Advanced Example: Optimizing Using Geographic Quantities¶
In the previous section we saw how to use the SingleMetricOptimizer to optimize
for plans that contain the minimum number of cut edges. However, sometimes we may wish to
include other geographic quantities in our optimization equation. Obtaining and working
with this sort of data can be a bit more involved, so here we will show how to use the
requests package to download data directly from the Census API and how to use that data
for optimization.
Getting the Data¶
First, we will need to install the requests package:
pip install requests
Then we can import the package in the head of our jupyter notebook and download the data:
import requests
import pandas as pd
shape_url = "https://www2.census.gov/geo/tiger/TIGER2020PL/LAYER/BG/2020/tl_2020_01_bg20.zip"
shape_response = requests.get(shape_url)
with open("tl_2020_01_bg20.zip", "wb") as f:
f.write(shape_response.content)
pop_url = "https://api.census.gov/data/2020/dec/pl?get=group%28P1%29&for=block%20group&in=state%3A02%20county%3A*"
pop_response = requests.get(pop_url)
pop_df = pd.DataFrame(pop_response.json()[1:], columns=pop_response.json()[0])
pop_df.to_pickle("01_bg_P1_2020.pkl")
Note that we have now saved the data for later so that we can use it more easily in the next section.
Preparing the Data¶
We are now ready to work with the optimizer. First, we will need to import the necessary packages:
from gerrychain import Graph, GeographicPartition, MarkovChain
from gerrychain.updaters import Tally
from gerrychain.metrics.compactness import polsby_popper
from gerrychain.proposals import recom
from gerrychain.tree import bipartition_tree
from gerrychain.accept import always_accept
from gerrychain.optimization import SingleMetricOptimizer
from functools import partial
import numpy as np
import pandas as pd
import geopandas as gpd
import random
random.seed(2024)
Now we need to import the data and check the Coordinate Reference System (CRS) for reasons that will be explained momentarily:
gdf = gpd.read_file("tl_2020_01_bg20.zip")
gdf.crs
<Geographic 2D CRS: EPSG:4269>
Name: NAD83
Axis Info [ellipsoidal]:
- Lat[north]: Geodetic latitude (degree)
- Lon[east]: Geodetic longitude (degree)
Area of Use:
- name: North America - onshore and offshore: Canada - Alberta; British Columbia; Manitoba; New Brunswick; Newfoundland and Labrador; Northwest Territories; Nova Scotia; Nunavut; Ontario; Prince Edward Island; Quebec; Saskatchewan; Yukon. Puerto Rico. United States (USA) - Alabama; Alaska; Arizona; Arkansas; California; Colorado; Connecticut; Delaware; Florida; Georgia; Hawaii; Idaho; Illinois; Indiana; Iowa; Kansas; Kentucky; Louisiana; Maine; Maryland; Massachusetts; Michigan; Minnesota; Mississippi; Missouri; Montana; Nebraska; Nevada; New Hampshire; New Jersey; New Mexico; New York; North Carolina; North Dakota; Ohio; Oklahoma; Oregon; Pennsylvania; Rhode Island; South Carolina; South Dakota; Tennessee; Texas; Utah; Vermont; Virginia; Washington; West Virginia; Wisconsin; Wyoming. US Virgin Islands. British Virgin Islands.
- bounds: (167.65, 14.92, -40.73, 86.45)
Datum: North American Datum 1983
- Ellipsoid: GRS 1980
- Prime Meridian: Greenwich
In this example, we will be interested in optimizing the average Polsby-Popper score for the example data, but before we can do that, we need to make sure that the CRS for our data is appropriate for the measurements we wish to take. For this example, this means that we would like avoid coordinate systems like the geographic coordinate system (lat, long) which measures distances in degrees in favor of something like a Mercator or transverse Mercator projection which measures distances in meters and is subject to less distortion.
