Note
Go to the end to download the full example code
Forecasting#
In this example, we present a full forecasting workflow for the Sioux Falls example model.
Imports
from uuid import uuid4
from tempfile import gettempdir
from os.path import join
from aequilibrae.utils.create_example import create_example
import logging
import sys
We create the example project inside our temp folder
fldr = join(gettempdir(), uuid4().hex)
project = create_example(fldr)
logger = project.logger
# We get the project open, and we can tell the logger to direct all messages to the terminal as well
stdout_handler = logging.StreamHandler(sys.stdout)
formatter = logging.Formatter("%(asctime)s;%(levelname)s ; %(message)s")
stdout_handler.setFormatter(formatter)
logger.addHandler(stdout_handler)
Traffic assignment with skimming#
from aequilibrae.paths import TrafficAssignment, TrafficClass
We build all graphs
project.network.build_graphs()
# We get warnings that several fields in the project are filled with NaNs.
# This is true, but we won't use those fields
2023-07-10 09:02:47,983;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
2023-07-10 09:02:48,028;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
2023-07-10 09:02:48,073;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
2023-07-10 09:02:48,116;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
2023-07-10 09:02:48,160;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
2023-07-10 09:02:48,204;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
We grab the graph for cars
graph = project.network.graphs["c"]
# Let's say we want to minimize the free_flow_time
graph.set_graph("free_flow_time")
# And will skim time and distance while we are at it
graph.set_skimming(["free_flow_time", "distance"])
# And we will allow paths to be computed going through other centroids/centroid connectors
# required for the Sioux Falls network, as all nodes are centroids
graph.set_blocked_centroid_flows(False)
2023-07-10 09:02:48,234;WARNING ; Cost field with wrong type. Converting to float64
We get the demand matrix directly from the project record So let’s inspect what we have in the project
proj_matrices = project.matrices
print(proj_matrices.list())
name file_name ... description status
0 demand_omx demand.omx ... Original data imported to OMX format
1 demand_mc demand_mc.omx ... None
2 skims skims.omx ... Example skim
3 demand_aem demand.aem ... Original data imported to AEM format
[4 rows x 8 columns]
Let’s get it in this better way
demand = proj_matrices.get_matrix("demand_omx")
demand.computational_view(["matrix"])
assig = TrafficAssignment()
# Create the assignment class
assigclass = TrafficClass(name="car", graph=graph, matrix=demand)
# The first thing to do is to add at list of traffic classes to be assigned
assig.add_class(assigclass)
# We set these parameters only after adding one class to the assignment
assig.set_vdf("BPR") # This is not case-sensitive
# Then we set the volume delay function
assig.set_vdf_parameters({"alpha": "b", "beta": "power"}) # And its parameters
assig.set_capacity_field("capacity") # The capacity and free flow travel times as they exist in the graph
assig.set_time_field("free_flow_time")
# And the algorithm we want to use to assign
assig.set_algorithm("bfw")
# Since I haven't checked the parameters file, let's make sure convergence criteria is good
assig.max_iter = 1000
assig.rgap_target = 0.001
assig.execute() # we then execute the assignment
2023-07-10 09:02:48,613;INFO ; Traffic Class specification
2023-07-10 09:02:48,613;INFO ; {'car': {'Graph': "{'Mode': 'c', 'Block through centroids': False, 'Number of centroids': 24, 'Links': 76, 'Nodes': 24}", 'Matrix': "{'Source': '/tmp/605a246ed3434856bcb0123287fe45e2/matrices/demand.omx', 'Number of centroids': 24, 'Matrix cores': ['matrix'], 'Matrix totals': {'matrix': 360600.0}}"}}
