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optimize_stops.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>optimize_stops</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
<style type="text/css">
/*!
*
* Twitter Bootstrap
*
*//*! normalize.css v3.0.2 | MIT License | git.io/normalize */html{font-family:sans-serif;-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%;font-size:10px;-webkit-tap-highlight-color:transparent}article,aside,details,figcaption,figure,footer,header,hgroup,main,menu,nav,section,summary{display:block}audio,canvas,progress,video{display:inline-block;vertical-align:baseline}audio:not([controls]){display:none;height:0}[hidden],template{display:none}a{background-color:transparent}a:active,a:hover{outline:0}abbr[title]{border-bottom:1px dotted}b,optgroup,strong{font-weight:700}dfn{font-style:italic}h1{font-size:2em;margin:.67em 0}mark{background:#ff0;color:#000}small{font-size:80%}sub,sup{font-size:75%;line-height:0;position:relative;vertical-align:baseline}sup{top:-.5em}sub{bottom:-.25em}img{border:0;vertical-align:middle}svg:not(:root){overflow:hidden}hr{-moz-box-sizing:content-box;box-sizing:content-box;height:0}pre,textarea{overflow:auto}code,kbd,pre,samp{font-size:1em}button,input,optgroup,select,textarea{color:inherit;font:inherit;margin:0}button{overflow:visible}button,select{text-transform:none}button,html input[type=button],input[type=reset],input[type=submit]{-webkit-appearance:button;cursor:pointer}button[disabled],html input[disabled]{cursor:default}button::-moz-focus-inner,input::-moz-focus-inner{border:0;padding:0}input{line-height:normal}input[type=checkbox],input[type=radio]{box-sizing:border-box;padding:0}input[type=number]::-webkit-inner-spin-button,input[type=number]::-webkit-outer-spin-button{height:auto}input[type=search]::-webkit-search-cancel-button,input[type=search]::-webkit-search-decoration{-webkit-appearance:none}table{border-collapse:collapse;border-spacing:0}td,th{padding:0}/*! Source: https://github.com/h5bp/html5-boilerplate/blob/master/src/css/main.css */@media print{*,:after,:before{background:0 0!important;color:#000!important;box-shadow:none!important;text-shadow:none!important}a,a:visited{text-decoration:underline}a[href]:after{content:" (" attr(href)")"}abbr[title]:after{content:" (" attr(title)")"}a[href^="javascript:"]:after,a[href^="#"]:after{content:""}blockquote,pre{border:1px solid #999;page-break-inside:avoid}thead{display:table-header-group}img,tr{page-break-inside:avoid}img{max-width:100%!important}h2,h3,p{orphans:3;widows:3}h2,h3{page-break-after:avoid}select{background:#fff!important}.navbar{display:none}.btn>.caret,.dropup>.btn>.caret{border-top-color:#000!important}.label{border:1px solid #000}.table{border-collapse:collapse!important}.table td,.table th{background-color:#fff!important}.table-bordered td,.table-bordered th{border:1px solid #ddd!important}}@font-face{font-family:'Glyphicons 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<h2 id="Introduction">Introduction<a class="anchor-link" href="#Introduction">¶</a></h2><h3 id="Traveling-Salesman-Problem">Traveling Salesman Problem<a class="anchor-link" href="#Traveling-Salesman-Problem">¶</a></h3><p>The traveling salesman problem is a classic optimization problem that seeks to find the most efficient route to connect a given set of points. I recently discovered a set of services built by the open-source mapping company, Mapzen that make this complex problem easy to approximate for a relatively small numbers of stops. Given a set of coordinates, the Mapzen <a href="https://mapzen.com/documentation/mobility/optimized/api-reference/">optimize route</a> service uses road network data to produce a time-distance matrix between these points, and then uses an optimization algorithm to determine a route that minimizes total travel time. This can be done for one of three modes of transportation - pedestrian, bicycle, and automobile. They have a great <a href="https://mapzen.com/blog/optimized-route/">example</a> with a cool map where they determine the optimal route to visit burrito 'dispensaries' in San Francisco.</p>
<p>This optimization tool can also be used in conjunction with Mapzen's <a href="https://mapzen.com/documentation/search/">Search</a> Service, which uses open source data to geocode addresses, landmarks, and businesses. Using these two services together is really handy, because it means that one can pass a list of addresses or business names rather than lat / long coordinates.</p>
<h3 id="Building-Off-the-Optimize-Route-Service">Building Off the Optimize Route Service<a class="anchor-link" href="#Building-Off-the-Optimize-Route-Service">¶</a></h3><p>The Mapzen optimize route service takes a set of points and finds the optimal route that a person should take to visit all of these points. However, what if we have multiple "salesmen?” How should the stops be split up between people and in what order should each person visit their stops?</p>
<p>The idea for this was spurred by a project I'm involved with at work, in which we are sending out multiple research assistants to conduct surveys at a dozen or so different sites in Oakland. In this case, it doesn't matter if one person conducts more surveys than the others or who goes to which site - the goal is just to minimize the total time to get them all done.</p>
<p>I decided to test these services in an application that hits closer to home (literally): the optimization of Sunday morning errands between my girlfriend, Celeste, and I. Say we're both starting and ending at our apartment in the Inner Richmond, SF and have 6 different places that we need to stop at. How should Celeste and I split up these errands so that we're finished as quickly as possible?</p>
<p>In the post below, I write a set of functions in Python that call the Mapzen Search and Mapzen Optimize Route API services, making it really easy to determine the most efficient route between a given set of locations. I also extend this function to determine the most efficient way to split the stops among multiple salesmen, and which route each person should take.</p>
<p>Additionally, I use the Python package <code>folium</code> to create leaflet.js slippy maps to display the results of this optimization problem. Folium has a number of built-in tilesets from OpenStreetMap, MapQuest, MapBox, and makes it really easy to build web maps using Python. I find this package to be really useful for data visualization – since I tend to generate data in Python anyway it’s nice to be able to do it all within one work environment.</p>
<h3 id="A-Few-Caveats">A Few Caveats<a class="anchor-link" href="#A-Few-Caveats">¶</a></h3><p>The purpose of this blog post is NOT to develop an efficient algorithm to approximate a solution to the vehicle routing problem at any large scale. It is instead to show-case an easy way to access and visualize Mapzen routing services, which I find to be very useful and fun to work with. This post only scratches the surface of the capabilities and range of these routing tools. My use of this service to optimize routes among multiple salesmen addresses a specific aspect of this service that they do not provide, but my approach is more of a 'quick and dirty' demonstration than anything else.</p>
<p>The number of unique ways that stops can be partitioned grows very quickly as the number of stops and salesmen increases, so my approach of testing these unique combinations using Mapzen’s optimize route tool will only work for relatively small numbers before exceeding API service limits. For my purposes right now, this is just fine. A better approach would perhaps be to address this problem more “up-stream”, using the Mapzen generated <a href="https://mapzen.com/documentation/mobility/matrix/api-reference/">Time-Distance Matrix</a> rather than the results from a tool that uses that matrix behind the scenes anyway. However, my approach provides a relatively simple way to get an answer without having to develop my own traveling salesman optimization algorithm.</p>
<p>Anyway, let’s get started!</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">requests</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">itertools</span>