We can see that the Census uses the CRS EPSG:4269 which is a geographic coordinate system and
not useful for computing things like the Polsby-Popper score, so we need to transform the data
mildly before we can use it. In general, to find a good choice of CRS, it is best to consult
the official EPSG website epsg.io. In this case, we are working with Alabama,
and we know that the Albers Equal Area Conic projection with epsg code 5070 is a good choice. So
we will modify our geodataframe to use this CRS and then make a graph from it:
gdf.to_crs(epsg=5070, inplace=True)
graph = Graph.from_geodataframe(gdf)
# And we should check to make sure that the CRS is set properly
graph.data.crs
<Projected CRS: EPSG:5070>
Name: NAD83 / Conus Albers
Axis Info [cartesian]:
- X[east]: Easting (metre)
- Y[north]: Northing (metre)
Area of Use:
- name: United States (USA) - CONUS onshore - Alabama; Arizona; Arkansas; California; Colorado; Connecticut; Delaware; Florida; Georgia; Idaho; Illinois; Indiana; Iowa; Kansas; Kentucky; Louisiana; Maine; Maryland; Massachusetts; Michigan; Minnesota; Mississippi; Missouri; Montana; Nebraska; Nevada; New Hampshire; New Jersey; New Mexico; New York; North Carolina; North Dakota; Ohio; Oklahoma; Oregon; Pennsylvania; Rhode Island; South Carolina; South Dakota; Tennessee; Texas; Utah; Vermont; Virginia; Washington; West Virginia; Wisconsin; Wyoming.
- bounds: (-124.79, 24.41, -66.91, 49.38)
Coordinate Operation:
- name: Conus Albers
- method: Albers Equal Area
Datum: North American Datum 1983
- Ellipsoid: GRS 1980
- Prime Meridian: Greenwich
Since we used a shapefile that was directly from the US Census, we will need to add in the population data to the graph. Here we have the 2020 P1 table from the US Census with the column “P1_001N” corresponding to the total population of each geograpic unit.
population_data = pd.read_pickle('01_bg_P1_2020.pkl')
population_data.head()
GEO_ID NAME P1_001N P1_001NA P1_002N P1_002NA P1_003N P1_003NA P1_004N P1_004NA P1_005N P1_005NA P1_006N P1_006NA P1_007N P1_007NA P1_008N P1_008NA P1_009N P1_009NA P1_010N P1_010NA P1_011N P1_011NA P1_012N P1_012NA P1_013N P1_013NA P1_014N P1_014NA P1_015N P1_015NA P1_016N P1_016NA P1_017N P1_017NA P1_018N P1_018NA P1_019N P1_019NA P1_020N P1_020NA P1_021N P1_021NA P1_022N P1_022NA P1_023N P1_023NA P1_024N P1_024NA P1_025N P1_025NA P1_026N P1_026NA P1_027N P1_027NA P1_028N P1_028NA P1_029N P1_029NA P1_030N P1_030NA P1_031N P1_031NA P1_032N P1_032NA P1_033N P1_033NA P1_034N P1_034NA P1_035N P1_035NA P1_036N P1_036NA P1_037N P1_037NA P1_038N P1_038NA P1_039N P1_039NA P1_040N P1_040NA P1_041N P1_041NA P1_042N P1_042NA P1_043N P1_043NA P1_044N P1_044NA P1_045N P1_045NA P1_046N P1_046NA P1_047N P1_047NA P1_048N P1_048NA P1_049N P1_049NA P1_050N P1_050NA P1_051N P1_051NA P1_052N P1_052NA P1_053N P1_053NA P1_054N P1_054NA P1_055N P1_055NA P1_056N P1_056NA P1_057N P1_057NA P1_058N P1_058NA P1_059N P1_059NA P1_060N P1_060NA P1_061N P1_061NA P1_062N P1_062NA P1_063N P1_063NA P1_064N P1_064NA P1_065N P1_065NA P1_066N P1_066NA P1_067N P1_067NA P1_068N P1_068NA P1_069N P1_069NA P1_070N P1_070NA P1_071N P1_071NA state county tract block group
0 1500000US010610503006 Block Group 6, Census Tract 503, Geneva County, Alabama 639 None 576 None 396 None 163 None 0 None 4 None 0 None 13 None 63 None 60 None 29 None 17 None 0 None 0 None 10 None 3 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 3 None 3 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050300 6
1 1500000US010610504003 Block Group 3, Census Tract 504, Geneva County, Alabama 950 None 884 None 819 None 24 None 5 None 1 None 0 None 35 None 66 None 63 None 11 None 28 None 3 None 0 None 20 None 0 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 3 None 3 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050400 3
2 1500000US010610505001 Block Group 1, Census Tract 505, Geneva County, Alabama 1158 None 1084 None 958 None 94 None 4 None 4 None 2 None 22 None 74 None 73 None 20 None 35 None 2 None 1 None 14 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 1 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050500 1
3 1500000US010610505004 Block Group 4, Census Tract 505, Geneva County, Alabama 1022 None 950 None 746 None 170 None 4 None 1 None 0 None 29 None 72 None 67 None 14 None 25 None 4 None 0 None 21 None 0 None 0 None 0 None 3 None 0 None 0 None 0 None 0 None 0 None 0 None 5 None 0 None 0 None 0 None 3 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050500 4
4 1500000US010610506003 Block Group 3, Census Tract 506, Geneva County, Alabama 1386 None 1281 None 1192 None 40 None 10 None 2 None 0 None 37 None 105 None 99 None 23 None 42 None 5 None 1 None 26 None 0 None 0 None 0 None 2 None 0 None 0 None 0 None 0 None 0 None 0 None 5 None 5 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 1 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050600 3
We now need to merge the population data with the graph data. Unfortunately, the Census data for the shapefile and for the P1 table do not have consistent formatting for the geoids, so we need to fix that.
