGjRoUL0PfkV8cuvYxx9/vOwkVVJSEvfee2/ce++9UVBQEEOHDo3hw4fHoYceGocddlitE+pMX4+IT/pp25PnkiVLUga/SktLY+HChWXTmzdvrnOl8YoVK9Jq16NHj4zX3VB9XZXNmzenXPgUFRVVSGRqUr76NN1fEMh0O9veAm3bC9ltXXbZZXHnnXemtb7bb789zjvvvGrb1CXGiKrj/PDDD1OmDzrooIy2U15paWmsWrUqo+rZdO2zzz5RVFRUdvu9be/mEPHJBfK21b1biyEKCwtj5MiRZYnaU089lVIMMX78+Fi3bl3ZdHW37yy/T2V67KjtPlqb93R5K1asiGHDhqXcvvDss8+O2267LeWWwulwzsnOcbAmr7/+enzrW9+KF154odbryKRwIhvHxm0H9iMio1/XqUn549k999wT99xzT53Wme55F4DmSV6fHnl9Knl99baXvL78telLL72U8a+AlZfLa9NsXsdnU12PjTvuuGPKlxGrkotjxUMPPRSXXHJJzJ07t1brzyQ3jMjsPZbumNShhx6a9pe95s6dm/KlgLq+trU5Z6Sjbdu2ceutt8Zpp51W9uH1Rx99FL/85S/jl7/8ZXTu3DmGDx8ew4cPjxEjRsRBBx0UrVu3zkosVfnb3/4WV155Zcr4UCYaw77TkGMLmf4SYWVWrFihGAKaMXljeuSNqeSN1ZM3Vk3emDl5Y9Uaw7W/vFHeWF5zyRvrcs1XlUz36fLvmWx8t6WhPt9vqONBc/i+Ql2up6oqqProo49S3svvv/9+Vq6JGut5gfTkvkwQqNK2v6Serk6dOqVM19cJr3xVbn3EVl+6desWEyZMiFNPPbXC/0pKSuKVV16Jm2++Oc4888zo06dPHHzwwXHbbbdVecFblWy8HitXrqxQsVlXa9asSatdhw4dMl53Q/V1Vcrvh7XZp2r7HmkMlfU1yVaMy5cvr/d1prufZiovLy+OOuqosulZs2bFggULyqZffPHFsoGmVq1apdxacNvb1pUvoih/S9LqiiHqup+2a9cu5Rcp0t1Ha/OeLm/NmjUpAxadO3eO//f//l/GhRB15ZxTOy+99FIcfPDBdSqEiKj4SwLVycZxp/wxJ9NkOZN114dsHc8A2D7I69Mjr08lr6/e9pLXb2/Xptm8js+mhjo2NvSx4g9/+EOcfPLJtf5CS0REkiQZtW9s77G6vrbZOudFRJxyyinxxBNPxMCBAyv8b9WqVfH444/HT3/60zjiiCOiqKgozj777LTvHFpXl1xySfzf//1frb/QEpHZuEKEsYUIYwvQ3Mkb0yNvTCVvrJ68sWryxszJG6smb5Q31pa8MXMNcfyu63sgG99taai+bKjjQVPdNzLREO/X+pDL/YDsaFxXGUCKvLy8RrGOhlxvbRUVFcX9998fr732WvzgBz+IPffcs9IYkySJCRMmxNe+9rXYc889Y8aMGWlvIxuvR/nbUjYFDdHXVSmfTDfm98j2JBv7aaYDI5koX6iwbSHDtn8fcsghKbcW3Ha5d955J+VWdNsu16FDh2rvjlHf+2lD7qM9evRIuW3bqlWrYsSIETFnzpwGi6Eyje19msvjYFVWr14dp59+ekrC1qlTp7jgggvi7rvvjmnTpsXixYtj3bp1UVJSEkmSlD2uuuqqrMVVH+rz9W9qxzMAmr7GnLM0x2ssef0n5PWNw/Z+bdpUX5dsxd2Qx4pJkybFpZdemjKvf//+ceWVV8YjjzwSs2bNihUrVsSGDRuitLQ0JT/c9kcjtjeZvrbZ3oePOeaYePPNN+OBBx6IM888M3r27Flpu7Vr18Zdd90VBx54YHz1q1+NDRs2ZC2m++67L/7whz+kzNtjjz3i5z//eTz55JMxe/bsWLVqVWzcuDFlv0mSJPr165e1uOqDsQWgMWvM18SN7ZpO3thw5I2Nw/Z+3dFUXxd5o7yxtu0zJW9sWPLGusvGe2J768vt7fk0lFz1W2M7L1A9xRDQiGV6W7DKltm2cvXqq6+ucLFZ1aP87bHKV8DWR2zZ8JnPfCauu+66mDlzZqxYsSKeeOKJ+MlPfhIjRoxI+aX1iIjZs2fHUUcdlXale32/HhGf/LLGtgYNGpT2a1TdoyFks6+r0rVr15TpbLwmDemOO+5I+zXd9paoDa179+5lf7du3brCgEdtHtm87fu2d3iISL3Lw7Z/l2+32267xU477VSh7YoVK+KVV14pm3/EEUdU2Me3Vdf9dN26dSm3fmvIfbRNmzbxzDPPxNFHH102b968eXHooYfGtGnTMlqXc052joNVufXWW1Nu5Tls2LCYM2dO3HrrrXHmmWfG0KFDo0ePHtG2bdsKlfirV6/OSky1te0xJ6J+b+tYft3XXnttnY9nd9xxR73FB8D2R16fOXm9vL4m20teX/7a9Otf/3qd95vnnnuu3p9jSUlJWu2yeR2fTQ11bGzIY8U111yT8guLX//612POnDnxy1/+Mk488cQYMmRIdOnSJVq3bl3hA7rGlh++//77tR5rqutru2rVqjpGX7MWLVrEKaecEnfffXd89NFHMWfOnPjHP/4RF1xwQQwYMKBC+9tvvz3OPvvsrMVT/scSfv7zn8drr70WP/7xj+PYY4+NQYMGRadOnSq9g2hj23cacmxh4cKFdX4vjxw5st7iA5oeeWPm5I3yxprIG+WN9UneKG+sirxR3pjuurORN9blmq8qmb5GDXG+bajP98vHXte+yPXz2d6U77djjz22zv227Q/kbtUUzgtUTTEENGJvv/12Ru2Li4tTDtQFBQUVBgtqq0ePHinTtfmV8EyfT1117tw5Ro0aFT/72c/ihRdeiMWLF8f111+fckui5cuXx09+8pO01leb+Mv3U/l+bNmyZcqJdO7cufV2C9GGVN99XZWWLVumrHPJkiUZX0jMnj07Zbr8a0JF2/7CwMaNG+ODDz7IYTQ169u3b+y2225l088880wkSRJLliyJmTNnls0vXwwRkXp3iK3FEGPHjk0ZDCp/54nyyu9TmR47cr2Ptm/fPh555JH4whe+UDZvyZIlccQRR8SLL77YIDE452TuoYceKvs7Ly8v7rrrrigqKkpr2YULF2Ylptrq1atXyvSsWbPqbd3lfzGlofcTAJofeX3dyOsbjry+4TXktWn5LyltW4Bfk/K3Bq9KNq/js6n865DpsfHDDz+MjRs31tiuoY4V69ati7Fjx5ZNDxgwIG655ZZqf9RhW9sW2Td1dX1tc5EvDhw4ML785S/HrbfeGu+++25MmzYtRo8endLmwQcfjGeeeabetz1nzpx48803y6YPO+yw+PGPf5zWL9pt2LCh0X3Ya2wBaErkjXUjb2w48saGJ29sHOSNqeSNn5I3yhur0lTzxkzjrOkaqD40VF821PGgqe4buba97Qdkh2IIaMReeeWVjJLMGTNmpCRRe+21V6XVtrXRpUuX2GWXXcqm33nnnVi+fHnayy9dujRrv4adrq5du8Zll10WTz75ZMrF+MMPP5zyReeqvPvuu7Fs2bK0t7ds2bJ47733UrZfWWX2wQcfXPb3li1bsvJrDA2trn1dnf333z9lesKECRkt//LLL6dMH3DAAXWKpznYdh+NSL27Qn2rr1uGbVvosHTp0pg+fXo8/fTTZb9+UVRUFEOHDq2w3LaFDs8++2yUlpZWeL41FUOU30fL73M1aQz7aKtWreI///lPfPWrXy2b9/HHH8eoUaPisccey/r2nXMyt20SNmTIkErPN1XJ9DiabUOGDEn58G727Nnx0Ucf1cu6hw8fnvJ6bHtcAIBskNfXL3l9w5HXZ98ee+yR8gWfCRMmxJo1a7KyrY4dO6ZMZ/Lh8xtvvJFWu2xex2dT+f1x4sSJGS0/adKktNs2xLFi3rx5KbeNP+6449L+Qst7773XJF6zdDXka5stQ4cOjbvuuisuvPDClPkPPvhgpe3rMq5W/sPdk046Ke1lJ0yY0Ohy60MOOSRluj7fbw05Vgo0D/LG+iVvbDjyxuyTNzYO8sZPyRtTyRvljVVpqnljXd8D2TjfNtTn+w11PPB9hdrp2LFj7LHHHmXT77//fq0Kt2uyPZwXmjPFENCIrVy5Mp544om02991110p04ceemi9xrPt+pIkiXvuuSftZe+6665Gc/IeNmxYfOYznymbXrNmTVqDWpk+57vvvjvlOR9yyCGVJhajRo1Kmf7rX/+a9jYau9r2dXXK79f//ve/01525cqV8cgjj6TMK5/gUFH5ffRvf/tb1rZVfsB+06ZNtVpP+YKFp556Kp5++umy6aOPPrrS9+PRRx8d+fmfXB6tXLkypkyZkrLcTjvtFIMHD6522+X30bvvvjujQd9//vOf1a6voRQUFMRtt90Wl112Wdm8DRs2xMknn1zhfJMNzfGcs+3+n+m+v+2g9LYD4zV59tlnG93dXvLy8uLII48sm06SJP7yl7/Uy7qLiopin332KZtesGBBPP744/WybgCojLw+O+T1DUdenz0FBQVx1FFHlU1v2rSpQj5YX8r/Klsmv3T36KOPptUum9fx2dS3b9/o169f2fRrr72W9hd5IjLbfxviWFH+C0uZ5Id33HFH/QaTY/vvv3+0bt26bPrJJ5+MFStWpL18Jq9ttp1//vkp01V9ybQu42rb275z+OGHp3yh66mnnqq3L+eWfy//85//TOuXfgGqIm/MDnljw5E3Zo+8sXGQN36qMV7714W8Ud4ob0x19913p912+fLlKUUe+fn5MXz48HqPqaE+36/sez7pWrp0adoFL76vUHsNcY7cns4LzZFiCGjkrr766rS+RDt//vwKieK5555br7Gcc845KdO//vWvY/369TUut2bNmvj1r39dr7HUVfnK9nR/MeW6666LtWvX1thu7dq1FZ5zVa/Hl7/85ejcuXPZ9H333ZdyW8KmrrZ9XZUvfelLZV9Wj4i4995747XXXktr2auvvjolmRs5cmTKwAWVO/7441N+CWjy5Mnx97//PSvb2va9EFH722yOHDkyCgsLy6afeuqplFtBbnvniG1169Yt9t1337Lpm2++OebNm1c2XdNdISI+uR3kzjvvXDb94Ycfxp///Oe04n7wwQdj8uTJZdMdO3aMk08+Oa1ls+X666+Pa6+9tmx6y5Yt8aUvfSn++Mc/ZnW7zfGcs+3+n+m+v+1tc+fMmZPWtcOWLVviiiuuyGg7DeVb3/pWyvRvf/vblF/XqouLLrooZfqyyy5L69wOALUlr88OeX3Dkddnz8UXX5wyfc0119Q6D67OtnluRMT//ve/tJZ744034oEHHkh7O9m8js+m8sfGq666Kq3lpkyZEg8//HDa22mIY8W2uWFExFtvvZXWcvPmzYsbb7yxXmPJtdatW8cXv/jFsunNmzenjG9UZ8yYMTF9+vQsRZa52owrRGQ2tlDbfWfq1KkZfWG0oXTu3DnOPvvssunS0tL49re/XS/r3nPPPePwww8vm/7www/T3rcAqiJvzA55Y8ORN2aPvLFxkDfKG8uTN8obq9NU88ZXXnklHnroobTa/uxnP0u5y8wJJ5wQRUVFWYmrIT7fP+yww6J///5l01OnTq1QXFmVn/3sZ7Fly5a0t+X7CrXzzW9+M+VYd9NNN2VUnJiO7em80BwphoBG7pVXXonLL7+82jYbNmyIs846K+XEeMghh8R+++1Xr7EceeSRseeee5ZNf/DBB/F///d/1Q7OlZSUxFe+8pVYuHBhvcay1fTp0+PBBx+MkpKStJeZOXNmzJgxo2y6V69eaVcsz58/P84///xqn3NpaWmcf/75MX/+/LJ5/fv3j89//vOVtu/cuXN8//vfT5l32mmnxUsvvZRWTFuVlJTEAw88kFFFYiYauq+rMnDgwPjc5z5XNl1cXBxnnnlmjb8wcv/998fNN9+cMu/SSy+tUyzNRYsWLeJnP/tZyrxvfvObGQ1sbfXMM89UO6A1ZMiQlOna3i6wffv2KVXn48aNiwULFpRNV1UMEZFa8FC+ajedYoj8/Pz4zne+kzLv8ssvTylyqMzs2bPjG9/4Rsq8//u//6twW9pcuOKKK+LWW28tG3hOkiS+9a1vxS9+8YusbbM5nnO23f/nzZsXs2fPTns7e++9d9nfy5Ytq/EOLiUlJXHBBRfUuF/mysiRI+Owww4rm169enV87nOfiw8//DDtdVR1m95zzjkndtttt7LpN998M0