2023-07-10 09:02:48,613;INFO ; Traffic Assignment specification
2023-07-10 09:02:48,613;INFO ; {'VDF parameters': {'alpha': 'b', 'beta': 'power'}, 'VDF function': 'bpr', 'Number of cores': 2, 'Capacity field': 'capacity', 'Time field': 'free_flow_time', 'Algorithm': 'bfw', 'Maximum iterations': 250, 'Target RGAP': 0.0001}
2023-07-10 09:02:48,616;WARNING ; Cost field with wrong type. Converting to float64
2023-07-10 09:02:48,616;INFO ; bfw Assignment STATS
2023-07-10 09:02:48,616;INFO ; Iteration, RelativeGap, stepsize
2023-07-10 09:02:48,625;INFO ; 1,inf,1.0
2023-07-10 09:02:48,631;INFO ; 2,0.8550751349428284,0.32839952448634563
2023-07-10 09:02:48,637;INFO ; 3,0.4763455007221067,0.18660240547488702
2023-07-10 09:02:48,646;INFO ; 4,0.2355126365951965,0.2411477440291793
2023-07-10 09:02:48,654;INFO ; 5,0.10924072010481088,0.8185470737942447
2023-07-10 09:02:48,661;INFO ; 6,0.1980945227617506,0.14054330572978305
2023-07-10 09:02:48,669;INFO ; 7,0.0668172221544687,0.36171152718899247
2023-07-10 09:02:48,675;INFO ; 8,0.06792122267870587,0.9634685345644044
2023-07-10 09:02:48,682;INFO ; 9,0.10705582933092855,0.13757153109677187
2023-07-10 09:02:48,687;INFO ; 10,0.04038814432034622,0.1609403425427973
2023-07-10 09:02:48,693;INFO ; 11,0.025801226183773084,0.716435057617116
2023-07-10 09:02:48,700;INFO ; 12,0.042846437173170424,0.08581544277016687
2023-07-10 09:02:48,705;INFO ; 13,0.016971662333407043,0.1660157969033195
2023-07-10 09:02:48,712;INFO ; 14,0.020396548012132195,0.4461322062863191
2023-07-10 09:02:48,718;INFO ; 15,0.025887901335905694,0.08515995223661561
2023-07-10 09:02:48,725;INFO ; 16,0.015188959427663162,0.1988698342670051
2023-07-10 09:02:48,730;INFO ; 17,0.01475141964322897,0.3548856159715819
2023-07-10 09:02:48,737;INFO ; 18,0.015582407302127808,0.06145415154081679
2023-07-10 09:02:48,743;INFO ; 19,0.008935871473338547,0.08603462968532699
2023-07-10 09:02:48,748;INFO ; 20,0.008477045208211683,0.1668913886047936
2023-07-10 09:02:48,754;INFO ; 21,0.009517581409988221,0.4917099156011133
2023-07-10 09:02:48,760;INFO ; 22,0.013060711845093087,0.060284308755231206
2023-07-10 09:02:48,767;INFO ; 23,0.006861821876765184,0.10954009782378307
2023-07-10 09:02:48,772;INFO ; 24,0.006201113315688483,0.12230718464290123
2023-07-10 09:02:48,778;INFO ; 25,0.0074574049738041406,0.3080614235512652
2023-07-10 09:02:48,784;INFO ; 26,0.006900497787039256,0.32835666337221175
2023-07-10 09:02:48,790;INFO ; 27,0.006963554132391016,0.7377893941135681
2023-07-10 09:02:48,796;INFO ; 28,0.006817764279834173,0.0443870768699142
2023-07-10 09:02:48,808;INFO ; 29,0.004277860366532555,0.05431813621783447
2023-07-10 09:02:48,812;INFO ; 30,0.004136181096381436,0.05758294976347482
2023-07-10 09:02:48,816;INFO ; 31,0.0031483923250298237,0.0918038853550363
2023-07-10 09:02:48,822;INFO ; 32,0.0034184967969881734,0.12279944254979965
2023-07-10 09:02:48,828;INFO ; 33,0.002738614050254322,0.08799214942487946
2023-07-10 09:02:48,835;INFO ; 34,0.0023403784016331874,0.1098259985006849
2023-07-10 09:02:48,841;INFO ; 35,0.0023185435502055523,0.18741920884713098
2023-07-10 09:02:48,847;INFO ; 36,0.0023838181828793143,0.1404967362503087
2023-07-10 09:02:48,855;INFO ; 37,0.0017801377860521138,0.25278698153070905
2023-07-10 09:02:48,861;INFO ; 38,0.0019264349761422953,0.30768123024764726
2023-07-10 09:02:48,866;INFO ; 39,0.0018408894375062524,0.3982324050247662
2023-07-10 09:02:48,872;INFO ; 40,0.0018205742523357215,0.5255149131180074
2023-07-10 09:02:48,878;INFO ; 41,0.0020224171108353135,0.012343794696331265
2023-07-10 09:02:48,885;INFO ; 42,0.001423836778473865,0.03045402621736974
2023-07-10 09:02:48,891;INFO ; 43,0.0011877471305860427,0.02283308748607117
2023-07-10 09:02:48,898;INFO ; 44,0.0012106681494599195,0.06969126002892805
2023-07-10 09:02:48,903;INFO ; 45,0.0011336232568064097,0.038970964685986896