# This grabs the UID part of the GEO_ID column and puts it into a new column called GEOID20
population_data["GEOID20"] = population_data["GEO_ID"].apply(lambda x: x.split("US")[1])
full_data = pd.merge(population_data, graph.data, on='GEOID20')
# Check to make sure the number of rows in the full data is the same as the number of rows
# in the graph.data dataframe. This is a sanity check to make sure we didn't lose any data.
assert full_data.shape[0] == graph.data.shape[0]
full_data.set_index("GEOID20", inplace=True)
full_data.head()
GEO_ID NAME P1_001N P1_001NA P1_002N P1_002NA P1_003N P1_003NA P1_004N P1_004NA P1_005N P1_005NA P1_006N P1_006NA P1_007N P1_007NA P1_008N P1_008NA P1_009N P1_009NA P1_010N P1_010NA P1_011N P1_011NA P1_012N P1_012NA P1_013N P1_013NA P1_014N P1_014NA P1_015N P1_015NA P1_016N P1_016NA P1_017N P1_017NA P1_018N P1_018NA P1_019N P1_019NA P1_020N P1_020NA P1_021N P1_021NA P1_022N P1_022NA P1_023N P1_023NA P1_024N P1_024NA P1_025N P1_025NA P1_026N P1_026NA P1_027N P1_027NA P1_028N P1_028NA P1_029N P1_029NA P1_030N P1_030NA P1_031N P1_031NA P1_032N P1_032NA P1_033N P1_033NA P1_034N P1_034NA P1_035N P1_035NA P1_036N P1_036NA P1_037N P1_037NA P1_038N P1_038NA P1_039N P1_039NA P1_040N P1_040NA P1_041N P1_041NA P1_042N P1_042NA P1_043N P1_043NA P1_044N P1_044NA P1_045N P1_045NA P1_046N P1_046NA P1_047N P1_047NA P1_048N P1_048NA P1_049N P1_049NA P1_050N P1_050NA P1_051N P1_051NA P1_052N P1_052NA P1_053N P1_053NA P1_054N P1_054NA P1_055N P1_055NA P1_056N P1_056NA P1_057N P1_057NA P1_058N P1_058NA P1_059N P1_059NA P1_060N P1_060NA P1_061N P1_061NA P1_062N P1_062NA P1_063N P1_063NA P1_064N P1_064NA P1_065N P1_065NA P1_066N P1_066NA P1_067N P1_067NA P1_068N P1_068NA P1_069N P1_069NA P1_070N P1_070NA P1_071N P1_071NA state county tract block group STATEFP20 COUNTYFP20 TRACTCE20 BLKGRPCE20 NAMELSAD20 MTFCC20 FUNCSTAT20 ALAND20 AWATER20 INTPTLAT20 INTPTLON20 geometry
GEOID20
010610503006 1500000US010610503006 Block Group 6, Census Tract 503, Geneva County, Alabama 639 None 576 None 396 None 163 None 0 None 4 None 0 None 13 None 63 None 60 None 29 None 17 None 0 None 0 None 10 None 3 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 3 None 3 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050300 6 01 061 050300 6 Block Group 6 G5030 S 822081 0 +31.0405326 -085.8752036 POLYGON ((961077.073 936796.629, 961083.626 936803.369, 961095.821 936814.627, 961102.231 936819.116, 961084.582 936950.221, 961082.266 936979.055, 961116.056 936969.132, 961155.759 936956.71, 961179 936948.792, 961232.612 936931.593, 961246.545 936927.49, 961271.133 936918.598, 961439.601 936860.997, 961465.562 936852.7, 961500.477 936839.432, 961543.872 936824.721, 961594.435 936808.317, 961633.596 936794.721, 961677.216 936777.91, 961703.213 936769.281, 961715.774 936764.585, 961729.648 936761.035, 961785.664 936737.497, 961852.088 936707.915, 961876.868 936698.15, 961944.441 936664.105, 961939.71 936645.702, 961929.858 936614.336, 961926.593 936601.012, 961919.627 936577.561, 961917.321 936561.544, 961917.144 936545.306, 961918.138 936524.384, 961920.066 936509.938, 961923.366 936478.19, 961926.832 936437.734, 961928.985 936400.606, 