455ZRYuXJlRjEuXbq0VsdBAJofeX315PWfktc3v7x+5MiRKXnmkiVL4oQTTkjZ99KxZs2aau/gt+uuu8aOO+5YNj116tT473//W+06Fy9eHF/84hcz2l+yeR2fTRdccEHKL36NGTOmxh81WLJkSXzpS1/K6E6QDXGs2GWXXaJ9+/Zl04888ki8/vrr1a5v2bJl8YUvfCE+/vjjjOJoCr797W+n/DLzDTfcUOMH2W+//XZceOGFWYvp3//+d7z55psZLfOPf/wjZbr8+FlV8zMZV9t2XCEi4s4776zx/fjee+/FF7/4xYw+8G9IV1xxRcqPpTzyyCPx3e9+N+337YYNG6p8X/zyl79M2bd+/vOfVzhHpWPSpEkxbdq0jJcDtj/yxurJGz8lb5Q3yhvljemQN6ZP3ihvlDem+sY3vhHvvvtutW3++9//xi233JIyr/x3ZOpTQ3y+n5+fX6FI4YILLqjxbiEPPPBAxj8k6vsKtTNw4MD4yle+Uja9cePGOOGEEzK6m1XEJ3fEqe5uNY3xvECaEqDRGDduXBIRZY8uXbqU/X3WWWcl8+fPr7DM5MmTk/322y9luZYtWyavvfZaVmKcMGFCkp+fn7K94447Lnn77bcrtH3zzTeTo446qtLnExHJ3Llzq9xO+b646qqrKm334IMPJhGR9OvXL/n+97+fjB8/Ptm8eXOlbbds2ZLcd999yQ477JCy7h/+8IeVtp87d26Vr8exxx6bzJ49u8Iys2fPTo455piU5SIiefLJJ6t8rltjO/bYY1OWKSgoSC688MLkrbfeqnK5zZs3J+PHj09+8IMfJP369auxX7dd/+GHH15tTOVls68zje2DDz6osD8NHDgweeKJJ5LS0tKUtqtXr05++tOfJoWFhSntzzjjjGq3ke4+WJWtr8fWPsuWumznqquuSnmO48aNq7b9V7/61Qr79llnnZVMnTq1ymWKi4uTV199Nbn66quTIUOG1Lid559/PmX9HTt2TK677rpkwoQJyZw5c5K5c+eWPRYtWlRtvL/4xS8qxBsRyR577FHtcuVf+62PvLy8ZOnSpdUuu9WWLVuSYcOGVXgut9xyS7Jx48YKbf/1r38lRUVFFfbp1atXV7udurynt8pkH7rnnnsqvJcuueSSCu+7+tKczjlJkiTXXHNNStvBgwcnt99+ezJt2rTkvffeS9n/V65cmbLs3/72t5RlCwsLkxtuuCHZtGlThe1Mnjw5Oeyww8ralt/3qnuPNuSx8f3330+6deuWsr2ioqLkhhtuqPK9sXTp0uSvf/1rctBBByXnnntulet+/fXXk44dO6asu2/fvskf//jHat93y5cvT+65557kzDPPTFq1alXr9x0A2y95/acawzWWvD6VvP6qatuX11B5/cKFC5O+fftW2Fevu+66anPQ1atXJw899FDy1a9+NenQoUONMZbPN9q1a5fcddddFdoVFxcn//nPf5Kddtqp0vd9ddfZSZLd6/hMXpPbb789JYbbb7+92va//vWvU9rn5+cn3/ve95IVK1ZUaPvkk08mu+yyS9nxul27dmnH1RDHii996Usp6+/du3fy+OOPV2hXXFyc3H///Un//v2TiE/GPcq/dtXJdFxpW+WPzzXtV3Vx4YUXpmyrVatWybXXXpusW7cupV1xcXFyzz33JD169Kh036/puHbuueemdY78/Oc/n+Tl5SUjR45Mbr755mqP+UuWLEkuvfTSJC8vL2XffOONN6pcZsCAASlxnHXWWcnjjz+evPXWWynjCnPnzk22bNmSsuyhhx6asuxuu+2WTJgwocI2Nm7cmPz1r38tG09o3bp10r59+7TfB+n2VWUyPbbfdNNNFc7phx56aPLss88mJSUllS4zffr05Morr0yKioqq3a/LH1e3XlONGzeuynWXlpYmb775ZvLrX/86OeCAA9I6PgHbH3njp+SN8sbqyBs/JW+UN8ob5Y1VkTdWJG9M3+GHH17pddAOO+yQ3HvvvRViXLt2bfLzn/88admyZYV9qDp1Pd8mScN8vr958+Zk7733TtlGr169kvvuu6/SvrjmmmvKrj3KHw9qeo4N9X2F2h6HM1mursfr8vthddasWZPstddeKe3btGmTXHnllckHH3xQ5XLr169Pnn766eTiiy8uOy5Vp6HOC9QvxRDQiJQ/+f/whz9Mhg4dmnLBOmzYsOT0009PTj755GTw4MEVLpoiIrn11luzGuevfvWrSrc7dOjQ5LTTTktOPfXUChcHJ5xwQnLOOeekfbGa6eDXto+WLVsmQ4cOTU488cTk7LPPTs4888xk5MiRSadOnSq03W233ZK1a9dWuu7yJ+tzzjknOeGEE9J+zlsfV1xxRVr9umrVquTggw+udB19+vRJRo0alYwePTo544wzkuOPPz7Zc889Kwzo1NSvdTnhZrOvaxPbI488krRq1arCdvr27ZucdNJJyejRo5ORI0cmrVu3rnRfXbVqVbXrbyqDXw1ZDLF58+bklFNOqXQfLSoqSo4++ujkjDPOSEaPHp2ceOKJyT777FNp/9e0nf3337/SbZR/1LSfTJo0qdLlLrnkkmqX27RpU8qA1NbHfvvtV+1y5b333nvJjjvuWGE9HTt2TI455phk9OjRyXHHHZd07969QpuuXbsmr776ao3bqI+L6Ez3occffzxp27Ztyra/8pWvJMXFxbXafk2ayzknSZJkwYIFSYcOHdLa/8vHuGXLlgpJX8QnydZxxx2XnH322clJJ51UNli57X7zox/9KO33aEMfG59//vmkc+fOFZ5XixYtkgMPPDA55ZRTkrPOOis54YQTkoEDB6YM9NWUZD/99NOVvk4FBQXJ0KFDk8997nPJl770peQLX/hCcuSRR1b4oKEu7zsAtl/y+qr7Ql4vry9PXv+p6dOnJ717967wPPPy8pLdd989Oemkk5Kzzz47Oe2005Kjjz462XnnnVOufdOJcc2aNcnOO+9c6b75+c9/PjnrrLOSY489NuUDm/bt2ydjxoxJaZ/Oh1nZuo7P5pdaiouLkxNPPLFCzIWFhcmIESOSM888M/nsZz9b9mWfrY/rrrsu430l28eKd955J+ULBtvGdvLJJ1f6WkdE8qMf/SijDx+bypda1q5dW+HLoxGRtG3bNjnyyCOT0aNHJyeccELZh5ZbH/fcc09Gx7VMvtRSPpZu3bolhx12WHLKKaeU5aFDhw5NCgoKKrT98Y9/XG0clX2Jo6pH+RjHjx+ftGjRokK7wYMHJ6eeemoyevTo5Mgjj6ywf/31r3/N6H3QkF9qSZIkueSSSyp9/t26dUuOPvro5Mwzz0y++MUvJiNHjky6du2a0X590UUXVbruTp06JSNHjky++MUvJmeddVZy0kknJQceeGCl703FEND8yBur7gt5o7yxPHnjp+SN8sb6PFbIG1PJG6t+yBu377yx/Pu5/D7ds2fP5IQTTih7Xct/TyTikx8jXb58ebXbqY9iiCRpmM/3X3/99QpFX5X1RZs2bVJey7/85S8ZP8eGeD7bWzFEknxSMLvbbrtV+r4aMGBAcsIJJyRnnXVWcvrppyejRo1KBg8eXOmxsjoNdV6gfimGgEakspP/woULkz333DOti9DCwsLkT3/6U4PEeu2111b4RZCqHiNHjkxWr16d0cVqXQa/0n0ccsghyeLFi6uMobKT9erVq5MjjjgirfXn5eUlP/rRjzLq182bNyff+973Kj0Jp/No27ZtsnDhwirXX5cTbjb7uraxvfDCCxUuLGp6nHjiiTX+2n6SNJ3Br4YshkiST6rQr7vuukoHFdM9Tk2ePLnabbz77rtVXrhmsp+UlJRUSEQjotJftSiv/EB3RPW/ZFOVBQsWVHqBXN1j1113rfZXPbZVl/f0VrXZh8aPH19hgPKUU06pcNeL+tIczjlbPfbYY5UO/pZ/VBbjvHnzyn5lJp3H0UcfnXz88ccZHQtycWx86623kj322CPjPk8nyZ4zZ07aBViVPU4++eSMnj8A2z95ffV9URl5fepDXl/zY3vL67davHhxhV9+zOQxdOjQGrcxY8aMCr/aWtWje/fuyYsvvljrD7OycR2fzS+1JMknv1p48sknpx3rpZdemnFcW2X7WPHEE09U+uF5VY/vf//7SZJk9uFjU/lSS5IkycqVK6v8IlH5R35+fvKHP/whSZLMjmt1+VJLOo8WLVok11xzTY3PtbS0NPnGN76R1jori/H222+v9EtUlT0KCgqSG264IUmSzN4HDf2lliRJkj//+c+Vfmmjpkc6+/Wdd95Z4dcc033k5+cnDzzwQNrPH9g+yBur74vKyBtTH/LGmh/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      "text/plain": [