2023-07-10 09:02:48,911;INFO ; 46,0.0009780989052684459,0.022071990851560294
2023-07-10 09:02:48,911;INFO ; bfw Assignment finished. 46 iterations and 0.0009780989052684459 final gap
Convergence report is easy to see
import pandas as pd
convergence_report = assig.report()
print(convergence_report.head())
iteration rgap alpha warnings beta0 beta1 beta2
0 1 inf 1.000000 1.000000 0.000000 0.0
1 2 0.855075 0.328400 1.000000 0.000000 0.0
2 3 0.476346 0.186602 1.000000 0.000000 0.0
3 4 0.235513 0.241148 1.000000 0.000000 0.0
4 5 0.109241 0.818547 0.607382 0.392618 0.0
volumes = assig.results()
print(volumes.head())
matrix_ab matrix_ba matrix_tot ... PCE_AB PCE_BA PCE_tot
link_id ...
1 4565.043510 NaN 4565.043510 ... 4565.043510 NaN 4565.043510
2 8152.210795 NaN 8152.210795 ... 8152.210795 NaN 8152.210795
3 4552.603997 NaN 4552.603997 ... 4552.603997 NaN 4552.603997
4 5988.789717 NaN 5988.789717 ... 5988.789717 NaN 5988.789717
5 8164.650309 NaN 8164.650309 ... 8164.650309 NaN 8164.650309
[5 rows x 15 columns]
We could export it to CSV or AequilibraE data, but let’s put it directly into the results database
assig.save_results("base_year_assignment")
And save the skims
assig.save_skims("base_year_assignment_skims", which_ones="all", format="omx")
2023-07-10 09:02:48,998;WARNING ; Matrix Record has been saved to the database
Trip distribution#
Calibration#
We will calibrate synthetic gravity models using the skims for TIME that we just generated
import numpy as np
from aequilibrae.distribution import GravityCalibration
Let’s take another look at what we have in terms of matrices in the model
print(proj_matrices.list())
name ... status
0 demand_omx ...
1 demand_mc ...
2 skims ...
3 demand_aem ...
4 base_year_assignment_skims_car ...
[5 rows x 8 columns]
We need the demand
demand = proj_matrices.get_matrix("demand_aem")
# And the skims
imped = proj_matrices.get_matrix("base_year_assignment_skims_car")
We can check which matrix cores were created for our skims to decide which one to use
imped.names
# Where ``free_flow_time_final`` is actually the congested time for the last iteration
['distance_blended', 'distance_final', 'free_flow_time_blended', 'free_flow_time_final']
But before using the data, let’s get some impedance for the intrazonals Let’s assume it is 75% of the closest zone
imped_core = "free_flow_time_final"
imped.computational_view([imped_core])
# If we run the code below more than once, we will be overwriting the diagonal values with non-sensical data
# so let's zero it first
np.fill_diagonal(imped.matrix_view, 0)
# We compute it with a little bit of NumPy magic
intrazonals = np.amin(imped.matrix_view, where=imped.matrix_view > 0, initial=imped.matrix_view.max(), axis=1)
intrazonals *= 0.75
# Then we fill in the impedance matrix
np.fill_diagonal(imped.matrix_view, intrazonals)
Since we are working with an OMX file, we cannot overwrite a matrix on disk So we give a new name to save it
imped.save(names=["final_time_with_intrazonals"])
This also updates these new matrices as those being used for computation As one can verify below
imped.view_names
['final_time_with_intrazonals']
We set the matrices for being used in computation
demand.computational_view(["matrix"])
for function in ["power", "expo"]:
gc = GravityCalibration(matrix=demand, impedance=imped, function=function, nan_as_zero=True)
gc.calibrate()
model = gc.model
# We save the model
model.save(join(fldr, f"{function}_model.mod"))
# We can save the result of applying the model as well
# We can also save the calibration report
with open(join(fldr, f"{function}_convergence.log"), "w") as otp:
for r in gc.report:
otp.write(r + "\n")
Forecast#
We create a set of ‘future’ vectors using some random growth factors. We apply the model for inverse power, as the trip frequency length distribution (TFLD) seems to be a better fit for the actual one.