<span class="kn">import</span> <span class="nn">shapely</span>
<span class="kn">from</span> <span class="nn">shapely.geometry</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="kn">import</span> <span class="nn">geopandas</span> <span class="kn">as</span> <span class="nn">gpd</span>
<span class="kn">import</span> <span class="nn">json</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">folium</span>
<span class="kn">from</span> <span class="nn">numpy.random</span> <span class="kn">import</span> <span class="n">RandomState</span><span class="p">,</span> <span class="n">uniform</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">sys</span>
<span class="kn">import</span> <span class="nn">os</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">search_key</span><span class="o">=</span><span class="n">os</span><span class="o">.</span><span class="n">getenv</span><span class="p">(</span><span class="s1">'MAPZEN_SEARCH_KEY'</span><span class="p">)</span>
<span class="n">matrix_key</span><span class="o">=</span><span class="n">os</span><span class="o">.</span><span class="n">getenv</span><span class="p">(</span><span class="s1">'MAPZEN_MATRIX_KEY'</span><span class="p">)</span>
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<h2 id="Geocoding-Locations-with-Mapzen's-Search-Tool">Geocoding Locations with Mapzen's Search Tool<a class="anchor-link" href="#Geocoding-Locations-with-Mapzen's-Search-Tool">¶</a></h2><p>I first write a function that wraps Mapzen's Search tool in order to geocode (obtain the lat / long coordinates for) an address, landmark, or business. The function returns a dictionary containing the raw result output from Mapzen (including information such as data source, geocoding confidence, neighborhood data, etc), as well as the crucial piece of information for me: a formatted set of coordinates. By default, I return only 1 result (the best match), but if I were to use this tool in a different context, I would perhaps be interested in returning a set of results. Below I use this function to geocode two famous San Francisco landmarks - the Transamerica Pyramid and Sutro Tower.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">geocode_address_venue</span><span class="p">(</span><span class="n">text</span><span class="p">,</span> <span class="n">key</span> <span class="o">=</span> <span class="n">search_key</span><span class="p">,</span><span class="n">params</span> <span class="o">=</span> <span class="bp">None</span><span class="p">):</span> <span class="c1">#allow for additional Mapzen search parameters</span>
<span class="n">search_parameters</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'api_key'</span><span class="p">:</span> <span class="n">key</span><span class="p">,</span><span class="s1">'text'</span><span class="p">:</span> <span class="n">text</span><span class="p">,</span><span class="s1">'size'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span><span class="s1">'layers'</span><span class="p">:</span> <span class="s1">'address,venue'</span><span class="p">}</span>
<span class="k">if</span> <span class="n">params</span><span class="p">:</span>
<span class="n">search_parameters</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
<span class="n">url</span> <span class="o">=</span> <span class="s1">'http://search.mapzen.com/v1/search'</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">requests</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">url</span><span class="p">,</span> <span class="n">params</span> <span class="o">=</span> <span class="n">search_parameters</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">r</span><span class="o">.</span><span class="n">json</span><span class="p">()</span>
<span class="k">return</span> <span class="p">{</span><span class="s1">'raw'</span><span class="p">:</span> <span class="n">data</span><span class="p">,</span><span class="s1">'coords'</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s1">'features'</span><span class="p">][</span><span class="mi">0</span><span class="p">][</span><span class="s1">'geometry'</span><span class="p">][</span><span class="s1">'coordinates'</span><span class="p">])}</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">transamerica</span> <span class="o">=</span> <span class="n">geocode_address_venue</span><span class="p">(</span><span class="s1">'Transamerica Pyramid, San Francisco, CA'</span><span class="p">)[</span><span class="s1">'coords'</span><span class="p">]</span>
<span class="n">sutro</span> <span class="o">=</span> <span class="n">geocode_address_venue</span><span class="p">(</span><span class="s1">'Sutro Tower, San Francisco, CA'</span><span class="p">)[</span><span class="s1">'coords'</span><span class="p">]</span>
<span class="k">print</span> <span class="n">transamerica</span>
<span class="k">print</span> <span class="n">sutro</span>
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<pre>(-122.40303, 37.79465)
(-122.45285, 37.755246)
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<h2 id="Displaying-Points-on-Leaflet-Maps">Displaying Points on Leaflet Maps<a class="anchor-link" href="#Displaying-Points-on-Leaflet-Maps">¶</a></h2><p>Now let's put these points on a map. I wrote a plotting function that uses folium to plot a set of points and polylines with labels on leaflet.js maps. By default, I use the Stamen Watercolor tiles because I think they look really cool, but if something like OpenStreetMap is more useful, that can also be specified. The full set of available tile layers can be found <a href="https://github.com/python-visualization/folium">here</a>. The function also takes an optional set of colors and point labels, a zoom-level, and a center location. My function calculates default values if not specified.</p>
<p>The function is written in a way that it accepts either a list of point coordinates, or a list of lists of point coordinates. If the latter is specified, each sublist is treated as a group of coordinates and will be symbolized in the same color. The function was ultimately written this way to distinguish the routes of each salesman in the optimization problem coming later. Additionally, I allow for the specification of polyline coordinates, which can be used to plot the optimized route between the points.</p>
<p>Below I map my two previously geocoded San Francisco landmarks along with the "as the crow flies" polyline that connects them. Note that on the 'live' map if you click on the points you will see that they are labeled appropriately.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">plot_stops</span><span class="p">(</span><span class="n">point_coords</span><span class="p">,</span> <span class="n">zoom_level</span> <span class="o">=</span> <span class="mi">15</span><span class="p">,</span><span class="n">tiles</span> <span class="o">=</span> <span class="s1">'Stamen Watercolor'</span><span class="p">,</span> <span class="n">point_colors</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span>
<span class="n">labels</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span> <span class="n">center_location</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span> <span class="n">line_coords</span> <span class="o">=</span> <span class="bp">None</span><span class="p">,</span> <span class="n">line_colors</span> <span class="o">=</span> <span class="bp">None</span><span class="p">):</span>
<span class="c1">#if not a list of lists, make it one, which then allows the function to handle either</span>
<span class="n">point_coords</span> <span class="o">=</span> <span class="p">[[</span><span class="n">x</span><span class="p">]</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">point_coords</span><span class="p">]</span> <span class="k">if</span> <span class="nb">all</span><span class="p">([</span><span class="nb">type</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">list</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">point_coords</span><span class="p">])</span> <span class="k">else</span> <span class="n">point_coords</span>
