usage_demos.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Ants in Space! An introduction to the code in [beam_paco__gtoc5](https://github.com/lfsimoes/beam_paco__gtoc5)\n",
    "\n",
    "\n",
    "Luís F. Simões\n",
    "\n",
    "2017-04"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<h1 id=\"tocheading\">Table of Contents</h1>\n",
    "<div id=\"toc\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# https://esa.github.io/pykep/\n",
    "# https://github.com/esa/pykep\n",
    "# https://pypi.python.org/pypi/pykep/\n",
    "import PyKEP as pk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from tqdm import tqdm, trange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "plt.rcParams['figure.figsize'] = 10, 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from gtoc5 import *\n",
    "from gtoc5.multiobjective import *\n",
    "from gtoc5.phasing import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from paco import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from paco_traj import *\n",
    "from experiments import *\n",
    "from experiments__paco import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Taking a look at our Python environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPython 3.5.3\n",
      "IPython 5.3.0\n",
      "\n",
      "PyKEP {'major': 1, 'minor': 3, 'bugfix': 9}\n",
      "numpy 1.12.1\n",
      "scipy 0.19.0\n",
      "tqdm 4.11.2\n",
      "pandas 0.19.2\n",
      "matplotlib 2.0.0\n",
      "seaborn 0.7.1\n",
      "\n",
      "compiler   : MSC v.1900 64 bit (AMD64)\n",
      "system     : Windows\n",
      "release    : 10\n",
      "machine    : AMD64\n",
      "processor  : Intel64 Family 6 Model 94 Stepping 3, GenuineIntel\n",
      "CPU cores  : 8\n",
      "interpreter: 64bit\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -m -p PyKEP,numpy,scipy,tqdm,pandas,matplotlib,seaborn\n",
    "# https://github.com/rasbt/watermark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Solving a TSPLIB problem with P-ACO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this section we show the steps to solve a Travelling Salesman Problem (TSP) instance with the Population-based Ant Colony Optimization (P-ACO) algorithm.\n",
    "\n",
    "We'll use a TSP instance downloaded from the [TSPLIB](http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/): `eil101` (symmetric, 101 cities, total distance in best known solution: [629](http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/STSP.html))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from urllib.request import urlretrieve\n",
    "import gzip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "urlretrieve('http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/tsp/eil101.tsp.gz', filename='eil101.tsp.gz');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Load each city's (x, y) coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[41, 49],\n",
       "       [35, 17],\n",
       "       [55, 45],\n",
       "       [55, 20],\n",
       "       [15, 30]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with gzip.open('eil101.tsp.gz') as f:\n",
    "    xy_locs = np.loadtxt(f, skiprows=6, usecols=(1,2), comments='EOF', dtype=np.int)\n",
    "nr_cities = len(xy_locs)\n",
    "xy_locs[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Calculate distances matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.        ,  32.55764119,  14.56021978,  32.20248438],\n",
       "       [ 32.55764119,   0.        ,  34.40930107,  20.22374842],\n",
       "       [ 14.56021978,  34.40930107,   0.        ,  25.        ],\n",
       "       [ 32.20248438,  20.22374842,  25.        ,   0.        ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distances = np.zeros((nr_cities, nr_cities))\n",
    "for a in range(nr_cities):\n",
    "    for b in range(a, nr_cities):\n",
    "        distances[a,b] = distances[b,a] = np.linalg.norm(xy_locs[a] - xy_locs[b])\n",
    "\n",
    "distances[:4, :4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Instantiate the TSP \"path handler\" with this distances matrix, and P-ACO, with its default parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Seed: 2608067369\n"
     ]
    }
   ],
   "source": [
    "rng, seed = initialize_rng(seed=None)\n",
    "print('Seed:', seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "path_handler = tsp_path(distances, random_state=rng)\n",
    "aco = paco(path_handler.nr_nodes, path_handler, random_state=rng)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Solve it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 6.88 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "672.14610316279925"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time (quality, best) = aco.solve(nr_generations=100)\n",
    "quality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Continue refining the solution for a few more generations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 27.2 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "647.17563526781532"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time (quality, best) = aco.solve(nr_generations=400, reinitialize=False)\n",
