Note
Go to the end to download the full example code.
Re-estimation of best models
After running the assisted specification algorithm for the 432 specifications in Combination of many specifications, we use post processing to re-estimate all Pareto optimal models, and display some information about the algorithm. See Bierlaire and Ortelli (2023).
- author:
Michel Bierlaire, EPFL
- date:
Thu Jul 20 17:15:37 2023
try:
import matplotlib.pyplot as plt
can_plot = True
except ModuleNotFoundError:
can_plot = False
import biogeme.biogeme_logging as blog
import biogeme.biogeme as bio
from biogeme.assisted import ParetoPostProcessing
from everything_spec import model_catalog, database
logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b08selected_specification')
PARETO_FILE_NAME = 'saved_results/b07everything_assisted.pareto'
Example b08selected_specification
Create the biogeme object from the catalog.
the_biogeme = bio.BIOGEME(database, model_catalog)
the_biogeme.modelName = 'b09post_processing'
Biogeme parameters read from biogeme.toml.
Create the post processing object.
post_processing = ParetoPostProcessing(
biogeme_object=the_biogeme, pareto_file_name=PARETO_FILE_NAME
)
Pareto set initialized from file with 192 elements [11 Pareto] and 29 invalid elements.
Re-estimate the models.
all_results = post_processing.reestimate(recycle=True)
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000000.iter
Cannot read file __b09post_processing_000000.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_TRAIN ASC_TRAIN_GA B_COST_CAR B_COST_SM B_COST_TRAIN B_TIME B_TIME_commuter cube_tt_coef mu_existing square_tt_coef Function Relgrad Radius Rho
0 0.16 -1.3 -0.92 1.6 -0.24 -0.74 -0.77 0 0 0.00019 1.5 -0.1 1e+04 0.28 0.5 -1.5 -
1 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.5 0.52 +
2 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.25 0.52 -
3 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.12 0.52 -
4 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.062 0.52 -
5 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.031 0.52 -
6 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.016 -1.6 -
7 -0.25 -1.3 -0.95 1.5 -0.67 -0.24 -0.75 -0.3 -0.047 0.0075 1.5 -0.1 9.2e+03 5.3 0.0078 -0.7 -
8 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.039 -0.00034 1.5 -0.1 8.9e+03 9.9 0.0078 0.78 +
9 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.039 -0.00034 1.5 -0.1 8.9e+03 9.9 0.0039 -0.36 -
10 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.039 -0.00034 1.5 -0.1 8.9e+03 9.9 0.002 -0.4 -
11 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.039 -0.00034 1.5 -0.1 8.9e+03 9.9 0.00098 -0.0026 -
12 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.039 0.00064 1.5 -0.1 8.8e+03 3.7 0.00098 0.41 +
13 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.039 0.00064 1.5 -0.1 8.8e+03 3.7 0.00049 -0.82 -
14 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.04 0.00015 1.5 -0.1 8.8e+03 4 0.00049 0.67 +
15 -0.25 -1.3 -0.96 1.5 -0.66 -0.25 -0.75 -0.29 -0.04 0.00023 1.5 -0.1 8.8e+03 0.19 0.0049 0.97 ++