<span class="k">if</span> <span class="n">labels</span><span class="p">:</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[[</span><span class="n">x</span><span class="p">]</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">labels</span><span class="p">]</span> <span class="k">if</span> <span class="nb">all</span><span class="p">([</span><span class="nb">type</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">list</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">labels</span><span class="p">])</span> <span class="k">else</span> <span class="n">labels</span>
<span class="k">if</span> <span class="n">line_coords</span><span class="p">:</span>
<span class="n">line_coords</span> <span class="o">=</span> <span class="p">[</span><span class="n">line_coords</span><span class="p">]</span> <span class="k">if</span> <span class="nb">all</span><span class="p">([</span><span class="nb">type</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="ow">is</span> <span class="nb">tuple</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">line_coords</span><span class="p">])</span> <span class="k">else</span> <span class="n">line_coords</span>
<span class="k">if</span> <span class="n">line_colors</span><span class="p">:</span>
<span class="n">line_colors</span> <span class="o">=</span> <span class="p">[</span><span class="n">line_colors</span><span class="p">]</span> <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">line_colors</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">list</span> <span class="k">else</span> <span class="n">line_colors</span>
<span class="c1">#get all points as the flattened list to calculate the center</span>
<span class="n">all_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">item</span> <span class="k">for</span> <span class="n">sublist</span> <span class="ow">in</span> <span class="n">point_coords</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">sublist</span><span class="p">]</span>
<span class="c1">#calculate start location as the mean x and mean y of all input points</span>
<span class="k">if</span> <span class="n">center_location</span><span class="p">:</span>
<span class="n">center_location</span> <span class="o">=</span> <span class="p">[</span><span class="n">center_location</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="n">center_location</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">center_location</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">all_points</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">tolist</span><span class="p">()[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="c1">#create a leaflet map, specifying center location, zoom level, and tiles</span>
<span class="n">map_1</span> <span class="o">=</span> <span class="n">folium</span><span class="o">.</span><span class="n">Map</span><span class="p">(</span><span class="n">location</span> <span class="o">=</span> <span class="n">center_location</span><span class="p">,</span><span class="n">zoom_start</span> <span class="o">=</span> <span class="n">zoom_level</span><span class="p">,</span><span class="n">tiles</span> <span class="o">=</span> <span class="n">tiles</span><span class="p">)</span>
<span class="c1">#specify a set of default colors</span>
<span class="n">color_options</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'black'</span><span class="p">,</span> <span class="s1">'blue'</span><span class="p">,</span> <span class="s1">'red'</span><span class="p">,</span> <span class="s1">'green'</span><span class="p">,</span> <span class="s1">'purple'</span><span class="p">,</span> <span class="s1">'orange'</span><span class="p">,</span> <span class="s1">'pink'</span><span class="p">,</span> <span class="s1">'white'</span><span class="p">]</span>
<span class="c1">#if no point colors specified use the default</span>
<span class="n">point_colors</span> <span class="o">=</span> <span class="n">point_colors</span> <span class="k">if</span> <span class="n">point_colors</span> <span class="k">else</span> <span class="n">color_options</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">point_coords</span><span class="p">)]</span>
<span class="c1">#if plotting lines as well, get line colors, otherwise use default</span>
<span class="k">if</span> <span class="n">line_coords</span><span class="p">:</span>
<span class="n">line_colors</span> <span class="o">=</span> <span class="n">line_colors</span> <span class="k">if</span> <span class="n">line_colors</span> <span class="k">else</span> <span class="n">color_options</span><span class="p">[</span><span class="mi">1</span><span class="p">:][:</span><span class="nb">len</span><span class="p">(</span><span class="n">line_coords</span><span class="p">)]</span>
<span class="c1">#loop through each point or grouping of points</span>
<span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">point_coords</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">point_coords</span><span class="p">):</span>
<span class="n">point_color</span> <span class="o">=</span> <span class="n">point_colors</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="c1">#get color from color list</span>
<span class="k">if</span> <span class="n">labels</span><span class="p">:</span> <span class="n">sublabel_list</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="c1">#get labels from label list</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">stop_coord</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">point_coords</span><span class="p">):</span>
<span class="n">label</span> <span class="o">=</span> <span class="n">sublabel_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">if</span> <span class="n">labels</span> <span class="k">else</span> <span class="bp">None</span>
<span class="c1">#Add point to map at specified coordinate </span>
<span class="n">folium</span><span class="o">.</span><span class="n">Marker</span><span class="p">([</span><span class="n">stop_coord</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">stop_coord</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span> <span class="n">popup</span> <span class="o">=</span> <span class="n">label</span><span class="p">,</span> <span class="c1">#need to reverse long/lat to lat/long</span>
<span class="n">icon</span> <span class="o">=</span> <span class="n">folium</span><span class="o">.</span><span class="n">Icon</span><span class="p">(</span><span class="n">color</span> <span class="o">=</span> <span class="n">point_color</span><span class="p">,</span><span class="n">icon</span><span class="o">=</span><span class="s1">'mapmarker'</span><span class="p">))</span><span class="o">.</span><span class="n">add_to</span><span class="p">(</span><span class="n">map_1</span><span class="p">)</span>
<span class="c1">#if plotting lines, loop through each set of lines and plot</span>
<span class="k">if</span> <span class="n">line_coords</span><span class="p">:</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">pline</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">line_coords</span><span class="p">):</span>
<span class="n">line_color</span> <span class="o">=</span> <span class="n">line_colors</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">folium</span><span class="o">.</span><span class="n">PolyLine</span><span class="p">([(</span><span class="n">y</span><span class="p">,</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">pline</span><span class="p">],</span> <span class="n">color</span> <span class="o">=</span> <span class="n">line_color</span><span class="p">)</span><span class="o">.</span><span class="n">add_to</span><span class="p">(</span><span class="n">map_1</span><span class="p">)</span> <span class="c1">#need to reverse long/lat to lat/long</span>
<span class="k">return</span> <span class="n">map_1</span>
</pre></div>
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<div class="prompt input_prompt">In [5]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">sf_landmarks</span> <span class="o">=</span> <span class="n">plot_stops</span><span class="p">([</span><span class="n">transamerica</span><span class="p">,</span> <span class="n">sutro</span><span class="p">],</span> <span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'Transamerica Pyramid'</span><span class="p">,</span><span class="s1">'Sutro Tower'</span><span class="p">],</span>