       "<Figure size 2000x1000 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 588,
       "width": 1569
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axarr = plt.subplots(1, 3, figsize=(20, 10))\n",
    "fig.subplots_adjust(wspace=-0.01)\n",
    "for i, m in enumerate(\n",
    "    [pdispersion_from_cm, pdispersion_from_gdf, pdispersion_from_gdf_pre]\n",
    "):\n",
    "    plot_results(m, P_FACILITIES, facility_points, ax=axarr[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff2ce865",
   "metadata": {},
   "source": [
    "All 3 solutions to the $p$-dispersion problem vary spatially, as seen above, but they also all include facility $y_1$ since it is the most isolated location. A good demonstration of the intended results of dispersion can be seen in the first two models, `P-Dispersion-network-distance` and `P-Dispersion-euclidean-distance`, where the selected candidate facilites are arranged to form pseudo-equilateral triangles. Of course, the `P-Dispersion-euclidean-distance-predefined` model does not follow this pattern due to the stipulation that facilities $y_{11}$ and $y_{12}$ be included in the optimal solution.\n",
    "\n",
    "\n",
    "## References\n",
    "\n",
    "- [Kuby, Michael J. 1987. Programming Models for Facility Dispersion: The p-Dispersion and Maximum Dispersion Problems. Geographical Analysis, 19, 315–329.](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1538-4632.1987.tb00133.x)\n",
    "- [Maliszewski, Paul J., Michael J. Kuby, and Mark W. Horner. 2012. A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas. Computers, Environment and Urban Systems. 36 (4):331-341.](https://www.sciencedirect.com/science/article/pii/S0198971511001293?via%3Dihub)"
   ]
  }
 ],
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