from aequilibrae.distribution import Ipf, GravityApplication, SyntheticGravityModel
from aequilibrae.matrix import AequilibraeData
We compute the vectors from our matrix
origins = np.sum(demand.matrix_view, axis=1)
destinations = np.sum(demand.matrix_view, axis=0)
args = {
"file_path": join(fldr, "synthetic_future_vector.aed"),
"entries": demand.zones,
"field_names": ["origins", "destinations"],
"data_types": [np.float64, np.float64],
"memory_mode": False,
}
vectors = AequilibraeData()
vectors.create_empty(**args)
vectors.index[:] = demand.index[:]
# Then grow them with some random growth between 0 and 10%, and balance them
vectors.origins[:] = origins * (1 + np.random.rand(vectors.entries) / 10)
vectors.destinations[:] = destinations * (1 + np.random.rand(vectors.entries) / 10)
vectors.destinations *= vectors.origins.sum() / vectors.destinations.sum()
Impedance#
imped = proj_matrices.get_matrix("base_year_assignment_skims_car")
imped.computational_view(["final_time_with_intrazonals"])
# If we wanted the main diagonal to not be considered...
# ``np.fill_diagonal(imped.matrix_view, np.nan)``
for function in ["power", "expo"]:
model = SyntheticGravityModel()
model.load(join(fldr, f"{function}_model.mod"))
outmatrix = join(proj_matrices.fldr, f"demand_{function}_model.aem")
args = {
"impedance": imped,
"rows": vectors,
"row_field": "origins",
"model": model,
"columns": vectors,
"column_field": "destinations",
"nan_as_zero": True,
}
gravity = GravityApplication(**args)
gravity.apply()
# We get the output matrix and save it to OMX too,
gravity.save_to_project(name=f"demand_{function}_modeled", file_name=f"demand_{function}_modeled.omx")
2023-07-10 09:02:49,983;WARNING ; Matrix Record has been saved to the database
2023-07-10 09:02:50,108;WARNING ; Matrix Record has been saved to the database
We update the matrices table/records and verify that the new matrices are indeed there
proj_matrices.update_database()
print(proj_matrices.list())
name ... status
0 demand_omx ...
1 demand_mc ...
2 skims ...
3 demand_aem ...
4 base_year_assignment_skims_car ...
5 demand_power_modeled ...
6 demand_expo_modeled ...
[7 rows x 8 columns]
IPF for the future vectors#
args = {
"matrix": demand,
"rows": vectors,
"columns": vectors,
"column_field": "destinations",
"row_field": "origins",
"nan_as_zero": True,
}
ipf = Ipf(**args)
ipf.fit()
ipf.save_to_project(name="demand_ipfd", file_name="demand_ipfd.aem")
ipf.save_to_project(name="demand_ipfd_omx", file_name="demand_ipfd.omx")
2023-07-10 09:02:50,192;WARNING ; Matrix Record has been saved to the database
2023-07-10 09:02:50,210;WARNING ; Matrix Record has been saved to the database
<aequilibrae.project.data.matrix_record.MatrixRecord object at 0x7f95e4ad2250>
df = proj_matrices.list()
Future traffic assignment#
from aequilibrae.paths import TrafficAssignment, TrafficClass
logger.info("\n\n\n TRAFFIC ASSIGNMENT FOR FUTURE YEAR")
2023-07-10 09:02:50,221;INFO ;
TRAFFIC ASSIGNMENT FOR FUTURE YEAR
demand = proj_matrices.get_matrix("demand_ipfd")
# Let's see what is the core we ended up getting. It should be 'gravity'
demand.names
['matrix']
Let’s use the IPF matrix
demand.computational_view("matrix")
assig = TrafficAssignment()
# Creates the assignment class
assigclass = TrafficClass(name="car", graph=graph, matrix=demand)
# The first thing to do is to add at a list of traffic classes to be assigned
assig.add_class(assigclass)
assig.set_vdf("BPR") # This is not case-sensitive
# Then we set the volume delay function
assig.set_vdf_parameters({"alpha": "b", "beta": "power"}) # And its parameters
assig.set_capacity_field("capacity") # The capacity and free flow travel times as they exist in the graph
assig.set_time_field("free_flow_time")
# And the algorithm we want to use to assign
assig.set_algorithm("bfw")