<span class="n">zoom_level</span> <span class="o">=</span> <span class="mi">13</span><span class="p">,</span> <span class="n">tiles</span> <span class="o">=</span> <span class="s1">'Stamen Toner'</span><span class="p">,</span> <span class="n">point_colors</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'red'</span><span class="p">,</span><span class="s1">'blue'</span><span class="p">],</span>
<span class="n">line_coords</span> <span class="o">=</span> <span class="p">[</span><span class="n">transamerica</span><span class="p">,</span> <span class="n">sutro</span><span class="p">],</span> <span class="n">line_colors</span> <span class="o">=</span> <span class="s1">'purple'</span><span class="p">)</span>
<span class="n">sf_landmarks</span>
</pre></div>
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<p>I also demonstrate how a list of lists of points can be passed to my plotting function, resulting in each set of points being symbolized in a different color. I write a function that generates random points within a polygon, and use that to generate 6 lists of 5 points located in San Francisco (boundaries read in from a geosjon). I plot them below. The points are labeled by their group number (1-6) and their point number within their group (1-5).</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">gen_random_points</span><span class="p">(</span><span class="n">poly</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">random_seed</span> <span class="o">=</span> <span class="bp">None</span><span class="p">):</span>
<span class="n">xmin</span><span class="p">,</span> <span class="n">ymin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">,</span> <span class="n">ymax</span> <span class="o">=</span> <span class="n">poly</span><span class="o">.</span><span class="n">bounds</span>
<span class="n">Points</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">Points</span><span class="p">)</span> <span class="o"><=</span> <span class="n">n</span><span class="p">:</span>
<span class="k">if</span> <span class="n">random_seed</span><span class="p">:</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">RandomState</span><span class="p">(</span><span class="n">random_seed</span> <span class="o">+</span> <span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">),</span> <span class="n">RandomState</span><span class="p">(</span><span class="n">random_seed</span> <span class="o">+</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">uniform</span><span class="p">(</span><span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">),</span><span class="n">uniform</span><span class="p">(</span><span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span><span class="p">)</span>
<span class="k">if</span> <span class="n">Point</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">within</span><span class="p">(</span><span class="n">poly</span><span class="p">):</span>
<span class="n">Points</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">))</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">Points</span>
</pre></div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">SF</span> <span class="o">=</span> <span class="n">gpd</span><span class="o">.</span><span class="n">read_file</span><span class="p">(</span><span class="s1">'SF.geojson'</span><span class="p">)</span><span class="o">.</span><span class="n">iloc</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="s1">'geometry'</span><span class="p">]</span>
<span class="n">rand_points</span> <span class="o">=</span> <span class="p">[</span><span class="n">gen_random_points</span><span class="p">(</span><span class="n">SF</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="mi">5</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">)]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[[</span><span class="nb">str</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">i</span><span class="p">))</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">l</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="k">for</span> <span class="n">t</span><span class="p">,</span> <span class="n">l</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">rand_points</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span>
<span class="n">sf_rand_points</span> <span class="o">=</span> <span class="n">plot_stops</span><span class="p">(</span><span class="n">rand_points</span><span class="p">,</span> <span class="n">zoom_level</span> <span class="o">=</span> <span class="mi">12</span><span class="p">,</span> <span class="n">tiles</span> <span class="o">=</span> <span class="s1">'OpenStreetMap'</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">labels</span><span class="p">)</span>
<span class="n">sf_rand_points</span>
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                var icon_9f42008aca10400eb4d758ff21ac67cf = L.AwesomeMarkers.icon({
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                var icon_95d19bc693404c0fa79e54eb88f8221f = L.AwesomeMarkers.icon({
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                var icon_3daba3b7468740b8b542930bc736e645 = L.AwesomeMarkers.icon({
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            var marker_50756e9a6cc64643a1a22285d8b2ca86 = L.marker(
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                var icon_5d7030a565f34263bf6b9feb9f093169 = L.AwesomeMarkers.icon({
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            var marker_3ce31d07973e485b96e62a0da8745d6c = L.marker(
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                var icon_6cac4aabdcba4e72ba74cb1790bf68a5 = L.AwesomeMarkers.icon({
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            var marker_d06d7e40d9c44be9bcdadb72501201b4 = L.marker(
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                var icon_e3e41d3451d346e6abdadd19806d74f8 = L.AwesomeMarkers.icon({
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                var icon_f1536915f707409686a6978a335eae42 = L.AwesomeMarkers.icon({
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                var icon_d83f5def033d4412aba7f79713d6f71b = L.AwesomeMarkers.icon({
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            var marker_3259165b46034c71bcc82661dfc2a9b7 = L.marker(
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                var icon_82f7b651425342d39084e4e3fcd08c1d = L.AwesomeMarkers.icon({
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                var icon_8fbe182872c348989e4e968392c702ca = L.AwesomeMarkers.icon({
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                var icon_06c12e44b0c146a989ecfe3497a77899 = L.AwesomeMarkers.icon({
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                var icon_79d56fadae844f78b2e07ae2e73c7f2a = L.AwesomeMarkers.icon({
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                var icon_ca24afe4a8fd4506a059088e9ccaea4d = L.AwesomeMarkers.icon({
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<h2 id="Determining-Stop-Order-using-Mapzen's-Optimize-Route-Service">Determining Stop Order using Mapzen's Optimize Route Service<a class="anchor-link" href="#Determining-Stop-Order-using-Mapzen's-Optimize-Route-Service">¶</a></h2><p>Now that I have tools to geocode and visualize points, I’m ready to write a function that calls the Mapzen Optimize route service to calculate the optimal route that one person should use to visit a set of stops, starting and ending at a “home” location. Later on, I will build off of this function to optimize stops for multiple people, but this is an initial building-block. The key pieces of information that this function returns are trip length, trip distance, optimize stop order, an ordered set of stop coordinates, and the polyline that connects these stops.</p>
<p>Note that Mapzen uses the <a href="https://developers.google.com/maps/documentation/utilities/polylinealgorithm">Google Maps encoded polyline format</a> to store a series of latitude, longitude coordinates as a single string (this is done to reduce the size of the route response). Mapzen provides <a href="https://mapzen.com/documentation/mobility/decoding/">code</a> that can be used to decode the string, which I use in order to get a set of lat / long coordinates that I can plot.</p>