961935.467 936386.535, 961949.815 936379.458, 961965.89 936376.815, 961998.263 936373.903, 962017.141 936372.79, 962063.248 936371.235, 962103.57 936370.963, 962112.311 936368.879, 962117.658 936361.845, 962119.302 936353.632, 962124.922 936293.945, 962129.063 936264.188, 962137.653 936183.008, 962148.254 936091.083, 962150.336 936067.145, 962151.957 936059.154, 962156.239 936043.282, 962161.906 936027.893, 962164.047 936019.51, 962165.077 935994.677, 962181.001 935895.044, 962191.743 935823.267, 962188.29 935809.028, 962201.408 935800.924, 962223.588 935790.435, 962230.579 935785.926, 962236.127 935779.696, 962239.983 935772.279, 962241.71 935764.187, 962253.696 935673.641, 962253.956 935667.628, 962266.474 935571.211, 962269.645 935551.417, 962271.112 935544.863, 962273.987 935527.834, 962259.945 935532.036, 962220.731 935542.492, 962153.351 935556.759, 962046.296 935575.953, 962028.209 935578.604, 961983.27 935589.792, 961905.079 935611.18, 961789.403 935642.989, 961725.526 935660.317, 961579.971 935698.553, 961568.781 935701.159, 961514.238 935716.244, 961538.003 935721.357, 961581.167 935723.176, 961570.182 935827.699, 961568.266 935839.351, 961563.963 935884.078, 961561.692 935899.941, 961559.99 935922.129, 961554.479 935964.714, 961548.224 936021.425, 961548.035 936028.563, 961542.229 936072.123, 961540.337 936094.291, 961534.863 936142.808, 961531.256 936174.747, 961525.214 936221.414, 961516.191 936295.948, 961511.19 936352.569, 961510.245 936368.575, 961508.128 936383.896, 961506.307 936393.768, 961499.387 936394.929, 961483.313 936396.678, 961443.228 936402.794, 961418.791 936405.774, 961402.551 936406.387, 961383.165 936404.202, 961359.532 936398.768, 961345.149 936394.546, 961333.511 936413.882, 961317.84 936432.452, 961306.012 936443.715, 961280.299 936464.007, 961252.659 936481.745, 961245.929 936486.506, 961238.726 936490.322, 961232.185 936495.104, 961225.207 936499.503, 961218.844 936504.415, 961208.093 936516.353, 961149.846 936594.798, 961114.662 936641.035, 961110.664 936646.2, 961102.031 936659.818, 961098.661 936667.175, 961093.493 936682.394, 961090.36 936698.278, 961083.87 936746.463, 961081.613 936771.165, 961079.484 936779.438, 961077.073 936796.629))
010610504003 1500000US010610504003 Block Group 3, Census Tract 504, Geneva County, Alabama 950 None 884 None 819 None 24 None 5 None 1 None 0 None 35 None 66 None 63 None 11 None 28 None 3 None 0 None 20 None 0 None 0 None 0 None 1 None 0 None 0 None 0 None 0 None 0 None 0 None 3 None 3 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 0 None 01 061 050400 3 01 061 050400 3 Block Group 3 G5030 S 89084411 1388652 +31.0355522 -085.6754867 POLYGON ((974553.169 933731.527, 974546.304 933804.61, 974526.239 934035.777, 974523.391 934059.406, 974518.527 934114.027, 974517.988 934127.839, 974517.476 934139.641, 974530.233 934138.562, 974538.823 934138.821, 974553.814 934140.11, 974647.95 934153.33, 974674.462 934156.986, 974746.403 934168.249, 974774.106 934175.055, 974793.349 934181.279, 974808.31 934187.263, 974852.085 934209.234, 974892.955 934235.924, 974946.392 934278.295, 975121.557 934419.436, 975146.328 934440.914, 975278.773 934547.672, 