# Since I haven't checked the parameters file, let's make sure convergence criteria is good
assig.max_iter = 500
assig.rgap_target = 0.00001
OPTIONAL
# If we want to execute select link analysis on a particular TrafficClass, we set the links we are analyzing.
# The format of the input select links is a dictionary (str: list[tuple]).
# Each entry represents a separate set of selected links to compute. The str name will name the set of links.
# The list[tuple] is the list of links being selected, of the form (link_id, direction), as it occurs in the Graph.
# Direction can be 0, 1, -1. 0 denotes bi-directionality
# For example, let's use Select Link on two sets of links:
select_links = {
"Leaving node 1": [(1, 1), (2, 1)],
"Random nodes": [(3, 1), (5, 1)],
}
# We call this command on the class we are analyzing with our dictionary of values
assigclass.set_select_links(select_links)
assig.execute() # we then execute the assignment
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/traffic_class.py:145: UserWarning: Input string name has a space in it. Replacing with _
warnings.warn("Input string name has a space in it. Replacing with _")
2023-07-10 09:02:50,585;INFO ; Traffic Class specification
2023-07-10 09:02:50,585;INFO ; {'car': {'Graph': "{'Mode': 'c', 'Block through centroids': False, 'Number of centroids': 24, 'Links': 76, 'Nodes': 24}", 'Matrix': "{'Source': '/tmp/605a246ed3434856bcb0123287fe45e2/matrices/demand_ipfd.aem', 'Number of centroids': 24, 'Matrix cores': ['matrix'], 'Matrix totals': {'matrix': 382536.20097205363}}", 'select_links': "{'Leaving node 1': [(1, 1), (2, 1)], 'Random nodes': [(3, 1), (5, 1)]}"}}
2023-07-10 09:02:50,585;INFO ; Traffic Assignment specification
2023-07-10 09:02:50,585;INFO ; {'VDF parameters': {'alpha': 'b', 'beta': 'power'}, 'VDF function': 'bpr', 'Number of cores': 2, 'Capacity field': 'capacity', 'Time field': 'free_flow_time', 'Algorithm': 'bfw', 'Maximum iterations': 250, 'Target RGAP': 0.0001}
2023-07-10 09:02:50,588;WARNING ; Cost field with wrong type. Converting to float64
2023-07-10 09:02:50,588;INFO ; bfw Assignment STATS
2023-07-10 09:02:50,588;INFO ; Iteration, RelativeGap, stepsize
2023-07-10 09:02:50,597;INFO ; 1,inf,1.0
2023-07-10 09:02:50,607;INFO ; 2,0.8795919869953654,0.31331063682955723
2023-07-10 09:02:50,617;INFO ; 3,0.5360129873389503,0.17597819200958426
2023-07-10 09:02:50,626;INFO ; 4,0.2924614505718223,0.16482489782032997
2023-07-10 09:02:50,635;INFO ; 5,0.1052366041857067,0.6349735624197105
2023-07-10 09:02:50,644;INFO ; 6,0.2715136772478963,0.10459945679965084
2023-07-10 09:02:50,656;INFO ; 7,0.11781011966163812,0.21111735540988738
2023-07-10 09:02:50,664;INFO ; 8,0.0850776283739523,0.575286412372591
2023-07-10 09:02:50,673;INFO ; 9,0.12322167565410132,0.12643870939740742
2023-07-10 09:02:50,681;INFO ; 10,0.044833141154050314,0.26088861278030745
2023-07-10 09:02:50,691;INFO ; 11,0.07118456106039972,0.1307238518677271
2023-07-10 09:02:50,699;INFO ; 12,0.039141468289747135,0.3239761053686282
2023-07-10 09:02:50,707;INFO ; 13,0.054521372480731745,0.10992762611035817
2023-07-10 09:02:50,715;INFO ; 14,0.02742691631925726,0.3060594266344289
2023-07-10 09:02:50,724;INFO ; 15,0.037248656511930406,0.11470875303026531
2023-07-10 09:02:50,732;INFO ; 16,0.022168393029814968,0.23127947168080548