<p>The decoding function is listed below, applied to a sample coded string, and then mapped.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="c1">#Decoding function used to extract lat/long coordinates from google maps encoded polylines</span>
<span class="c1">#https://mapzen.com/documentation/mobility/decoding/</span>
<span class="c1">#six degrees of precision in valhalla</span>
<span class="n">inv</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="mf">1e6</span><span class="p">;</span>
<span class="c1">#decode an encoded string</span>
<span class="k">def</span> <span class="nf">decode</span><span class="p">(</span><span class="n">encoded</span><span class="p">):</span>
<span class="n">decoded</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">previous</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
<span class="c1">#for each byte</span>
<span class="k">while</span> <span class="n">i</span> <span class="o"><</span> <span class="nb">len</span><span class="p">(</span><span class="n">encoded</span><span class="p">):</span>
<span class="c1">#for each coord (lat, lon)</span>
<span class="n">ll</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]:</span>
<span class="n">shift</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">byte</span> <span class="o">=</span> <span class="mh">0x20</span>
<span class="c1">#keep decoding bytes until you have this coord</span>
<span class="k">while</span> <span class="n">byte</span> <span class="o">>=</span> <span class="mh">0x20</span><span class="p">:</span>
<span class="n">byte</span> <span class="o">=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">encoded</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="mi">63</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">ll</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">|=</span> <span class="p">(</span><span class="n">byte</span> <span class="o">&</span> <span class="mh">0x1f</span><span class="p">)</span> <span class="o"><<</span> <span class="n">shift</span>
<span class="n">shift</span> <span class="o">+=</span> <span class="mi">5</span>
<span class="c1">#get the final value adding the previous offset and remember it for the next</span>
<span class="n">ll</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">previous</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="o">~</span><span class="p">(</span><span class="n">ll</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">>></span> <span class="mi">1</span><span class="p">)</span> <span class="k">if</span> <span class="n">ll</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&</span> <span class="mi">1</span> <span class="k">else</span> <span class="p">(</span><span class="n">ll</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">>></span> <span class="mi">1</span><span class="p">))</span>
<span class="n">previous</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">ll</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<span class="c1">#scale by the precision and chop off long coords also flip the positions so</span>
<span class="c1">#its the far more standard lon,lat instead of lat,lon</span>
<span class="n">decoded</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="nb">float</span><span class="p">(</span><span class="s1">'</span><span class="si">%.6f</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">ll</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">inv</span><span class="p">)),</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'</span><span class="si">%.6f</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">ll</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">inv</span><span class="p">))])</span>
<span class="c1">#hand back the list of coordinates</span>
<span class="k">return</span> <span class="n">decoded</span>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">coded_polyline</span><span class="o">=</span><span class="n">decode</span><span class="p">(</span><span class="s1">'ciz`gAzxrqhF}wArEkZ|@`BvaA^|TbAhl@</span><span class="se">\\</span><span class="s1">|T|@xk@`BvaAbBfbAsFLaRzA'</span><span class="p">)</span>
<span class="n">coded_polyline</span>
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<pre>[[-122.464158, 37.779106],
[-122.464264, 37.780529],
[-122.464295, 37.780967],
[-122.465363, 37.780918],
[-122.465714, 37.780902],
[-122.466439, 37.780868],
[-122.46679, 37.780853],
[-122.467507, 37.780822],
[-122.468575, 37.780773],
[-122.469651, 37.780723],
[-122.469658, 37.780845],
[-122.469704, 37.78115]]</pre>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">map2</span> <span class="o">=</span> <span class="n">folium</span><span class="o">.</span><span class="n">Map</span><span class="p">(</span><span class="n">location</span> <span class="o">=</span> <span class="p">(</span><span class="n">coded_polyline</span><span class="p">[</span><span class="mi">5</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span><span class="n">coded_polyline</span><span class="p">[</span><span class="mi">5</span><span class="p">][</span><span class="mi">0</span><span class="p">]),</span><span class="n">zoom_start</span> <span class="o">=</span><span class="mi">17</span><span class="p">)</span>
<span class="n">folium</span><span class="o">.</span><span class="n">PolyLine</span><span class="p">([(</span><span class="n">y</span><span class="p">,</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">coded_polyline</span><span class="p">],</span><span class="n">color</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span><span class="o">.</span><span class="n">add_to</span><span class="p">(</span><span class="n">map2</span><span class="p">)</span>
<span class="n">map2</span>
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<p>My function also wraps the geocoding function I wrote above, so that the user can specify any combination of addresses, venues, and coordinates. It defaults to pedestrian mode of transportation, but the user can also specify driving or biking optimization. I also allow the user to specify a set of stop labels, which will be returned as the ordered list of stops. Otherwise, the function defaults to the raw input that was passed to the function</p>
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<div class="prompt input_prompt">In [11]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">optimize_stops</span><span class="p">(</span><span class="n">home</span><span class="p">,</span> <span class="n">stops</span><span class="p">,</span> <span class="n">costing</span> <span class="o">=</span> <span class="s1">'pedestrian'</span><span class="p">,</span> <span class="n">api_key</span> <span class="o">=</span> <span class="n">matrix_key</span><span class="p">,</span> <span class="n">home_label</span> <span class="o">=</span> <span class="s1">'Home'</span><span class="p">,</span>
<span class="n">stop_labels</span> <span class="o">=</span> <span class="bp">None</span><span class="p">):</span>
<span class="c1">#geocode home and stops if not a coordinate</span>
<span class="n">home</span> <span class="o">=</span> <span class="n">home</span> <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">home</span><span class="p">)</span> <span class="ow">is</span> <span class="nb">tuple</span> <span class="k">else</span> <span class="n">geocode_address_venue</span><span class="p">(</span><span class="n">home</span><span class="p">)</span>
<span class="n">stops</span> <span class="o">=</span> <span class="p">[</span><span class="n">geocode_address_venue</span><span class="p">(</span><span class="n">stop</span><span class="p">)[</span><span class="s1">'coords'</span><span class="p">]</span> <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">stop</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">tuple</span> <span class="k">else</span> <span class="n">stop</span> <span class="k">for</span> <span class="n">stop</span> <span class="ow">in</span> <span class="n">stops</span><span class="p">]</span>
<span class="c1">#full set of points are list of points that start and end with the home location</span>