    "quality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's see what we found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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rXXe62fXE1bquOMOh5kSPlIquRATSzrNF5pfBf+X1ue6P0aS8qRORt+x5Gv+E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fHysanYk7gLFoYWWBCwEGHTwnFt5h30ceon8zFVsb3D0I7DWDu3pmNrgQAhAHDm4SlUC6sxhi7r\naSWakSI6RV6x+EcXP0RJzRMAgB3PHm/6vo2JHlMQZN8Lehzx7xtPqotxKTMcZgZmcDbrgJTiJHS1\n8sTCwMXtXuzNMAyuZUcAANws3PGw9IHKzq3p2FwgQAgAHE0VX9Yb5zaR5UhIe6BEiugUeQXb5bVl\nmO39OiZ5TEFvx77Q19NvcsymmA0orSnB532+xvs9FrV3qI1czDiPyNxbGO06DltfpD33miNiRMir\neIzMsgxklmXgiyufyjzup5vfYbzbJJnfa0KUpaK2AufSz8DN0h2e1l5sh0PaASVSRKfIK8zmcDj4\nefAaufcrqynFX1HrYGVkhbnd32iv8ORafetHAMDinh+p/NzqhGEYFFcXIaMsA1llmcgsy0BWaaY0\nacoqy0R2eRZqRS3vSZhSnIwum5zQ1coT3aw94WntDS9rL3hae8OJ7wwOh6OCZ0S03bn0MFTUVWBs\nlwn0mtJSlEgRncAwDLbHbYGIEcn8eksF21vu/Y2i6iIsC14BvqFZe4Qo19WsK7iWHYHhHV+AnyBA\npedWtbLaMmliJE2UyjLrEyfxv+WtnOSAA3tTB/gJ/OHEd4ET3xkufBdsiFqHjLJHTY63MLRAR/PO\nSCiMQ1TenUZfMzM0h6e1V4M/3vC09oaAJ2iX5020l6QJJ7U90F6USBGtl12WhQ8vvIdz6WEw4fJQ\nKeMHcXMF2xW1FVh/dy3MDM0xz3d+e4Yq0yrpbNTHKj93Q6HJ+7AmchWSihLQ1coTi4KWtKnGqEZY\ng6yyTJkJUmZZJrLKMlBcXSz3/tbG1uhi6Q5nvjOc+S5w4rtI/+1s5gIHniMM9A2a3M+OZ9+oRkri\nx0G/YJLHVNSJ6vCw5D7iC+KRUBiHhMJ4JBbG43buLdzMud7oPrYmtvC09pbOYIn/eMLCyLLdxo1o\nrmphNc48PIWOZp20/pcgXUaJFNFaDMMgNGUflocvQXF1MYZ0GIY1Q/7AtewI/Hp7tfQHW0sF2//E\nbUV+ZR4+DFra7A/M9nAr5wbCM85joMsQ9HQIVum5G2qpYFsoEuJxRW6DmaRMZJY9kiZImWWZyKt4\nDAaMzMc3NeDDme+MHnZB9UmSs/RvFzMXOJo6g2fAUyh2yfdW3vecq8eFm6UH3Cw9GvX4qRZWI7U4\nRZxcFcQjoSgeCQVxuJJ5CZczwxudw8nUGZ42Xuhm5QUvG294WnvBw6obTj84QYXuOiz80XmU1pRg\nltdsuqynxTgMw8j+ZFOivLzSVh0nEJi1+ljyFI1bUwWVBVgWvhiHU0PB4/LwZd9v8Vr31xt9mLVm\n3KrqqhC80x8l1SWIfDUWNiY27R16I7OOTcOZh6dwcMJx9HXur9JzNzRodx+ZPax4XB5sTGyRXZ6F\nOlGdzPsa6hk2SowaJkiSWSVzQwuN+UFTXluO5KJEJBTGI74gDolF8UgoiEdWeWaj4zjggKvHlVmv\n5W3jgwvTI1QVskbT5M+3hefexa6Ef3B00hkEO4ao9NyaPG5skoybQND6Eg6akSJa5/SDE/jw/PvI\nq3yMYIfeWDvsT7hadFHosXYn7EROeTYWBCxUeRIVnXcXZx6eQm/HvqwmUYD8Iv2KugpYioQIEATK\nTJCc+C6wNbGVtpDQBqYGpgiwC0SAXWCj259UFyOhMAEJhXFILIxHQmF8k5krCepGr/1qhbU4ef8Y\nHEwd0dOhF9vhkHZEiRTRGqU1JfjiyqfYGb8dhnqG+LzP13jX/32Fl7fXCmux9s4vMNY3xtsB7yk5\n2patvvUTAPZrowD5XdW9bbrjwvSrLESkfiyMLBHi2Bshjr2lt8mbyXPgOaoyNMKCiKzLKKouwuse\nb2rVLxKkKfruEq1wJfMSBv/XFzvjt6O7jS9OT7uI93sseq4eQfuS/sOj0nS86j0H9jx7JUbbsviC\nOBy/fwSBdkEY5DJEpeeWZVHQEpm3LwyUfTsRkzduGWWPMP/0XBRVFao4IqIqR9OoCaeuoBkpHabJ\nq4kaxm5hZIHCqkLocfTwYdBSLOm5HIb6hs/52D8jvjAOHHDgZumuxMhbc+5VSCiMAwD0ceqnFrVD\nwzu9ACN9IwgZIQBQV/VWklXo/nK3WTiUGorQlP2IyLqCNUN+x7BOL7AcKVEmoUiI42lHYGtii96O\nfdkOh7QzSqR0lCZvm/Fs7IX1v9V/1OsTLOm5TKmPzYDB8ktLYWVs3e7j8uy5AeCPu7/BTxDA+vdk\nT+JuVAursTz4M3z34v+oiLUNJnlMxSSPqY2Kf+f5vY0/7v6KH258i5ePTcWr3nPwVd9vVd6jjLSP\nGznXkFf5GK96z6HO+TqALu3pKHlbpfx6e7WKI2m7NZE/y7z9SOohJTw2e+Oirt8ThmGwNXYTDPQM\n8Ir3HFZj0Rb6evr4IHAxTk29AG8bH+yI24rBe/rhWhat5NMGR+s/i2iTYt1AiZSOkrdqSN1XEyUW\nJiC+/rLXs5QRO5vjoq7fk4isy0gsSsA4twmw49mxGou28bH1xamp57EwcAkyStMx4eCLWHllBarq\nqtgOjShIxIhwLO0ILIws0d95INvhEBWgREpHmRtZyLy9pa1S2CIUCbHu7loM3ztA7jHKiF3eY6hi\nXNg8d3M2x24EAMz1eYvVOLSVkb4RVvReiSOTTqGzhSvWR63FiL0DEZ13l+3QiALuPI5EVnkmRnZ+\n8blqNYnmoERKB528f1zuaqFRnV9UcTQte1jyAJMPj8WXEStgZmiOd/zfl3lcc9u8tJa8VVZzus97\n7sdW9NzKeF6Kyi7LwvG0I+hu44tgB9U2FNQ1vRxCcO6lK3jd500kFiVg1P6hWHXrB7mNTol6Opoq\nXq03tssEliNpH6HJ+zBodx84rrfCoN19EJq8j+2QWEeJlI7JKsvEwnPvwFjfGJ/3+RreNj7g6nHR\nybwz9Dn62BTzFxIK49kOE4C4NmdH3FYM/q8vrmZdwZgu4xE+4zq+6vctNozYLI3d28YHG0ZsVkpB\n9iSPqY0e257nAAA4cf+I3A2PlUVybjMDccGxp7WX0p6XorbHbYGQEWKuzzy1WD2o7UwNTPH9wFXY\nO+4Q7Ezs8cONbzHmwHAkFyWxHRppBYZhcDTtEEwN+BjcYSjb4SidZEFMfOE9CBmhdJGSridTtEWM\nFmjtuAlFQkw5PA4RWZfxw8DVmOvTeJZlX9J/eDfsTTjzXXBiylk4mLLXNDC3PAcfnn8PYemnYW5o\nge8G/ISpXacr9Yd5a8ZNxIgw69g0nE0/g5V9vsGCHh8o7fzyzD4+AycfHEfKG4/kXoJVhRphDQJ3\ndEdVXRWiXkuAqYEpAHqfKqqt4/akuhgrLi/DnsRdMNY3xoreK/Gm3zs619xRk15vMfnRGLanPya6\nT8ZfL2xlNRZljxvDMOi7KwipxSlNvqZNWx4pskWMbr0jddwvkT8hIusyRruOw5zubzT5+tSu07Ei\nZCUyyzIw69hLKKth58PrYPJ+DNwdgrD00xjkMgQXp1/FtG4zWJkR0ePo4behf8KOZ49vr3+JO7mR\nKo+BLcfTjuBxRS5meM6UJlFEdSyMLPH7sA3YMmon+IZ8fH7lE0w5NA7pJQ/ZDo3Icax+tZ62NOF8\nVJqO3Qk7sSDsLQRs95KZRAHsL4hhGyVSOuJaVgR+vvU9nPku+GXIWrlJyQeBi/Gq91zE5Edh3unX\nUCtsuuFqeymsKsBbp+fgrTNzUS2sxvcDV2HPuINwNnNRWQyyCHgCrBu+EUKREG+dmYvSmhJW41GV\nLfc2AUCTmUuiWmO6jMPF6dfxoutYXMkSd/D/N34HVHAxgbTR0bTDMOGaYGjHEWyHopDcilwcSN6L\nxeffR69//BC0wwcfnHsHe5N2o1ZUA3NDc5n3Y3tBDNsokdIBRVWFeCdM/MNw/Yi/YWVsLfdYDoeD\nHwauwvCOL+BcehiWhS9WyQd22MNTGLi7Nw6mHEBP+2Cce+kyXvd5U23qcga6DMYHgYvxsOQBPrr4\nodb/EIsruIerWVcwyGUI3Cw92A5H5wl4AmwdtRNrh/4JDoeDRecX4NXj05Fbkct2aKReUmEikooS\nMaTDcI2ZwS2sKsCR1ENYHr4E/Xf1gu9WD7x95g38E78NRVVFGOU6Bt/2/wEXpl9F7JwU/DRojczH\neaHzKBVHrl6os7mWYxgGi86/h8yyDCwLXoHejn1avA9Xj4u/Rm7FxIOj8U/8NriYdVD6xrkNt3gx\nMzRHcXURDPQM8FnvL7EgYKFadgP+uNenuJwZjgPJe3EtKwK5FTkat7VOa22JFc9Gve5LLQ/UBYfD\nwXTPmejnPAALzy/A6YcnMWh3CH4atEZrLiVpsqNp4st6Y93UtwlnaU0JrmZdweXMS7icGY57+TFg\nIP6lkMc1xdCOw9HfeRD6Ow+Ar61/k8/hZ7c8cjJ1RmZZBv6KWochHYahj1M/lT8ndUCJlJbbcm8T\nTtw/in5OA7AocGmr78c34GPnmL0YvX8Yvr/xDZz5LpjuOVMpMT27FUpxdREAYHnwZ3g/8EOlnKM9\nGOgbYLLHNETm3kRWeSYAzdpap7VKqp9gb+JuuPA74IVOuv2bpjpyMeuAveMOYkvsRnx99Qu8cWo2\nJntMw/cDfoalsRXb4emso2mHYaBnoFbvmYraCtzIuYbLGeG4khWOu4/vSPfLNNI3Qj/nAejvPBD9\nnQehh10gDPQNWnxMyZZHEqcfnMDck69g5rFp2DMuFL10sE0KJVJaLK7gHlZe+RTWxtZYN3xjm2d5\n7Hn22DVmP8aEjsCHF96DI98JA10GP3dc8rZC+ePub+ho3gm9HELgxHd+7vO0h3/itsm8fcXlZeAb\n8NHTIbjZS6eaYE/iLlTUlWNR9yVqOTNIxIsg3vCdj8EdhuK9s2/jQPJeRGRdxpohf2Box+Fsh6dz\n7j9JQ2x+NIZ3fIHVlbbVwmrczr2FSxkXcSMvAlcfXUWtSFznytXjItC+JwY4D0R/l0HoaR8MY67x\nc5/zhc4v4q8XtmLeqdmYcXQK9o07hB72Qc/9uJqEEiktVVFbgbdOz0G1sBqbRm6HI99Jocfpat0N\n21/chWmHJ2DuyVdwZNIpeNt0f67Y5K3wKKwqwJun5wAAXPgd0MshGMGOvdHLIUTa14lt8mLPr8zD\nrOMvAQA8LLtK4w526A03S3e1qfVqCcMw2BK7CYZ6hpjl9Rrb4ZAWuFl64MikU/j9zhr8dPM7zDg6\nGa91fwMr+/4PfAM+2+HpjKNp9U043VTbhLNOVIeovDu4nBGOS5nhuJlzDZV1lQAADjjwEwSgv/NA\nDHAZiGDHPu32mhjTZRzWD9+Et8PewEtHJ+HAhKPwtfVrl3OpI/Z/MpF28fmV5UgqSsSbvm9j5HN2\nK+/j1A+/DVuPt8+8gZlHp+LElLMKJ2aAeIVHfOG9Jrd3NnfFq93n4mb2NdzMuY7QlP0ITdkPQHz9\nPsi+pzS5CrLvBQsjS4VjUJS82DuadcZL3WbgRs51RObexM747dgZvx0AYG1sjZ72T5PCALtAmHBN\nVB16q1zKvIjk4iRM8XgJAp6A7XBIK3D1uFgUtBTDO43EgrC3sO3e37jw6CzWDtvQqppI8vyOpR6C\nPkcfo1xHt+t5RIwI9wpicTkjHJczL+JqVgTKap+2qfGy7o7+zgPQ32UQxvmORF2Z6n7ET/SYghpR\nDd4/+zamHR6P0AnH4WXjrbLzs4kacmqBZ8ftcEoo5p1+DT62fjgx5SyM9I2Ucp7fbv+Cb66tRHcb\nXxyedAJmcpbCtuTZGimJhl28GYbB/SepuJFzHTdzruNG9jUkNpgN4oADT2sv9HQIQbBDCHo5hsDV\nvAs4HE6jQvbmisEVeb21JnahSIj4wjjcyLmGm9nXcTP3BtJLHkiP5epx4WfrL56xqk+uJM1PQ5P3\nYcmFhSirLUU3K08s7vmxSmuv5p58BcfSDuPY5DNyax3ofaoYVYxbtbAaP934Dr/fXQOGYfBuwAdY\nFrxCKZdw2KLur7fM0gz02OGNAS6DsX/8YaU+NsMwSC5KwqXMi7icGY6IzEsoqodY6JMAACAASURB\nVK8pBQA3S3f0cxLPOPV1GtDolx+2xu3f+B1YdH4BbE0EODTxBDysuqo8huehSENOSqS0QMNxSy95\niKF7+qNOVIewaeFwt1Le0nWGYbAsfDG23vsbg1yG4N8x+1pVnChLaPI+6cqPrlaeWBi4uMWEobiq\nCJG5N8UJSs4N3M69hYq6CunXbU0EcOa7ICrvTpP7ytpqRdHXmyKx55Rn42bODdzIuYZbOdcRnRcl\nrV0AgA5mHeFg6oibOddbFXt7yCrLRNAOH3jb+CBsWrjcy5H0PlWMKsftRvZ1vHf2LTwouQ9Pay/8\nMewv+Ar8VXJuZVP319tfUevw2ZXl+HHgL5jj07TRcVswDIMHJfdxJfMSLmdexOXMS3jcoMWFC78D\nBrgMkhaJN1dLyua4bYndhGXhi2HPc8ChicfRxdKdlTgUQYmUjpKMW62wFuMPjkJk7k38NnQ9ZnjO\nUvq56kR1mHNiJk4/PImXPV/BmiF/sFb/UyusRVxBrHjGqj65yizLkHmsrC0M2Hy9VdZVIurxHdzI\nuY5b9fEXytlIWlXbL3x//X9YHfkTfhn8O2Z5z5Z7HL1PFaPqcSuvLcfXVz/HlthN4OpxsbTncnwQ\nuFgtag3bQt1fb+NDR+F69lVEz0mCPc++zffPKsvE5cxw8Z+McGSUPZJ+zY5nX7+qTvynk3nnVn/e\nsj1ukgTTydQZhyadQCfzzqzF0haUSOkoybh9e+0r/Hp7FSZ7TMP64ZvaLcEpry3HpIOjcTfvDj7q\n9Qk+6vVJu5xHEY7rraTLexvicrjIeqdxoqJOrzeGYeD0p7Xs2PW4yHpbdpKlLDXCGvTY7o0aUQ2i\nZieAZ8CTe6w6jZsmYWvczqefxaLzC5BdnoVAuyD8Puwvpc5Utzd1fr3lVuTCb2tXhDj2weFJJ1t1\nn7yKPERkXcKl+jqntCep0q9ZGVmhn/NA9HcZiP5OA+Fh1VXhz3F1GLff7/yKr69+jg5mHXFo4gm4\nmHVgNZ7WUCSR0qxfTYhc4RkX8Nvt1ehs7oqfBv3SrrNEpgam+Ke+x9RPN79DB7OO7TL7pQh5xeAi\niLAncRemdWVnz76WcDgcubGrYvuFo2mHkFf5GPP9FzSbRBHNM6TjMFycfhWfXv4Y+5L+w9A9/fB5\nn6/whu98ndsAWdlOpB0FAwZju8hvwllcVYSr2RG4nCGuc4ovjJN+jW9ghhc6jUJ/l4Ho5zwQ3W18\ntOp78l6PhagRVuP7G99g8qGxODTxxHMtVFJXzSZStbW1+PTTT5GZmYmamhq88847cHd3x/Lly8Hh\ncODh4YGVK1dCT097vvGapGFRNcABh8PBhhGbFS4Cbws7nh12jd2PMQeGY/GF9+Fg6ojBHYa2+3lb\nsihoicxicAM9A7x3dj5O3D+GIR2G4e+Yv1osRlc1ebEvDFzc7ufeHLMRADBXxmbWRPNZGlth3fCN\nGO06Dh9dXIgVl5fhxP1jGO06Fjvitqnde0HdST57JUmRPufpj9Ky2jJcz4qQdg+Pzrsr7R5uwjXB\nIJch0jonf0EPjbvU2laLe36MGmE1Vkf+hBf2DYa5kQXSilO06vXW7KW9/fv3IyEhAStWrEBxcTEm\nTpwIT09PzJ07FyEhIfjiiy8wYMAAjBjR/AaNdGlP+VqzekwVrmVfxbTD42GgZ4jDk07Cx9ZXZeeW\nR1YxeA+7IHxw7h1cy5Zda6TqcZNHkUL25xWbH4Ohe/phSIdh+G9caIvH0/tUMeoybo8rHmPpxYU4\nef+YzK+ry3tBQl3GTULeZ+9o17HIq8zDnceRqBPVAQAM9QwR5NBL3MvJeRB62AcpbRV1S9Rp3BiG\nwavHp+P0w6aXP9X19aa0Gqny8nIwDAM+n4+ioiJMnToVNTU1CA8Xr+gJCwvDlStXsHLlymZPQomU\n8vXb1QvJRYlNbldVYXJDh1IO4M3Tc+Bo6oQTU86qbVdyoUgI/+2ejVbBSLAxbupiyYWF2BG3BTtG\n/9eqnmP0PlWMOo0bwzDosd1butVRQ+r2XlCncQOAQbv7yLwEDwD6HH0E2PWo369uIHo5hLB2qVxT\nxk1dX29Kq5EyNRXvYF1WVoYPPvgAixYtwg8//CCtMTE1NUVpacvfKCsrHrjc1m010ZbgdYVQJMS9\nvHuIeBSBK4+uIOJRBNKK0mQem1SUoPIxnCd4DcVMHj468xFePfkSLs29BAtj9rZJaE5BZb7M29kY\nN3VQXFWM/cn/oZNFJ7wcNKXVW8Lo4lgpgzqNW25Fjszb1fG9oE7xyNvdQJ+jj8JlhTA3av/SitbS\nhHHThtdbixdns7OzsWDBAsycORPjxo3DTz/9JP1aeXk5zM1bftEUFVW0eAygfhk0W8pqShGZe6t+\nSf91RObeQmlNifTrlkaW4BvwUVZb1uS+Xa08WRnD2e5vISEnGX/H/IVxOydi15h9MNQ3VHkczQlN\n3ietVXgWW+PGtr+iNqCitgKver2OwgJ6n7YndRu35hY3qFOcmjJu3ay9UF3CQR7UI1ZNGTd1fb0p\nbUYqPz8fr7/+Or744gv06SPeasDb2xvXr19HSEgIwsPD0bt37+eLWscxDINHpenSpOlmzg3EFcRC\nxIikx7hbemBsl/EIdhB3wXa38sChlAOsFSbLwuFw8E2/H5BZmoGTD45j8YX3sXbon2qxQq6wqgDL\nLi7BodQDMNQzRA1T0+QYtsaNTSJGhC33NsFI3wizvOT3jSLaaWHgYrwd1nRxgS6+F9qCzUUhmkyb\nx63ZROrPP/9ESUkJ1q1bh3Xr1gEAVqxYgW+++QarV69Gly5dMHLkSJUEqi1qhDWIzY+WNpC8kX2t\n0RS7sb4xgh16i5MmxxD0tA+GjYlNk8eRFOepujC5Ofp6+vhzxGZMPjQGexJ34Vx6GIqqClldnXHm\nwUl8eOF9PK7IRS+HEKwd9ieiHt9Rq3FjS3jGBaQWp2Ba1xkyX2NEu5nU1+5YGFqgvK5cp98LbaGO\nn72aoOG4xRXEgqtngD+GbdCKcaOGnO2ssKoAN3Nu4Ga2uHv13ce3USWskn7djmcvTpwcQ9DLIQS+\ntv5tviSmbuO2LXYzPgpf1OR2Va7OKK0pwRdXPsXO+O0w1DPEx8ErsCDgg0Y1QOo2bqo2+8TLOHn/\nGE5MOYsg+16tvp+uj5ui1GncGIbBC/sGIzrvLi7NuIGu1t3YDkkudRo3TaLO4zbz6FSEpZ9G3Nw0\n2JrYsh1OI9SQk2UiRoSUouT6S3TixCmlOFn6dT2OHrysu0uTpmCH3uhg1lEtLn8p0+bYjTJvX35p\nKYSMsN2fd0TmZXxw7h2klz5Edxtf/DH8L3jbdG+Xc2mqjNJHOP3gBPwFPRBo15PtcIiKnX8Uhqi8\nOxjvNkmtkyiinfwE/ghLP42YvCgM6TiM7XCeGyVSz6GitgJ3H9+WJk23cm402pmbb2CGwR2GopeD\nOHEKsu+pkmaZbJO3OqOoqhDvhr0JALDnOSDYsTd6OQQj2KE3fGz9nrs4vbKuEv93/Wv8FbUOHA4H\nHwYtxZKey9Wu6F0dbL+3BSJGhNd93tS6RJ40j2EYrLr1IwBgUdBSlqMhushXEAAAiMmnRErnZJdl\nNdgg9zpi8qOljdcAoJN5Zwzr9IJ0tsnT2qvVy8m1ibzVGa4WXTCn+zzpGB5JPYgjqQcBiGvDAuwC\npbVhvRyCYW3c+rqdu49v472z85FUlAg3S3f8PmxDmy5X6ZJqYTX+id8KKyMrTPSYwnY4RMUuZ4bj\nZs51jOo8Wi0a6BLd4yfwBwDE5EWzHIly6Hwi1XCblYZF0XWiOsQX3JMmTTeyrzfaldtAzwD+gh7S\npKmXQzDsTR1YfCbqQ97qjOXBn2GSx1S8g/fAMAzSSx/iRvbT1YrXs6+KO4/fER/vbukhXakoWa0o\n2Yeq4ffNytgaBZX5YMBgnu98fNb7K9ovTo7Q5H346urnyK/Mh7WxDU7eP6YVxZ6k9X6JFLew+TDo\nI5YjIbrKhd8BVkZWiM6/y3YoSqHTxebyWv13s/ZCRukjlDfo02RjbCP+ge4o/sHuLwiACddEZbE2\nRx2LChXZ6qS0pkTcPyv7af+sstqnz8vKyAo9HYJhasDHwZT9Te6/KGgpPg35otUxquO4tSdlbSuk\na+OmLOowbtezr2Fc6Aut3g5IHajDuGkidR+3qYcnIDzjPFLeeARzI/Vp4EzF5m20JnKVzNsTC+PR\nzcpTPNtUX8fTxcKdaknaYJLH1DbPdJgZmmNwh6HSzY+FIiHiC+PqZwSv4WbuDZx5eEru/U8/ONmm\nRErXyHu9LwtfgsSiBNjzHMR/TO1hz3OAHc+e6su0zC+R4tqoxT2XsRwJ0XW+tn4IzziP2PwY9HXu\nz3Y4z0WnEyl5RdFcDheXXr6h4mjIs/T19OFj6wsfW1/M9ZkHAMgpz0bAdq9GDUsl5H0/iZi88Smu\nLsLq+uLjZ1kbW0uTKntTBzjwHOFm3wmmIkvYmTrAnidOuuhSqvq7kxuJc+lh6O88ECGO1EiZsEtS\nJxWdf5cSKU0mt2W9tScL0ZDWcDB1RDcrL7lbDRD55L3e3S098OOgX5BbnoPcitz6v3PwuP7fmWWZ\niC+Ma/axzQzNpUmVvak97J6Z3ZL829zQgmZ2WUK1UUSdSBOpvCiWI3l+Op1IaXPLem1G3zfFyBu3\nj3p9gv7OA5u9b0VthTixqshFFfcJkrPvi5OuihxpAva4IqdR3zRZjPWNG81kPZtoSRIwGxMb6cKC\n1pC3aETXScYlsSgBIkaILhbuLX6vCVEFVws3mBrwEUOJlGaTfND+cOP/kPYkBVbG1vh+wM/0Aazm\naIsGxTzPuPEMeOhs4YrOFq7iYkyB7CLWGmEN8ioeixMsGbNbkuTrdu4tCBmh3PNx9bgQmNiJEy5T\nh/oEyx4Opo6wb5CICXh2OJJ6sFGCGF94T/p/XX5NyFpckPYkBQdT9uv0uBD1oMfRg6+tH27kXENF\nbYVGlwfo9Ko9iaKqQnTb3BkjO7+IHaP/U/n5n5e6r85QVzRuilHGuAlFQhRUFYiTrGcuKUr+/bg+\n6aoWVst9HA440OPoyUzKvG18cGF6xHPFqUyqfr0N2t1H5qVcb5vuuDD9qsrieF70PlWMJozbZ5eX\n4a/o9Tg+OQw9HYLZDgcArdpTmKWRFXhcHjLLMtkOhRCdoK+nDzueHex4doCtn9zjGIbBk+riJpcR\nGyZgEVmXZd5X1xcfyHv+cQX3MPnQWOmuAkH2vWBpbKXi6AgBfG0lBedRapNIKYISKQAcDgeOfCdk\nUyJFiFrhcDiwNLaCpbEVuslZBNL33yCZtVm6vvhA3uICI30jXMm8hMuZ4dLbPK29pI1vgx1C4Grh\nRosCSLvzlXY41+w6KUqk6jnxXZBanILKukq1abRJCGleQWUBSqqfyPyari8+kLe44Leh6zG043BE\n5t6sb357A5G5t5BQGI8dcVsBALYmtujp8HRzdX9BAIy5xip+BkTbdbXqBmN9Y41fuUeJVD1nvjMA\nILssE10s3VmOhhDSksq6Ssw+MQOPKx9jZOfReFSaTosPGmhpccHQjiMwtOMIAECdqA5xBbGNtmw6\nef8YTt4/BkC8JZafIODplk2OIbDn2dNqSfJcuHpceNt0R0x+NKqF1TDSN2I7JIVQIlXPqT6RyqRE\nihC1J2JEWBD2Fm7mXMdkj6lYN3xTm9ol6IrW7jDA1ePCTxAAP0EA5vm9DQDIKst8uqtAznXcfXwb\nkbk3sT5qLQDxrFV+Zb70MWi1JFGEryAAtx9HIrEwHn6CALbDUQglUvWcTMWJVBbVSRGi9r6M+AxH\n0w6hr1N//Dp0PSVR7cCJ74wJ7pMxwX0yAKC8thx3H9+WJlfnHoXJvN+vt1dTIkVarWFjTkqkNJzk\n0h4lUoSot43R6/Fn1O/oatUNW0ft1NjLAZrG1MAU/ZwHoJ/zAACA43rZK/10fbUkaRu/+pV7Mfma\nWydFv8bVc+K7AAC1QCBEjR1LO4LPLi+HHc8eu8bup2X7LHKTUwKh66slSdt42niDq8fV6IJzSqTq\nPZ2RymA5EkKILLdybuCdM2/AhMvDv2P2ooNZR7ZD0mluFh4yb9f11ZKkbYz0jdDNygtxBbGoE9Wx\nHY5CKJGqZ2ZoDlMDPs1IEaKG0p6k4tXj01ErqsXfI7dpbC2FtiiuKsKlzIswMzCHl7V3/eorH2wY\nsZnqo0ib+Qn8UVlX2eJeneqKaqTqcTgcOPOdkV1OiRQh6iS/Mh8vH52CgqoC/DzoVwzr9ALbIem8\njTF/oqy2FCv7fIMFPT5gOxyi4fwE/tiV8A+i8+7C09qL7XDajGakGnDiO6O4uhjlteVsh0IIgbhX\n1KvHp+P+kzQsClyK2d3nsh2SziutKcHG6PWwNrbGaz5NG34S0la+tuIZZk3tcE6JVAPO9QXntHKP\nEPYJRUK8c2YeInNvYmrX6fgk5HO2QyIAtsRuQnF1Meb7LQDfgM92OEQLdLf1AQccRGvoyj1KpBp4\n2pRTOwrOP730ETpsEMBunTk6bBDg00sfsR0SIa22MuJTHL9/BP2dB2LNkD9o7zc1UF5bjvV318Lc\n0AJv+L7FdjhES5gamMLDqiti82MgYkRsh9NmlEg1IGnKmV2WxXIkz+/TSx9hU8wGVAurAQDVwmps\nitlAyRTRCH9G/Y6/otfD09oLW0b9A0N9Q7ZDIgB2xG1BQVUB5vnNh7mRBdvhEC3ia+uP0poSPCi5\nz3YobUaJVAPaNCMl2Xy06e3bVBsIIW10JPUgVl5ZAXueA/4dsw8WRpZsh0QAVNVV4Y87v8HUgI/5\nfu+yHQ7RMr71Hc41sU6KEqkGtKlGSjIT1fT2KhVHQkjr3ci+jnfD3gTPwBT/jt0HF7MObIdE6u2M\n347cihy87vMmrIyt2Q6HaJmGW8VoGkqkGnDiOwHQjhkpfY6+zNu5egZgGEbF0RDSstTiZMw+MR11\nojr8PXI7fG392A6J1KsR1uD3O2tgwjXB2/7vsR0O0UKS93t03l2WI2k7SqQa4BuawdzQAtnlml0j\n9WvkKggZocyv1YlqMe/0ayioLFBxVITIl1eRhxlHp6CwqhCrBv+GoR2Hsx0SaWBP4i5klmVgtvdc\nCHgCtsMhWsjCyBKdzDsjJj9K437Zp0TqGc58Z43ubr7+7u/49vpXcOF3wPRuM2GkbwwAMNI3xrSu\nLyPYoTeOpB7EwN0hOP3gBMvREgJU1Fbg1eMv4WHJAyzpuQwzvV5lOyRSLzR5Hwbt7o3FF94HBxy4\nWrixHRLRYn6CABRWFWrcVSHqbP4MJ74z4gvjUFpTAjNDc7bDaZO/YzZgZcSncDR1woEJR9HZwhVr\nh/3Z6BihSIj1Ub/j++v/wyvHp2Om56v4X//vNO65Eu0gFAnxdtgbuP04Ei91exkf9/qU7ZBIvdDk\nfZh/5mnDTQYMll9aAitjK9oGhrQLP1t/HEk9iJj8aI2qj6QZqWc41Reca9qs1PZ7W/DJpY9gx7PH\ngQlH0NnCVeZx+nr6eK/HQpyZFg5fW3/8m7ADg//riyuZl1QcMdF1DMNgxeWPcfL+MQx0GYLVg9dS\nryg1siZylczbf729WsWREF3hKy0416w6KUqkniEpOM/SoKnFrXe3YunFhbA1scX+8UfgZil7V/aG\nvGy8cWLKWSwO+ghZZZmYdGgMPr+8HJV1lSqImBBgfdTv2By7EV7W3bF55HbqFaVmkooS2nQ7Ic/L\n11YzWyBQIvWMpy0QNKPgfF/Sf3j90OuwMrLC3nGH0c3as9X3NdQ3xPKQz3Fs8hm4W3pgQ/Q6DN8z\nAHdyI9sxYkKAQykH8GXECjiaOmHX2H3U3FENdbXqJuf21n/GENIWAp4AjqZOGrdVDCVSz9CkppyH\nU0Lx3tn5sDC2wN7xh9Dd1kehxwm074mwaZfwlt87SC5OwugDw/H9jW9QK6xVcsREXLzbB47rrTBo\ndx+EJu9jOySVkTx3h/WWeOv0XBjpG+PfMfuk7zmiXgZ1GCrz9oWBi1UcSfvQ1vei5Hlxv+Zq5PPy\nE/gjpzwbuRW5bIfSapRIPcO5/kNd3Ztynrh/DG+HvQEe1xSnXjkFP0HAcz0ez4CHb/r/gP3jj8DR\n1Amrb/2IFw8MQ0JhvJIiJpLi3fjCexAyQsQX3sP8M69r3AedIho+dxEjAgMG1cIqukykphiGQUTW\nZQCAm6UHuHpceNv4YMOIzVpRaK6t70VteF6Sy3uxGnR5j1btPcPRVDIjpb6JVNjDU5h3ajYM9Yyw\ne+wBBDsHIy+vVCmPPcBlEC5Mj8DnVz7BroR/MGLvQHwS8gXm+70LfT3ZTT6JfGW1ZUgrTkFKcTI+\nu7xc5jG/3l6tFT+cmtNc4bK2P3dNdDb9NKLz7mK82yRsGqkd20qV1pQgoTAeCYXx+PbalzKPeTfs\nTSwPX6LawJSopKZE5u2a9D6TTApE50VhWKcXWI6mdSiRegbPgAcrIytkq2kidT79LOaefAVcPS7+\nHbMXwY4hSj+HuZEFfh26Di+6jsXiC+/jy4gVOHn/GH4bul7uakBdJhQJ8ag0HWlPUpBSlIyU4mSk\n1idPrWnuqguzMlS4rDkYhsGqWz8CAD4M0rxNzivrKpFclIj4gjgkFMYjsT55yih71OJ9hYwQDqaO\nKoiyfRRVF8m8XZPeZ9KtYjSoTooSKRmc+C64/yQNDMOo1XLsK5mX8NqJlwEA21/cjb7O/dv1fKNc\nR6OnQzA+vvghjqYdwuD/+uLrfv+HV73nqNW4qEpxVRFSihsnSqnFybj/JE3m3obOfBcMdBkCd0t3\nuFt64M+oP5Be+rDJcbpQvNvVyhPxhfdk3k7Uy6XMi4jMvYlRnUcrXHepCrXCWqQ+SUFCQRwSCuMQ\nX5803X+SBgaNO2Pb8xwwyGUIPG284WXtjTWRq/CgJK3JY3rb+ODC9AhVPQWlYhgGXlu6oLCq6a4V\nmvQ+czR1gq2JLWLyo9kOpdUokZLBme+MewUxeFJdDEtjK7bDAQBcz76GWcdegogRYduL/2JQhyEq\nOa+tiS3+Hrkd+5P34JNLH2HpxYU4cf8ofhnyu0b/5iZPrbAWD0seNEiYnv6dX5nf5Hi+gRm8rL3h\nZukBdysPuFm4w83KA10s3GBqYNroWBsT20YNDiW0pXi3ORM9JiP+etNESheeu6ZZXT8btbjnx+16\nntDkfVgTuQpJRQnoauWJRUFLZF5+EoqESHuSioSCeCQUipOmxMIEpBQno1bUeEGMlZEVejv1hae1\nFzytxUlTN2vPJpssm3BNtOq9KGJEWBa+RGYSBWjW8+JwOPC19cf5R2dRXFWkNj+Dm0OJlAxPV+5l\nqsU3MTL3Jl4+OgU1ompsHvmPyq8bczgcTO06HX2d+mPR+QU4m34GA3eH4IeBmnPdvSGGYZBXmYf4\nh3cQ+SC6UcL0sOQB6kR1jY7X4+iho1knBAgC4WblAXfLp3/sePatnp2b5DEVJdUl+Ch8ETjgwMum\nOxYGLtbIMWyrB0/uAwA6mnVCVnkmulp56sxz1yTXsiIQkXUZQzsOR4BdYLud59mu6ZKi6MLKQnS2\n6Iz4QknSFI/kosQm/e1MDfjwE/jD09pbmjR52njDzsSuVe9Hyevu19urpYmcpr4e60R1WHR+AfYk\n7kJ3G1/M9ZmHzbEbNfp5SRKpmPxoDHAZxHY4LaJESgZJIpVdnsn61HbU4zuYfmQyKusq8NcLWzHK\ndTRrsTjxnfHf2FBsvfc3vor4DPPPvI7jaUfxw6BVsDa2YS0uearqqpD2JFWcJBU9nVlKfZKKJ9XF\nTY63MrJCgCAQ7vXJklt9stTZwhVG+kZKicnDqisA4P0eH+KzPl8q5THVXWFVAUKT98HVoguuzrwN\nPQ4tFlZXqyMltVHtOxslb/HBJ5eXNvq/kb4RvARecDfvVj/D5AVPG284812e+3U0yWOqxiUYz6oR\n1uDdsDdxODUUQfY9sWvMflgaW2F297kQCMyUtghJ1aR1UnlRlEhpqoYzUmyKzY/BS0cmoqy2FOuG\nb8Q4twmsxgOIZ6fm+szDoA5D8P7Zt3Eo9QCuZl/BmiG/Y3inkSqPh2EYZJdnPb0U16DY+1FpepNa\nCQM9A7hadEFfp/7wc+oOJ8NO9Zfl3FWSDCbWF31KEipdsCt+J6qEVZjTfR4lUWrsdu4tXHh0Dv2d\nByLEsXe7nSerLBMJhXEyv8YBBx/1+kScNNl4oZO5KxztrTQ2IWhPVXVVmHdqNk4/PIk+Tv2wc/Qe\n8A3N2A5LKSRbxcTka8ZWMZRIyfC0uzl7TTkTCuMx7fB4FFcX49eh6zDZYxprscjSxcINhyeexLqo\ntfjh+jeYeWwaXvF6DV/3+792eTOX1ZRKC7ylM0vFqUgtTkFFXXmT4+149ujj1E86q+RuKa5d6mjW\nCVw98cuejd/YkosSAaBNHeg1mYgRYeu9TTDhmuBlz1lsh0Oa8UvkTwDapzaqVliLsPTT2Bm3DWHp\np5v8giPhZdMdS3vJbhNCniqvLcdrJ2YiPOM8BncYiq2j/gXPgMd2WErT2dwV5oYWiNaQXlKtSqSi\noqLw888/Y8eOHXj48CGWL18ODocDDw8PrFy5Enp62vVbJtszUilFyZhyaBwKqgqwavBvmKGmP4D0\n9fTxfo9FGNZxBBaEvYV/4rchPOMCfhu6XqEVhZI2ApJ6pZTiFOm/c8qzmxxvwjWBq4Xb00TJUnJJ\nzl1ttxxJrE+k3HVkRupc+hk8LHmAWV6z1aLekMgWkx+NUw9OoJdDCPo5DVDa46Y9ScW/cTuwO3En\nHtd3qu5hFwhvG1/sjG/an0qTiqLZUlpTgpnHpuF69lWM6jwaG0duU1rpgboQF5z7ISLrMspqy8A3\n4LMdUrNaTKQ2btyIw4cPw8TEBADw3XffYdGiRQgJCcEXX3yBs2fPYsSIEe0eqCo5mko2LlZ9InX/\nSRomHx6LvMrH+G7Az3jVe47KY2grb5vuODX1PFbd+l7c+O3QGAzrOAIZXmi7+gAAGfpJREFUZY+Q\nXJTUZEVOUVVhg/YBLbcRcOF3wCCXIU1ql5z4zhp3qSi5KBEu/A5q/8GgLJtjNgIAXvd5k+VIiCyS\nlXOSS219HPs+d2uTqroqHE07hJ1x23El6xIAwMLIEvN852Om12z42PoCAAa6DNKKYm9VKqoqxIyj\nk3Hn8W1MdJ+MP4ZthIG+AdthtQtfgT+uZF3CvfzYdr3UrAwtJlIdO3bE2rVr8fHH4unee/fuITg4\nGAAwcOBAXLlyResSKWOuMWxNbFWeSKWXPMSUQ+OQU56Nr/v9H97wfUul538ehvqG+CTkC7zQ+UW8\ndmImwtJPS78mWZHz443/Q3F1EQpkLNF9to2AJGHqYuGmNVPWT6qLkVOejSEdhrEdiko8eHIfZ9PP\noKd9sLTmgaiPZ1fOAcBvd35Bd1tfhRKae/mx2Bm/DfuS/kNx/WKOfk4DMMt7NsZ0GQ8Trkmj47Wh\n2FuV8iryMO3IBMQVxGKG5yz8Mvh3rd5tQlJwHpN3V/MTqZEjRyIj42mtUMMmlaampigt1c4iQCe+\nC5IKE1TWlDOzNAOTD49DRtkjfNb7S7zt/167n7M9BNn3grWxtXQav6HUJylwteiCQPuejS7DtbWN\ngKZKqr+s11VH6qO23dsMBgzm+sxjOxQigzK27SmtKUFo8n7sjN+GO49vAwAEJnb4oMdizPR6BV0s\n3ZUWry7LLsvClMPjkFKcjLk+8/DdgJ81bja+rSR77mlCh/M2F5s3rIcqLy+Hubl5i/exsuKBy21d\n5iwQqMeqA1frTojOuws9fg1sebbteq7s0my8tHsC0kse4KvBX+GLQV+0+THUZdwAILkoSebtXD0u\n0halqjia5qly3HIy0gEAPTsGqNX3SxEtxV9ZW4ldiTsg4AnwRu/ZMOJqVw2HotTl+15dVy135VxS\nUUKzcTIMg2sZ17Dx9kb8d+8/VNRWQI+jhzEeY/Bm4JsY7TFa6Zeb1GXc2PCg+AEmHRmNtOI0LO2z\nFD+O+LHVv3Rq8rhZ2wTChGuCuKIYlT+Ptp6vzYmUt7c3rl+/jpCQEISHh6N375an3IqKKlr12OrU\n98LGwA4AEP0goV0vSzyueIxJB0cjuTgZiwKX4m2vRW0eA3UaN6D57UDUKU5Vj9uth+KlvA7cTmo1\nDm3VmnHbnbAThZWFWBi4BCVFNQBqVBOcGlOX92lMfjTeC3tL7so5ee/TgsoC7E3ahZ1x26VtPDqa\ndcLMHq9ihucs6SKd4sIqAFVKi1ddxo0NqcXJmHJoPLLKM7G053J8FPAJ8vPLWnVfbRi37ja+uPM4\nEo+y82DMNVbJOSXj1pZkqs1zg8uWLcPatWsxffp01NbWYuRI1fcOUgUnSQuEVmw6q6iCygJMOzwe\nycVJeMf/fXwS8rlWXN5aFCR793RdX5EjaX3QVQdW7G2O+Qt6HD281r3pNhyEHXWiOvxy6yeM3DcY\n8YVxGOgyWOZxDd+nIkaEC4/O4c1Tc+C3rSu+uPIp7j9Jw0T3ydg77hBuvBKFxT0/liZRRHniC+Iw\nPvRFZJVn4os+/8PHwZ9qxc+HtvAT+EPICBFf0PQXc3XSqhkpFxcX7NmzBwDg6uqKf/75p12DUgfO\n0hYI7dNLqriqCNOOTEB8YRzm+c7Hl32/0Zo3iTZtv6BMSUWJEJjYNdn3S9vczr2Fu3l3MMp1DFzM\nOrAdDoG4pcr75+YjMvcWHEwdsWbIHxjacThCk/fJfJ9mlWVid8JO/Bu/Q7rRdjcrT7zi/Rqmdp0B\nGxP128lAm0Tn3cVLRyaisKoQ3w34WaMWHimTnyAAgLhOqod9EMvRyEcNOeWQNuUsVf7KvZLqJ5h+\ndBJi86Mx2/t1fNu/9de8NQWtyGmsvLYcj0rT0c9ZeT161NXmWGp5oC5EjAh/x2zAN9e+RGVdJaZ4\nvITvBvwk7enV8H1aK6zFmYenMOvYNJxNPwMRIwKPy8NMz1cxy3s2etoHa93nlDq6mXMdLx+ditKa\nEqwZ8gdmer3Kdkis8W2wVYw6o0RKDqd2mpEqqynFy8em4s7j23jZ8xX8OGg1fTjpgNTiZDBgtH5r\nmILKAhxKOQA3S3e5l46IamSUPsLCc+/iUuZFWBtb4/dhGzDObWKT49KKU7Azfgd2J+xEXuVjAECg\nXRBmeb+Gie6TYWbY8oIiohyXM8PxyrHpqBZWYf2ITWq3o4WqdbPyhKGeIWLVfOUeJVJyOJg6ggMO\nspVYI1VeW45Zx1/CzZzrmOLxElYPXqv1S1iJmLT1gZV2tz74N2EHqoXVmNP9DXpts4RhGPyX+C9W\nXF6G0poSjOz8In4e/BvsefbSYyrrKnEs7TD+iduGiKzLAJ42zZzl9Rrrm7XronPpZzDnxCzxLOLI\nHRjdZSzbIbHOUN8QnjbeiCu4h1phrdo2H6VESg5DfUMIeHZKm5GqrKvE7BMv42rWFYx3m4S1w/7U\n6mZqpLGkQkki1Y3lSNqPUCTEtti/wePy1HZbI22XV5GHJRc/wMn7x8A3MMOvQ9Zhhucs6ax3bH5M\nfdPMPXhS3zSzv/NAzPKajdFdxjVpmklU41jaEbx1eg70OfrYPno3hnYcznZIasPP1h/ReXeRVJSo\ntgk+JVLNcOY7415+LESM6Ll+u64WVmPuyVm4lHEBL7qOxfrhm6Qb5xLdoAvNOM+mn0Z66UO86j0H\nFkaWbIejc46mHsZHFxeioKoA/ZwG4Ldh69HBrCNKa0pwIHkfdsZtw928OwDEm3ovDFyCl71eQRcL\nN5Yj1237k/bgvbPzYaRvjJ1j9uhEHWVb+Ar8gXggJj+KEilN5MR3wZ3Ht5FfmQ87np1Cj1EjrMG8\nU7NxLj0MIzqNxF8vbFHb6UnSfpKKEmBpZAk7E8VeR5pAUmQ+l4rMVepJdTE+vfQx9ibthrG+Mb7p\n9z3m+b2NWzk38fPN73Eo5QAq6sRNM1/oNAqveM/BsI4j6HNIDfwTtw1LLnwAM0Nz7B67Hz0dgtkO\nSe34SQvO76rtTDclUs1wkm5enKFQIlUnqsPbZ97AqQcnMLjDUPw9cofW7dJNWlYjrMH9J2kItO+p\ntQsL0p6k4lx6GIIdeks3pSXt78Kjc1h0bgGyyjPRwy4QX/X7DndyIzFwd4h0FrSjeWfM8hQ3zXTk\nO7EcMZHYGL0eKy4vg42xDfaMO0j7UcrhbeMDfY6+Wq/co0SqGdKmnGVZCLALbNN9hSIhFoS9iaNp\nh9DfeSC2jvpXZZ1ZiXpJe5IKISNENy0uNN8a+zcA4HVfmo1ShfLacnx99XNsid0EPY4eejv2hbWx\nDaYcGotaUS0M9QwxyX0KZnm/hv7OA6nwX838dns1vrn2Jex49tg//gi6afEl/+dlwjVBV6tuiM2P\ngVAkVMvaYkqkmiFpypnVxoJzESPCwvPvIjRlP0Ic+2D76N3gGfDaI0SiAZIKxdtpeGhpoXlFbQV2\nJ/wDWxMBxnQZz3Y4Wu9G9nW8f24+7j9JAyD+vLmWHQEA8LT2wiyv2ZjWbQasjalpprphGAY/3PwW\nq2/9CGe+C/aPP0wbO7eCr8Af8YVxuP8kDe5WHmyH0wQlUs2QzEhllrW+KaeIEWHphYXYk7gLQfY9\n8e+YveAb8NsrRKIBJJdYullrZyJ1MGU/iquL8WHQUrp03Q5Ck/dhTeSq+jo7KxRWFTTaJ4/HNcUk\njymY5TUbQfa9tPbysaZjGAYrI1bgz6jf0dncFfsnHEEHs45sh6URfG39sCdxF6Lz71IipWmc+E9r\npFqDYRh8cmkp/onfBn9BD+wee4Ca2REkFWnvjBTDMNgcuxF6HD3M9qZ99ZQtNHkf5p95Oq4FVfnS\nfwfZ98QsL3HTTL5h23arJ6olYkRYFr4E2+79ja5W3bBv/GE4mDqyHZbGkG4Vkxellk1KKZFqhoOp\nI/Q4eq3auJhhGHxx5RNsid2E7ja+2DMulJaAEwBAUlESeFxT6bZD2iQy9yai8+5itOs4OJtp3/Nj\n25rIVTJvd7Nwx4kp51QcDVFEnagOH55/D/8l/ovuNr7YO/4QbE1s2Q5Lo0gWsMSoacE5JVLN4Opx\nYc9zQFYLl/YYhsE3177Ehuh18LT2wt7xh7R+Y1rSOkKREKnFyfCy9tbKgl/pvnpUZN4uJLOZz3pY\n+kC1gRCF1Ahr8G7YmzicGopAuyDsHntAus8haT0zQ3N0sXBDdH4UGIZRu8vX2vfJrmROfGdkl2dB\nKBLKPebHm/+HtXd+gZulO/aOP0y/bRCph6UPUC2s1srLenkVeTicEgoPy64Y4DyI7XC0krwthbR9\nqyFtUFVXhddPvoLDqaHo7dgXe8cfoiTqOfgJ/PGkuhjppQ/ZDqUJSqRa4Mx3QZ2oTrqZ57N+ufUT\nVt36AZ3NXXFg/NFG+1kRItkaRhuXN/8bvx01ohrM9Zmndr8haotFQUtk3r4wcLGKIyFtUV5bjleO\nT8fphycxuMNQqpdVAt8GdVLqhhKpFkga2Mnac++PO7/huxv/Q0ezTjgw4Sg1uyNNSFbsaduMlFAk\nxLZ7m8HjmuKlbi+zHY7WmuQxFRtGbIa3jQ+4elx42/hgw4jNmOQxle3QiBylNSWYcXQywjPOY1Tn\n0dgx+j9qf6MEfrbihqWx+eqXSFGNVAue9pLKQlCDyaaN0evx1dXP4GTqjP0TjsDFrANLERJ1Jqlx\n6aZlidSZh6eQUfYIs71fh7mRBdvhaLVJHlMpcdIQRVWFmHF0Mu48vo2J7pPxx7CNtBWPkvgK/ADQ\njJRGcpZ2N386I7U19m+suLwM9jwHHJhwBJ3MO7MUHVF3yUWJMNQzREcte41sjv0LABWZEyKRV5GH\nSYfG4s7j25jhOQvrh/9NSZQSWRvbwIXfAVF5d8EwTMt3UCFKpFrgVD8jJWnK+W/8Dnwc/iFsTQQ4\nMOEodaUlcjEMg6SiJLhZeoCrpz2Tv0kFSbjw6Bx6O/aFt013tsMhhHXZZVmYePBFxBXEYq7PPKwZ\n8odabmWi6XwF/sivzENuRQ7boTSiPZ/u7STq8V0AwIaoP3A4NRRZZZmwNrbG/vFH4GHVleXoiDrL\nKstEeW0ZumrJZT1Jh+2EwjgAgI+tH8sREcKOht3mXS26oLi6CPmV+Xg34AOs7PM/WnzRTiS/kAZs\n90I3Ky8sClqiFpe9KZFqRmjyPiy/JF41w4CR9pN6J+ADeNl4sxka0QCJ9fVRXbVga5hnO2wDwKaY\nP9HLIVgtPsgIUZVn3wspxckAgLFdxlMS1Y5Ck/fhSOpBAOJO8fGF96TfB7Y/gyiRaoa8rsKhyfto\n+TFp0dNCc81vffBL5E8yb//19mrWP8QIUSV5PxeuZUXg22tfqTga+Xg8Q1RU1LAdhtLsjN8u83Z1\n+AyiRKoZ8roKy7udkIaSi5IAaF7rg7KaUsQWxCIm7y6i86IQnXcXCYXxMo+l9wLRNfJe8/lV+fjt\nzmoVR0PU4TOIEqlmdLXyRHzhPZm3E9KSxMIE6HP00cXSje1Q5CquKkJMfjSi86IQky9OnFKLU8Dg\n6aoYHpcHEy4PlXUVTe5P7wWia+T9XHC16ILfh21gISLZrCxNUVRcznYYSrMg7C08KLnf5HZ1+Ayi\nRKoZi4KWNKkLAairMGmZeMVeAjpbuMJI34jtcACIl2dLkqXovChE50chveRBo2PMDM3R16k/fAX+\n8BcEwE8QgC4WbjicGkrvBUIg/+fC8uDP0MshhIWIZBMIzJBnXMp2GErzScjnavsZRIlUMyTXXX+9\nvRpJRQnoauWJhYGLWb8eS9RfXmUeiquL0cepv8rPzTAMcsqzEZ0vviwXU584ZZU33nzb2tgagzsM\nhZ9tAPwE/vAV+KOTeWeZmyvTe4EQMXovsEOdx53DqKCzVV5e67JigcCs1ceSp2jcFNOe43Yl8xIm\nHRqDhYFLsKL3ynY5ByBOmtJLH4ovzeVFIbp+xim/Mq/RcQ6mjvCzFSdLfoIA+Nn6w4nvrNAKI3q9\nKYbGTTE0boqhcVOMZNwEArNW34dmpAhpB9LWB0osNBcxItx/ktro0lxM3l0UVxc3Oq6DWUeMdh0H\nv/rLcz4Cf9pMmxBC2gklUoS0g+T6zYq7WStWCFknqkNyUZL40lx+VH0xeDTKa8saHdfFwg2DOwyF\nb/0sk6/AD9bGNs8dPyGEkNahRIqQdpBUKE6k3Cw9Wjy2RliDxMJ4ROdFISrvDmLyo3AvPxZVwirp\nMXocPXS16gZfW3/41V+e87H1hZmhebs9B0IIIS2jRIoQJQtN3oerWVcAAKP3D2+0jUFlXSXiCmIb\n1DRFIb7gHmpFtdL7c/W48LT2ltY0+QsC4G3jA54Bj5XnQwghRD5KpAhRome3j5BsY7AldhOeVBcj\nqSgRQkYo/bqRvhF8bf3El+YE/vCz9YenjbfatEwghBDSPEqkCFEiudtHZEeAxzVFT4fgRqvnPCy7\nwkDfQMVREkIIURZKpAhRInnbFehz9JE6LwP6evoqjogQQkh7atp5jxCiMHnbFXSz9qIkihBCtBAl\nUoQo0aKgJTJvV4dtDAghhCgfXdojRInUeRsDQgghykeJFCFKNsljKiVOhBCiI+jSHiGEEEKIgiiR\nIoQQQghRECVShBBCCCEKokSKEEIIIURBlEgRQgghhCiIEilCCCGEEAVRIkUIIYQQoiBKpAghhBBC\nFKRQQ06RSIQvv/wSiYmJMDQ0xDfffINOnTopOzZCCCGEELWm0IxUWFgYampq8N9//2HJkiX4/vvv\nlR0XIYQQQojaUyiRioyMxIABAwAAAQEBiI2NVWpQhBBCCCGaQKFLe2VlZeDz+dL/6+vro66uDlyu\n7IezsuKBy9Vv1WMLBGaKhKTzaNwUQ+OmGBo3xdC4KYbGTTE0bopp67gplEjx+XyUl5dL/y8SieQm\nUQBQVFTRqscVCMyQl1eqSEg6jcZNMTRu/9/e/YU01YBhAH/OzrJMi4joShRnDYouwkISlnVRGfSP\noj8WFGGFq0VlLOYqaeJpteqmulpUNyuIMOsuKuhiWU0kMlKsEIZRVmAZNTM3t/e7iEZ9n1+eHYId\n4fnd7RwYLw/v4Nk5umMMczOGuRnD3Ixhbsb8zC2TMmXo1l5paSnC4TAAoL29HXa73cjbEBEREY1p\nhq5ILV26FA8fPkRVVRVEBH6//2/PRURERGR6iohItocgIiIiGov4g5xEREREBrFIERERERnEIkVE\nRERkEIsUERERkUEsUkREREQGsUgRERERGWTod6T+tlQqBZ/Ph5cvXyInJweapqGoqCjbY5nas2fP\ncObMGYRCIfT09KCurg6KomDmzJk4duwYLBZ25F8lEgkcPnwYb9++RTwex+7duzFjxgzmNopkMomj\nR48iGo1CVVWcOHECIsLcdPr48SPWrVuHy5cvw2q1Mjcd1q5dm34EWUFBATZt2oTjx49DVVU4HA7s\n3bs3yxOaUzAYxP3795FIJLB582aUlZVx30bR3NyMmzdvAgCGhobQ1dWFUCiU+b6JCdy5c0c8Ho+I\niDx9+lScTmeWJzK3CxcuyMqVK2XDhg0iIlJTUyORSEREROrr6+Xu3bvZHM+UmpqaRNM0ERHp7++X\nRYsWMTcd7t27J3V1dSIiEolExOl0Mjed4vG47NmzR5YtWybd3d3MTYfv37/LmjVrfju2evVq6enp\nkVQqJTt37pTOzs4sTWdekUhEampqJJlMSiwWk3PnznHfMuTz+eTatWuG9s0U9fTJkydYuHAhAGDu\n3Lno6OjI8kTmVlhYiPPnz6dfd3Z2oqysDABQUVGBR48eZWs001q+fDn2798PABARqKrK3HRYsmQJ\nGhsbAQC9vb2YNm0ac9MpEAigqqoK06dPB8DPqR4vXrzA4OAgqqursW3bNrS1tSEej6OwsBCKosDh\ncDC3EbS0tMBut8PlcsHpdGLx4sXctww8f/4c3d3dWLFihaF9M0WRisVi6Uu5AKCqKoaHh7M4kblV\nVlb+9pBoEYGiKACAvLw8fP3KB1X+W15eHvLz8xGLxbBv3z4cOHCAuelktVrh8XjQ2NiIyspK5qZD\nc3Mzpk6dmv6CCPBzqseECROwY8cOXLp0CQ0NDfB6vcjNzU2fZ24j6+/vR0dHB86ePYuGhga43W7u\nWwaCwSBcLtd/uoje3EzxN1L5+fkYGBhIv06lUr8VBfqzX+97DwwMYPLkyVmcxrzevXsHl8uFLVu2\nYNWqVTh9+nT6HHP7s0AgALfbjY0bN2JoaCh9nLmN7MaNG1AUBY8fP0ZXVxc8Hg8+ffqUPs/cRlZc\nXIyioiIoioLi4mJMmjQJnz9/Tp9nbiObMmUKbDYbcnJyYLPZMH78eLx//z59nrn9vy9fviAajWLB\nggWIxWK/dRG9uZniilRpaSnC4TAAoL29HXa7PcsTjS2zZ89Ga2srACAcDmP+/PlZnsh8+vr6UF1d\njUOHDmH9+vUAmJset27dQjAYBADk5uZCURTMmTOHuY3i6tWruHLlCkKhEGbNmoVAIICKigrmNoqm\npiacPHkSAPDhwwcMDg5i4sSJeP36NUQELS0tzG0E8+bNw4MHDyAi6dzKy8u5bzq0tbWhvLwcwI+L\nOuPGjct430zx0OKf/7X36tUriAj8fj9KSkqyPZapvXnzBgcPHsT169cRjUZRX1+PRCIBm80GTdOg\nqmq2RzQVTdNw+/Zt2Gy29LEjR45A0zTm9gffvn2D1+tFX18fhoeHsWvXLpSUlHDfMrB161b4fD5Y\nLBbmNop4PA6v14ve3l4oigK32w2LxQK/349kMgmHw4Ha2tpsj2lKp06dQmtrK0QEtbW1KCgo4L7p\ncPHiRVitVmzfvh3Aj4s5me6bKYoUERER0Vhkilt7RERERGMRixQRERGRQSxSRERERAaxSBEREREZ\nxCJFREREZBCLFBEREZFBLFJEREREBrFIERERERn0D24GEHXfum7SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21e65e67eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xy = np.vstack([xy_locs[best], xy_locs[best][0]]) # to connect back to the start\n",
    "line, = plt.plot(xy[:,0], xy[:,1], 'go-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Basic steps for assembling GTOC5 trajectories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The two primary functions for assembling a GTOC5 trajectory are here `mission_to_1st_asteroid()` and `add_asteroid()`. The first initializes the mission's data structure with the details of the Earth launch leg, that takes the spacecraft towards the mission's first asteroid. Subsequently, via multiple calls to `add_asteroid()`, the mission is extended with additional exploration targets. Each call to `add_asteroid()` creates a rendezvous leg towards the specified asteroid, immediately followed by a flyby of that same asteroid, and so increases the mission's overall score by 1.\n",
    "\n",
    "Here's an example of a mission that launches towards asteroid `1712`, and moves next to asteroid `4893`. The `True` value returned by `add_asteroid()` indicates that a feasible transfer leg was found, and asteroid `4893` was therefore added to the mission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "t = mission_to_1st_asteroid(1712)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "add_asteroid(t, 4893)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can evaluate this trajectory with respect to its score (number of asteroids fully explored), final mass (in kg), and time of flight (here converted from days to years)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.0, 3484.7515275785117, 1.6150747703446979)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score(t), final_mass(t), tof(t) * DAY2YEAR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "An aggregation of the mission's mass and time costs can be obtained with `resource_rating()`. It measures the extent to which the mass and time budgets available for the mission have been depleted by the trajectory. It produces a value of 1.0 at the start of the mission, and a value of 0.0 when the mission has exhausted its 3500 kg of available mass, or its maximum duration of 15 years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8721092603416899"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resource_rating(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "As the score increments discretely by 1.0 with each added asteroid, and the resource rating evaluates mass and time available in a range of [0, 1], both can be combined to give a single-objective evaluation of the trajectory, that should be maximized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.87210926034169"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score(t) + resource_rating(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Calling `seq()`, we can see either the full sequence of asteroids visited in each leg, or just the distinct asteroids visited in the mission. In this example, we see that the mission starts on Earth (id `0`), performs a rendezvous with asteroid `1712`, followed by a flyby of the same asteroid, and then repeats the pattern at asteroid `4893`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1712, 1712, 4893, 4893]\n",
      "[0, 1712, 4893]\n"
     ]
    }
   ],
   "source": [
    "print(seq(t))\n",
    "print(seq(t, incl_flyby=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The trajectory data structure built by `mission_to_1st_asteroid()` and `add_asteroid()` is a list of tuples summarizing the evolution of the spacecraft's state. It provides the minimal sufficient information from which a more detailed view can be reproduced, if so desired. Each tuple contains:\n",