975286.787 934553.239, 975297.581 934576.447, 975300.256 934584.455, 975302.363 934592.402, 975303.906 934605.546, 975298.555 934657.541, 975279.777 934816.587, 975214.85 935402.982, 975209.605 935446.936, 975202.77 935502.909, 975178.131 935731.014, 975157.977 935916.874, 975154.572 935948.274, 975138.025 936110.586, 975120.165 936272.645, 975111.673 936353.61, 975103.843 936434.647, 975097.381 936526.907, 975093.998 936575.761, 975091.427 936611.839, 975079.54 936782.377, 975066.906 936970.398, 975060.211 937067.445, 975059.155 937102.792, 975059.49 937124.419, 975068.757 937161.669, 975076.352 937185.202, 975085.865 937207.824, 975097.698 937229.355, 975133.025 937274.353, 975173.16 937314.728, 975507.763 937643.56, 975659.482 937792.699, 975781.413 937911.984, 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And now we can add the population data to the graph:
for node, data in graph.nodes(data=True):
# Note that the pops are np.int64 types, so we convert them to ints here
data["TOTPOP"] = int(full_data.loc[data["GEOID20"]]["P1_001N"])
# Just a quick check of the data that is stored on the graph nodes
graph.nodes(data=True)[0]
{'boundary_node': False,
'area': 1100226.0333901227,
'STATEFP': '01',
'COUNTYFP': '033',
'TRACTCE': '020200',
'BLKGRPCE': '1',
'GEOID': '010330202001',
'NAMELSAD': 'Block Group 1',
'MTFCC': 'G5030',
'FUNCSTAT': 'S',
'ALAND': 994584,
'AWATER': 105643,
'INTPTLAT': '+34.7664259',
'INTPTLON': '-087.6960323',
'geometry': <POLYGON ((752587.971 1333045.744, 752581.759 1333117.737, 752581.362 133313...>,
'TOTPOP': 1171}
Using SingleMetricOptimizer¶
There is a polsby_popper updater in GerryChain, but you need to make sure that the
CRS for your data is correct before you use it. If is is not, then you can run into some issues with
distortion of the geometry. However, we already checked that our CRS is appropriate in this
tutorial, so we don’t need to worry. We can now follow the usual workflow laid out in the
optimization tutorial
with the only tweak being that we need to use a GeographicPartition object instead
of a regular Partition object for the SingleMetricOptimizer since we want to use the
polsby_popper updater which relies on the area and perimeter updaters.
updaters = {
"population": Tally("TOTPOP", alias="population"),
"polsby-popper": polsby_popper,
}
# We need to use the GeographicPartition class to make sure that area and perimeter
# updaters are also calculated. These are used in the calculation of the polsby-popper
# score.
initial_partition = GeographicPartition.from_random_assignment(
graph=graph,
n_parts=4,
epsilon=0.01,
pop_col="TOTPOP",
updaters=updaters
)
ideal_population = sum(initial_partition["population"].values())/len(initial_partition)
opt_metric = lambda x: sum(x["polsby-popper"].values())/len(x)
optimizer = SingleMetricOptimizer(
initial_state=initial_partition,
proposal=proposal,
constraints=[],
optimization_metric=opt_metric,
maximize=True,
)
tilt_best = -1
for i, part in enumerate(optimizer.tilted_run(1000, 0.1, with_progress_bar=True)):
tilt_best = max(tilt_best, opt_metric(part))
print(tilt_best)
100%|██████████| 1000/1000 [03:48<00:00, 4.38it/s]
0.30465552990184624