<span class="n">points</span> <span class="o">=</span> <span class="p">[</span><span class="n">home</span><span class="p">]</span> <span class="o">+</span> <span class="n">stops</span> <span class="o">+</span> <span class="p">[</span><span class="n">home</span><span class="p">]</span>
<span class="c1">#round_points to 5 decimal points</span>
<span class="n">points</span><span class="o">=</span><span class="p">[(</span><span class="nb">round</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span><span class="nb">round</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">points</span><span class="p">]</span>
<span class="c1">#define point labels</span>
<span class="n">names</span> <span class="o">=</span> <span class="p">[</span><span class="n">home_label</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="n">stop_labels</span> <span class="k">if</span> <span class="n">stop_labels</span> <span class="k">else</span> <span class="n">stops</span><span class="p">)</span> <span class="o">+</span> <span class="p">[</span><span class="n">home_label</span><span class="p">]</span>
<span class="c1">#set up parameters to pass to mapzen function</span>
<span class="n">js</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'locations'</span><span class="p">:[{</span><span class="s1">'lon'</span><span class="p">:</span> <span class="n">point</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="s1">'lat'</span><span class="p">:</span> <span class="n">point</span><span class="p">[</span><span class="mi">1</span><span class="p">]}</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">points</span><span class="p">],</span> <span class="s1">'costing'</span><span class="p">:</span> <span class="n">costing</span><span class="p">}</span>
<span class="n">params</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'json'</span><span class="p">:</span> <span class="n">json</span><span class="o">.</span><span class="n">dumps</span><span class="p">(</span><span class="n">js</span><span class="p">),</span> <span class="s1">'api_key'</span><span class="p">:</span> <span class="n">api_key</span><span class="p">}</span>
<span class="n">url</span> <span class="o">=</span> <span class="s1">'https://matrix.mapzen.com/optimized_route'</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">requests</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">url</span><span class="p">,</span> <span class="n">params</span> <span class="o">=</span> <span class="n">params</span><span class="p">)</span>
<span class="n">raw</span> <span class="o">=</span> <span class="n">r</span><span class="o">.</span><span class="n">json</span><span class="p">()</span>
<span class="c1">#get the coordinates of the stops in their new optimized order</span>
<span class="n">locs</span> <span class="o">=</span> <span class="n">raw</span><span class="p">[</span><span class="s1">'trip'</span><span class="p">][</span><span class="s1">'locations'</span><span class="p">]</span>
<span class="n">new_point_order</span> <span class="o">=</span> <span class="p">[(</span><span class="n">locs</span><span class="p">[</span><span class="n">loc</span><span class="p">][</span><span class="s1">'lon'</span><span class="p">],</span> <span class="n">locs</span><span class="p">[</span><span class="n">loc</span><span class="p">][</span><span class="s1">'lat'</span><span class="p">])</span> <span class="k">for</span> <span class="n">loc</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">locs</span><span class="p">))]</span>
<span class="c1">#round to 5 decimal points</span>
<span class="n">new_point_order</span><span class="o">=</span><span class="p">[(</span><span class="nb">round</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">5</span><span class="p">),</span><span class="nb">round</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span> <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="n">new_point_order</span><span class="p">]</span>
<span class="n">point_order</span> <span class="o">=</span> <span class="p">[</span><span class="n">points</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">new_point_order</span><span class="p">]</span>
<span class="n">name_order</span> <span class="o">=</span> <span class="p">[</span><span class="n">names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">point_order</span><span class="p">]</span>
<span class="c1">#Extract the path shape for each of the legs, decode them, and then combine into one polyline</span>
<span class="n">raw_path</span> <span class="o">=</span> <span class="p">[</span><span class="n">raw</span><span class="p">[</span><span class="s1">'trip'</span><span class="p">][</span><span class="s1">'legs'</span><span class="p">][</span><span class="n">x</span><span class="p">][</span><span class="s1">'shape'</span><span class="p">]</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">raw</span><span class="p">[</span><span class="s1">'trip'</span><span class="p">][</span><span class="s1">'legs'</span><span class="p">]))]</span>
<span class="n">decode_paths</span> <span class="o">=</span> <span class="p">[</span><span class="nb">tuple</span><span class="p">(</span><span class="n">item</span><span class="p">)</span> <span class="k">for</span> <span class="n">sublist</span> <span class="ow">in</span> <span class="p">[</span><span class="n">decode</span><span class="p">(</span><span class="n">z</span><span class="p">)</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">raw_path</span><span class="p">]</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">sublist</span><span class="p">]</span>
<span class="c1">#return a dictionary that contains raw mapzen output, trip time, trip distance, new ordered points, </span>
<span class="c1">#new ordered point names, and a decoded path</span>
<span class="k">return</span> <span class="p">{</span><span class="s1">'raw'</span><span class="p">:</span> <span class="n">raw</span><span class="p">,</span>
<span class="s1">'time'</span><span class="p">:</span> <span class="n">raw</span><span class="p">[</span><span class="s1">'trip'</span><span class="p">][</span><span class="s1">'summary'</span><span class="p">][</span><span class="s1">'time'</span><span class="p">]</span><span class="o">/</span><span class="mi">60</span><span class="p">,</span>
<span class="s1">'length'</span><span class="p">:</span> <span class="n">raw</span><span class="p">[</span><span class="s1">'trip'</span><span class="p">][</span><span class="s1">'summary'</span><span class="p">][</span><span class="s1">'length'</span><span class="p">],</span>
<span class="s1">'points'</span><span class="p">:</span> <span class="n">new_point_order</span><span class="p">,</span>
<span class="s1">'original_points'</span><span class="p">:</span><span class="n">points</span><span class="p">,</span>
<span class="s1">'order'</span><span class="p">:</span> <span class="n">name_order</span><span class="p">,</span>
<span class="s1">'line'</span><span class="p">:</span> <span class="n">decode_paths</span><span class="p">}</span>
<span class="k">return</span> <span class="n">point_order</span>
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<p>Before extending this function to multiple salesman, I’ll demonstrate the output of this initial function. Below I define my optimization parameters:</p>
<ol>
<li>A list of 6 stops in my neighborhood that Celeste and I will need to visit as part of our Sunday morning errands (note that I use a combination of business names, addresses, and coordinates)</li>
<li>A set of names that correspond to these stops that will make the labeling clearer</li>
<li>A home location that will be the start and end point.</li>
</ol>
<p>As much as I wish it were the case, our Sunday errands generally do not involve ice cream, pizza, bagels, and art museums. Nonetheless, for this example I've used some of our favorite neighborhood destinations despite the fact that they are somewhat unrealistic “errand” destinations.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">stops</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'Toy Boat Dessert Cafe, San Francisco, CA'</span><span class="p">,</span>
<span class="s1">'Pizzetta 211, San Francisco, CA'</span><span class="p">,</span>