2023-07-10 09:02:50,741;INFO ; 17,0.028421536520833044,0.6217799894523263
2023-07-10 09:02:50,750;INFO ; 18,0.03443458476548453,0.10013338528657975
2023-07-10 09:02:50,757;INFO ; 19,0.01792423440110266,0.136382999268021
2023-07-10 09:02:50,764;INFO ; 20,0.01624402913455306,0.1726291635312231
2023-07-10 09:02:50,773;INFO ; 21,0.01730505872104108,0.3414184028839711
2023-07-10 09:02:50,781;INFO ; 22,0.017224025319293332,0.07933633674991811
2023-07-10 09:02:50,789;INFO ; 23,0.008453754315633846,0.09851131023680491
2023-07-10 09:02:50,796;INFO ; 24,0.008959340766600123,0.25121581087844397
2023-07-10 09:02:50,805;INFO ; 25,0.012810859360898343,0.5846345453765212
2023-07-10 09:02:50,813;INFO ; 26,0.012182501418995828,0.06750141787551657
2023-07-10 09:02:50,821;INFO ; 27,0.00805109885593924,0.09448581388184552
2023-07-10 09:02:50,829;INFO ; 28,0.008086985650916074,0.06516453917555576
2023-07-10 09:02:50,837;INFO ; 29,0.004795922659532676,0.11402598084043394
2023-07-10 09:02:50,850;INFO ; 30,0.004581637707119888,0.11922158215850195
2023-07-10 09:02:50,855;INFO ; 31,0.003954985445439641,0.2620558755772106
2023-07-10 09:02:50,863;INFO ; 32,0.006045029505366215,0.6016057534665686
2023-07-10 09:02:50,871;INFO ; 33,0.005348195403870384,0.527951371363937
2023-07-10 09:02:50,878;INFO ; 34,0.005096634103988734,0.0262769807022434
2023-07-10 09:02:50,887;INFO ; 35,0.003949092198394268,0.03651730692390135
2023-07-10 09:02:50,897;INFO ; 36,0.0038003904720482094,0.03990543314685324
2023-07-10 09:02:50,905;INFO ; 37,0.003670045522030177,0.06034230149079298
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2023-07-10 09:02:52,566;INFO ; 234,1.4315547162781446e-05,0.0006100744608752764
2023-07-10 09:02:52,574;INFO ; 235,1.096192820554258e-05,0.0006306114672946604
2023-07-10 09:02:52,583;INFO ; 236,1.237550131122646e-05,0.0004098984181829807
2023-07-10 09:02:52,594;INFO ; 237,8.433735211950508e-06,0.0003753927609437029
2023-07-10 09:02:52,594;INFO ; bfw Assignment finished. 237 iterations and 8.433735211950508e-06 final gap
Now let us save our select link results, all we need to do is provide it with a name In addition to exporting the select link flows, it also exports the Select Link matrices in OMX format.
assig.save_select_link_results("select_link_analysis")
Say we just want to save our select link flows, we can call:
assig.save_select_link_flows("just_flows")
# Or if we just want the SL matrices:
assig.save_select_link_matrices("just_matrices")
# Internally, the save_select_link_results calls both of these methods at once.
# We could export it to CSV or AequilibraE data, but let's put it directly into the results database
assig.save_results("future_year_assignment")
# And save the skims
assig.save_skims("future_year_assignment_skims", which_ones="all", format="omx")
2023-07-10 09:02:52,684;WARNING ; Matrix Record has been saved to the database
We can also plot convergence#
import matplotlib.pyplot as plt
df = assig.report()
x = df.iteration.values
y = df.rgap.values
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(x, y, "k--")
plt.yscale("log")
plt.grid(True, which="both")
plt.xlabel(r"Iterations")
plt.ylabel(r"Relative Gap")
plt.show()
Close the project
project.close()
Total running time of the script: ( 0 minutes 5.325 seconds)