    "\n",
    "1. asteroid ID\n",
    "2. spacecraft mass\n",
    "3. [epoch][epoch]\n",
    "4. the leg's $\\Delta T$\n",
    "5. the leg's $\\Delta V$\n",
    "\n",
    "The mass and epoch values correspond to the state at the given asteroid, at the end of a rendezvous or self-fly-by leg, after deploying the corresponding payload. The $\\Delta T$ and $\\Delta V$ values refer to that leg that just ended.\n",
    "\n",
    "[epoch]: https://en.wikipedia.org/wiki/Epoch_(astronomy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4893,\n",
       " 3484.7515275785117,\n",
       " 59717.111314916867,\n",
       " 134.19998321371767,\n",
       " 965.6854249492379)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Epochs are given here as [Modified Julian Dates (MJD)](https://en.wikipedia.org/wiki/Julian_day#Variants), and can be converted as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2022-May-18 02:40:17.608817"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pk.epoch(t[-1][2], 'mjd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Greedy search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this section we perform a [Greedy search](https://en.wikipedia.org/wiki/Greedy_algorithm) for a GTOC5 trajectory. We'll start by going to asteroid `1712`. Then, and at every following step, we attempt to create legs towards all still available asteroids. Among equally-scored alternatives, we greedily pick the one with highest resource rating to adopt into the trajectory, and continue from there. Search stops when no feasible legs are found that can take us to another asteroid. This will happen either because no solutions were found that would allow for a leg to be created, or because adding a found solution would require the spacecraft to exceed the mission's mass or time budgets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import os\n",
    "from copy import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def greedy_step(traj):\n",
    "    traj_asts = set(seq(traj, incl_flyby=False))\n",
    "    progress_bar_args = dict(leave=False, file=os.sys.stdout, desc='attempting score %d' % (score(traj)+1))\n",
    "    \n",
    "    extended = []\n",
    "    for a in trange(len(asteroids), **progress_bar_args):\n",
    "        if a in traj_asts:\n",
    "            continue\n",
    "        tt = copy(traj)\n",
    "        if add_asteroid(tt, next_ast=a, use_cache=False):\n",
    "            extended.append(tt)\n",
    "    \n",
    "    return max(extended, key=resource_rating, default=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 11 s                                                                                                             \n"
     ]
    }
   ],
   "source": [
    "# measure time taken at one level to attempt legs towards all asteroids (that aren't already in the traj.)\n",
    "%time _ = greedy_step(mission_to_1st_asteroid(1712))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def greedy_search(first_ast):\n",
    "    t = mission_to_1st_asteroid(first_ast)\n",
    "    while True:\n",
    "        tt = greedy_step(t)\n",
    "        if tt == []:\n",
    "            # no more asteroids could be added\n",
    "            return t\n",
    "        t = tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 2min 30s                                                                                                         \n"
     ]
    }
   ],
   "source": [
    "%time T = greedy_search(first_ast=1712)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(14.0, 0.041241978351621127, 584.8278465118636, 12.926528012051794)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score(T), resource_rating(T), final_mass(T), tof(T) * DAY2YEAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1712, 4893, 4028, 6939, 1059, 3295, 4006, 4981, 6437, 5344, 2090, 3993, 4186, 1130]\n"
     ]
    }
   ],
   "source": [
    "print(seq(T, incl_flyby=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Greedy search gave us a trajectory that is able to visit 14 distinct asteroids. However, by the 14th, the spacecraft finds itself unable to find a viable target to fly to next, even though it has 84.8 kg of mass still available (the spacecraft itself weighs 500 kg, so the mission cannot go below that value), and 2 years remain in its 15 year mission."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Phasing indicators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A big disadvantage of the approach followed above is the high computational cost of deciding which asteroid to go to next. It entails the optimization of up to 7075 legs, only to then pick a single one and discard all the other results.\n",
    "\n",
    "An alternative is to use one of the indicators available in `gtoc5/phasing.py`. They can provide an indication of how likely a specific asteroid is to be an easily reachable target."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = mission_to_1st_asteroid(1712)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use here the (improved) orbital phasing indicator to rate destinations with respect to the estimated ΔV of hypothetical legs that would depart from `dep_ast`, at epoch `dep_t`, towards each possible asteroid, arriving there within `leg_dT` days. We don't know exactly how long the transfer time chosen by `add_asteroid()` would be, but we take `leg_dT=125` days as reference transfer time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "r = rate__orbital_2(dep_ast=t[-1][0], dep_t=t[-1][2], leg_dT=125)\n",