<span class="s1">'Arguello Super Market, San Francisco, CA'</span><span class="p">,</span>
<span class="s1">'4700 Geary Blvd, San Francisco, CA'</span><span class="p">,</span>
<span class="p">(</span><span class="o">-</span><span class="mf">122.465613</span><span class="p">,</span> <span class="mf">37.770016</span><span class="p">),</span>
<span class="s1">'3519 California St, San Francisco, CA 94118'</span><span class="p">]</span>
<span class="n">stop_labels</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'Toy Boat'</span><span class="p">,</span>
<span class="s1">'Pizzetta'</span><span class="p">,</span>
<span class="s1">'Arguello Market'</span><span class="p">,</span>
<span class="s1">'Lamps Plus'</span><span class="p">,</span>
<span class="s1">'de Young Museum'</span><span class="p">,</span>
<span class="s2">"Noah's Bagels"</span><span class="p">]</span>
<span class="n">home</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="mf">122.464186</span><span class="p">,</span> <span class="mf">37.779111</span><span class="p">)</span>
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<p>I then apply this function to my set of stops and return the optimized stop order, the route time, and the route distance. I first optimize the route as a pedestrian and then as a bicyclist. As you can see, the stop order is slightly different for these two modes of transit, likely keeping the bike route on roads and paths that are better for biking.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">walk_opt</span> <span class="o">=</span> <span class="n">optimize_stops</span><span class="p">(</span><span class="n">home</span><span class="p">,</span> <span class="n">stops</span><span class="p">,</span> <span class="n">stop_labels</span> <span class="o">=</span> <span class="n">stop_labels</span><span class="p">)</span>
<span class="k">print</span> <span class="n">walk_opt</span><span class="p">[</span><span class="s1">'order'</span><span class="p">]</span>
<span class="k">print</span> <span class="nb">str</span><span class="p">(</span><span class="n">walk_opt</span><span class="p">[</span><span class="s1">'time'</span><span class="p">])</span> <span class="o">+</span> <span class="s1">' minutes'</span>
<span class="k">print</span> <span class="nb">str</span><span class="p">(</span><span class="n">walk_opt</span><span class="p">[</span><span class="s1">'length'</span><span class="p">])</span> <span class="o">+</span> <span class="s1">' km'</span>
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<pre>['Home', 'de Young Museum', 'Arguello Market', "Noah's Bagels", 'Toy Boat', 'Pizzetta', 'Lamps Plus', 'Home']
116 minutes
9.625 km
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">walk_1_map</span><span class="o">=</span><span class="n">plot_stops</span><span class="p">(</span><span class="n">walk_opt</span><span class="p">[</span><span class="s1">'points'</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">zoom_level</span> <span class="o">=</span> <span class="mi">14</span><span class="p">,</span> <span class="n">tiles</span> <span class="o">=</span> <span class="s1">'Stamen Watercolor'</span><span class="p">,</span> \
<span class="n">labels</span> <span class="o">=</span> <span class="n">walk_opt</span><span class="p">[</span><span class="s1">'order'</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">line_coords</span> <span class="o">=</span> <span class="n">walk_opt</span><span class="p">[</span><span class="s1">'line'</span><span class="p">],</span> <span class="n">point_colors</span><span class="o">=</span><span class="p">[</span><span class="s1">'black'</span><span class="p">]</span><span class="o">+</span><span class="nb">len</span><span class="p">(</span><span class="n">stops</span><span class="p">)</span><span class="o">*</span><span class="p">[</span><span class="s1">'red'</span><span class="p">])</span>
<span class="n">walk_1_map</span>
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        " style="position:absolute;width:100%;height:100%;left:0;top:0;"></iframe></div></div>
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<div class="prompt input_prompt">In [15]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">bike_opt</span> <span class="o">=</span> <span class="n">optimize_stops</span><span class="p">(</span><span class="n">home</span><span class="p">,</span> <span class="n">stops</span><span class="p">,</span> <span class="n">stop_labels</span> <span class="o">=</span> <span class="n">stop_labels</span><span class="p">,</span><span class="n">costing</span> <span class="o">=</span> <span class="s1">'bicycle'</span><span class="p">)</span>
<span class="k">print</span> <span class="n">bike_opt</span><span class="p">[</span><span class="s1">'order'</span><span class="p">]</span>
<span class="k">print</span> <span class="nb">str</span><span class="p">(</span><span class="n">bike_opt</span><span class="p">[</span><span class="s1">'time'</span><span class="p">])</span> <span class="o">+</span> <span class="s1">' minutes'</span>
<span class="k">print</span> <span class="nb">str</span><span class="p">(</span><span class="n">bike_opt</span><span class="p">[</span><span class="s1">'length'</span><span class="p">])</span> <span class="o">+</span> <span class="s1">' km'</span>
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<pre>['Home', 'Pizzetta', 'Lamps Plus', 'Toy Boat', "Noah's Bagels", 'Arguello Market', 'de Young Museum', 'Home']
29 minutes
11.097 km
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<div class="prompt input_prompt">In [16]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">bike_1_map</span><span class="o">=</span><span class="n">plot_stops</span><span class="p">(</span><span class="n">bike_opt</span><span class="p">[</span><span class="s1">'points'</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">zoom_level</span> <span class="o">=</span> <span class="mi">14</span><span class="p">,</span> <span class="n">tiles</span> <span class="o">=</span> <span class="s1">'Stamen Watercolor'</span><span class="p">,</span> \
<span class="n">labels</span> <span class="o">=</span> <span class="n">bike_opt</span><span class="p">[</span><span class="s1">'order'</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">line_coords</span> <span class="o">=</span> <span class="n">bike_opt</span><span class="p">[</span><span class="s1">'line'</span><span class="p">],</span> <span class="n">point_colors</span><span class="o">=</span><span class="p">[</span><span class="s1">'black'</span><span class="p">]</span><span class="o">+</span><span class="nb">len</span><span class="p">(</span><span class="n">stops</span><span class="p">)</span><span class="o">*</span><span class="p">[</span><span class="s1">'red'</span><span class="p">])</span>
<span class="n">bike_1_map</span>
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<div class="output_area"><div class="prompt output_prompt">Out[16]:</div>
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<h2 id="Determining-Stops-and-Order-with-Multiple-People">Determining Stops and Order with Multiple People<a class="anchor-link" href="#Determining-Stops-and-Order-with-Multiple-People">¶</a></h2>
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<p>Now that I have a working function that wraps Mapzen's optimize route service, I am ready to extend it to work with multiple people. The general approach I take is to first find the unique combinations that a list of stops can be split among a given number of people, and then determine which of these combinations minimizes the maximum time of any one person.</p>
<p>Note that there are many different minimization criteria that can be used when optimizing a set of routes between multiple people. In this case, I’m assuming that Celeste and I start our errands at the same time and that they are completed when the last person is done. The length of time until all the errands are done (the max time of any person) is what I am trying to minimize. However, a more typical usage would perhaps be to minimize the sum or cumulative amount of time that it takes for all of the salesman to visit the stops. Nonetheless, the function can pretty easily be tweaked for any optimization criteria.</p>