    "r[seq(t)] = np.inf  # (exclude bodies already visited)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below are the 5 asteroids the indicator estimates would be most easily reachable. As we've seen above in the results from the greedy search, asteroid `4893`, here the 2nd best rated alternative, would indeed be the target reachable with lowest ΔV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1679, 4893, 1528, 5331, 1663], dtype=int64)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.argsort()[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The indicator is however not infallible. If we attempt to go from asteroid `1712` towards each of these asteroids, we find that none of them are actually reachable, except for `4893`! Still, the indicator allows us to narrow our focus considerably."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[False, True, False, False, False]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[add_asteroid(copy(t), a) for a in r.argsort()[:5]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Armed with the indicator, we can reimplement the greedy search, so it will only optimize legs towards a number of top rated alternatives, and then proceed with the best out of those."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def narrowed_greedy_step(traj, top=10):\n",
    "    traj_asts = set(seq(traj, incl_flyby=False))\n",
    "    \n",
    "    extended = []\n",
    "    ratings = rate__orbital_2(dep_ast=traj[-1][0], dep_t=traj[-1][2], leg_dT=125)\n",
    "    for a in ratings.argsort()[:top]:\n",
    "        if a in traj_asts:\n",
    "            continue\n",
    "        tt = copy(traj)\n",
    "        if add_asteroid(tt, next_ast=a, use_cache=False):\n",
    "            extended.append(tt)\n",
    "    \n",
    "    return max(extended, key=resource_rating, default=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def narrowed_greedy_search(first_ast, **kwargs):\n",
    "    t = mission_to_1st_asteroid(first_ast)\n",
    "    while True:\n",
    "        tt = narrowed_greedy_step(t, **kwargs)\n",
    "        if tt == []:\n",
    "            # no more asteroids could be added\n",
    "            return t\n",
    "        t = tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 105 ms\n"
     ]
    }
   ],
   "source": [
    "# measure time taken at one level to attempt legs towards the best `top` asteroids\n",
    "%time _ = narrowed_greedy_step(mission_to_1st_asteroid(1712), top=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.29 s\n"
     ]
    }
   ],
   "source": [
    "%time T = narrowed_greedy_search(first_ast=1712, top=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(14.0, 0.020976850009091538, 542.5005372055895, 13.845381094048889)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score(T), resource_rating(T), final_mass(T), tof(T) * DAY2YEAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1712, 4893, 4028, 6939, 1059, 505, 6060, 3907, 5051, 2413, 6819, 913, 6638, 6723]\n"
     ]
    }
   ],
   "source": [
    "print(seq(T, incl_flyby=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We were able to find another score 14 trajectory, but this time it took us ~1 second, whereas before it was taking us 2 and a half minutes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Finding a GTOC5 trajectory of score 17 with Beam Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "gtoc_ph = init__path_handler(multiobj_evals=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# configuring Beam P-ACO to behave as a deterministic multi-objective Beam Search\n",
    "_args = {\n",
    "    'beam_width': 20,\n",
    "    'branch_factor': 250,\n",
    "    'alpha': 0.0,        # 0.0: no pheromones used\n",
    "    'beta': 1.0,\n",
    "    'prob_greedy': 1.0,  # 1.0: deterministic, greedy branching decisions\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "bpaco = beam_paco_pareto(nr_nodes=len(asteroids), path_handler=gtoc_ph, random_state=None, **_args)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 2min 10s\n"
     ]
    }
   ],
   "source": [
    "# start the search\n",
    "# given we're running the algoritm in deterministic mode, we execute it for a single generation\n",
    "%time best_pf = bpaco.solve(nr_generations=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# being this a `_pareto` class, .best returns a Pareto front\n",
    "# pick the first solution from the Pareto front\n",
    "best_eval, best = best_pf[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17.0, 3496.8299418637093, 14.824982263414686)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Evaluation of the best found solution\n",
    "# (score, mass consumed, time of flight)\n",
    "best_eval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1712, 4893, 2579, 6979, 5469, 6740, 2445, 6301, 5174, 5884, 4165, 4028, 6240, 3988, 1779, 6813, 3243]\n"
     ]
    }
   ],
   "source": [
    "# sequence of asteroids visited (0 is the Earth)\n",
    "print(seq(best, incl_flyby=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 4000.0, 59127.205255048466, 0.0, 0.0),\n",
       " (1712,\n",
       "  3872.530999146394,\n",
       "  59181.08381655966,\n",
       "  53.87856151119195,\n",
       "  650.4716282561097),\n",
       " (1712,\n",
       "  3746.481928641157,\n",
       "  59325.360311294986,\n",
       "  144.27649473533114,\n",
       "  965.6854249492379),\n",
       " (4893,\n",
       "  3602.066962005158,\n",
       "  59582.911331703152,\n",
       "  257.55102040816325,\n",
       "  831.5807789590044),\n",
       " (4893,\n",
       "  3484.7515275785117,\n",
       "  59717.111314916867,\n",
       "  134.19998321371767,\n",
       "  965.6854249492379)]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mission data structure, up to the full scoring of the first two asteroids\n",
    "best[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Generate the Table of Contents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')\n",
       "// https://github.com/kmahelona/ipython_notebook_goodies"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')\n",
    "// https://github.com/kmahelona/ipython_notebook_goodies"
   ]
  }
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