<h3 id="Unique-ways-that-stops-can-be-split">Unique ways that stops can be split<a class="anchor-link" href="#Unique-ways-that-stops-can-be-split">¶</a></h3><p>I use a function adapted from <a href="http://stackoverflow.com/a/39199937/3776938">here</a> to find the unique ways in that a list of N elements can be partitioned into K groups. This function is written so that the order of groups or of elements within a group does not matter, as this is what the optimize route tool is going to determine! By this I mean that in terms of the input, <code>[['A','B'],['C','D']]</code> is considered identical to <code>[['C','D'],['A','B']]</code> as well as to <code>[['B','A'],['C','D']]</code>.</p>
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<div class="prompt input_prompt">In [17]:</div>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">sorted_k_partitions</span><span class="p">(</span><span class="n">seq</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">seq</span><span class="p">)</span>
<span class="n">working_partition</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">def</span> <span class="nf">generate_partitions</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">>=</span> <span class="n">n</span><span class="p">:</span>
<span class="k">yield</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">tuple</span><span class="p">,</span> <span class="n">working_partition</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">-</span> <span class="n">i</span> <span class="o">></span> <span class="n">k</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">working_partition</span><span class="p">):</span>
<span class="k">for</span> <span class="n">part</span> <span class="ow">in</span> <span class="n">working_partition</span><span class="p">:</span>
<span class="n">part</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">seq</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">for</span> <span class="n">bar</span> <span class="ow">in</span> <span class="n">generate_partitions</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">yield</span> <span class="n">bar</span>
<span class="n">part</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">working_partition</span><span class="p">)</span> <span class="o"><</span> <span class="n">k</span><span class="p">:</span>
<span class="n">working_partition</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">seq</span><span class="p">[</span><span class="n">i</span><span class="p">]])</span>
<span class="k">for</span> <span class="n">bar</span> <span class="ow">in</span> <span class="n">generate_partitions</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">yield</span> <span class="n">bar</span>
<span class="n">working_partition</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">generate_partitions</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># Sort the parts in each partition in shortlex order and then by the length of each part, </span>
<span class="c1">#and then lexicographically</span>
<span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="nb">sorted</span><span class="p">(</span><span class="n">ps</span><span class="p">,</span> <span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">p</span><span class="p">),</span> <span class="n">p</span><span class="p">))</span> <span class="k">for</span> <span class="n">ps</span> <span class="ow">in</span> <span class="n">result</span><span class="p">]</span>
<span class="n">result</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">ps</span><span class="p">:</span> <span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">len</span><span class="p">,</span> <span class="n">ps</span><span class="p">),</span> <span class="n">ps</span><span class="p">))</span>
<span class="k">return</span> <span class="n">result</span>
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<p>I demonstrate an application of the function below, showing the 7 unique ways that 4 stops can be split among 2 people.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">sorted_k_partitions</span><span class="p">([</span><span class="s1">'A'</span><span class="p">,</span> <span class="s1">'B'</span><span class="p">,</span> <span class="s1">'C'</span><span class="p">,</span> <span class="s1">'D'</span><span class="p">],</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">print</span> <span class="n">c</span>
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<pre>[('A',), ('B', 'C', 'D')]
[('B',), ('A', 'C', 'D')]
[('C',), ('A', 'B', 'D')]
[('D',), ('A', 'B', 'C')]
[('A', 'B'), ('C', 'D')]
[('A', 'C'), ('B', 'D')]
[('A', 'D'), ('B', 'C')]
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<p>More generally, I build a matrix that shows the number of stop combinations and number of optimize route requests that need to be made based on the number of stops and the number of salesman. The first number (labeled "C") is the number of unique combinations and the second (labeled "R") is the number of requests, which is just the number of combinations multiplied by the number of salesmen.</p>
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">num_test</span><span class="o">=</span><span class="mi">6</span>
<span class="n">nk_matrix</span><span class="o">=</span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">index</span><span class="o">=</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">num_test</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span><span class="n">columns</span><span class="o">=</span><span class="n">pd</span><span class="o">.</span><span class="n">MultiIndex</span><span class="o">.</span><span class="n">from_product</span><span class="p">([</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">num_test</span><span class="o">+</span><span class="mi">1</span><span class="p">),[</span><span class="s1">'C'</span><span class="p">,</span><span class="s1">'R'</span><span class="p">]]))</span>
<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">num_test</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">num_test</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="n">combos</span><span class="o">=</span><span class="n">sorted_k_partitions</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">k</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span><span class="n">n</span><span class="p">)</span>
<span class="n">nk_matrix</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">n</span><span class="p">,(</span><span class="n">k</span><span class="p">,</span><span class="s1">'C'</span><span class="p">)]</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">combos</span><span class="p">)</span>
<span class="n">nk_matrix</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">n</span><span class="p">,(</span><span class="n">k</span><span class="p">,</span><span class="s1">'R'</span><span class="p">)]</span><span class="o">=</span><span class="nb">len</span><span class="p">([</span><span class="n">item</span> <span class="k">for</span> <span class="n">sublist</span> <span class="ow">in</span> <span class="n">combos</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">sublist</span><span class="p">])</span>
<span class="n">nk_matrix</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">name</span><span class="o">=</span><span class="s1">'# of Salesman'</span>
<span class="n">nk_matrix</span><span class="o">.</span><span class="n">columns</span><span class="o">.</span><span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s1">'# of Stops'</span><span class="p">,</span><span class="bp">None</span><span class="p">]</span>
<span class="n">nk_matrix</span>
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<th># of Stops</th>
<th colspan="2" halign="left">1</th>
<th colspan="2" halign="left">2</th>
<th colspan="2" halign="left">3</th>
<th colspan="2" halign="left">4</th>
<th colspan="2" halign="left">5</th>
<th colspan="2" halign="left">6</th>
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<th></th>
<th>C</th>
<th>R</th>
<th>C</th>
<th>R</th>
<th>C</th>
<th>R</th>
<th>C</th>
<th>R</th>
<th>C</th>
<th>R</th>
<th>C</th>
<th>R</th>
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