16 -0.24 -1.3 -0.96 1.5 -0.66 -0.26 -0.75 -0.29 -0.04 0.00021 1.5 -0.098 8.8e+03 0.17 0.049 1 ++
17 -0.21 -1.3 -0.98 1.5 -0.62 -0.3 -0.76 -0.32 -0.047 6.8e-05 1.5 -0.067 8.7e+03 0.07 0.49 1 ++
18 -0.21 -1.3 -0.98 1.5 -0.62 -0.3 -0.76 -0.32 -0.047 6.8e-05 1.5 -0.067 8.7e+03 0.07 0.24 -0.1 -
19 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.24 0.82 +
20 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.12 -1.9 -
21 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.061 -1.5 -
22 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.031 -1.5 -
23 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.015 -1.9 -
24 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.0076 -2.3 -
25 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.0038 -2.7 -
26 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.0019 -2.9 -
27 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.00095 -2.6 -
28 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.00048 -1.7 -
29 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.00024 -1 -
30 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.0011 1.5 0.18 8.4e+03 6.1 0.00012 -0.13 -
31 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.00098 1.5 0.18 8.4e+03 1.1 0.00012 0.82 +
32 -0.09 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.00097 1.5 0.18 8.4e+03 0.06 0.0012 0.99 ++
33 -0.091 -1.2 -1.1 1.4 -0.49 -0.54 -0.74 -0.56 -0.1 -0.00097 1.5 0.18 8.4e+03 0.059 0.012 1 ++
34 -0.1 -1.2 -1.1 1.4 -0.5 -0.55 -0.73 -0.56 -0.1 -0.00093 1.5 0.17 8.4e+03 0.049 0.12 1 ++
35 -0.19 -1.2 -0.97 1.3 -0.53 -0.63 -0.63 -0.68 -0.099 -0.00076 1.4 0.12 8.3e+03 0.25 1.2 0.98 ++
36 -0.19 -1.2 -0.97 1.3 -0.53 -0.63 -0.63 -0.68 -0.099 -0.00076 1.4 0.12 8.3e+03 0.25 0.6 -35 -
37 -0.19 -1.2 -0.97 1.3 -0.53 -0.63 -0.63 -0.68 -0.099 -0.00076 1.4 0.12 8.3e+03 0.25 0.3 -4 -
38 -0.2 -1.1 -0.99 1.2 -0.42 -0.64 -0.69 -0.98 -0.12 -7.1e-05 1.4 -0.044 8.2e+03 2.1 0.3 0.78 +
39 -0.24 -1.1 -0.82 1.2 -0.4 -0.69 -0.66 -1.3 -0.21 -5e-05 1.4 -0.049 8.2e+03 2 3 1 ++
40 -0.24 -1.1 -0.82 1.2 -0.4 -0.69 -0.66 -1.3 -0.21 -5e-05 1.4 -0.049 8.2e+03 2 1.4 -1.2e+02 -
41 -0.24 -1.1 -0.82 1.2 -0.4 -0.69 -0.66 -1.3 -0.21 -5e-05 1.4 -0.049 8.2e+03 2 0.71 -19 -
42 -0.24 -1.1 -0.82 1.2 -0.4 -0.69 -0.66 -1.3 -0.21 -5e-05 1.4 -0.049 8.2e+03 2 0.36 -6.2 -
43 -0.24 -1.1 -0.82 1.2 -0.4 -0.69 -0.66 -1.3 -0.21 -5e-05 1.4 -0.049 8.2e+03 2 0.18 -1.3 -
44 -0.23 -1 -0.81 1.2 -0.37 -0.62 -0.72 -1.5 -0.27 0.00021 1.4 -0.11 8.2e+03 20 0.18 0.43 +
45 -0.23 -0.98 -0.66 1.2 -0.36 -0.69 -0.67 -1.6 -0.37 0.00012 1.4 -0.089 8.1e+03 6 1.8 0.9 ++
46 -0.14 -0.35 -0.27 0.97 -0.24 -0.63 -0.78 -2 -1 0.00029 1.7 -0.13 8.1e+03 21 1.8 0.12 +
47 -0.17 -0.49 -0.32 1 -0.24 -0.67 -0.77 -1.9 -0.98 0.00018 1.6 -0.1 8.1e+03 29 1.8 0.7 +
48 -0.17 -0.54 -0.34 1 -0.26 -0.66 -0.81 -2 -0.97 0.0002 1.6 -0.11 8.1e+03 10 1.8 0.87 +
49 -0.17 -0.56 -0.35 1 -0.27 -0.66 -0.82 -1.9 -0.94 0.0002 1.6 -0.11 8.1e+03 0.62 18 1 ++
50 -0.17 -0.55 -0.35 1 -0.27 -0.66 -0.82 -1.9 -0.93 0.0002 1.6 -0.11 8.1e+03 0.0046 1.8e+02 1 ++
51 -0.17 -0.55 -0.35 1 -0.27 -0.66 -0.82 -1.9 -0.93 0.0002 1.6 -0.11 8.1e+03 1.2e-05 1.8e+02 1 ++
Results saved in file b09post_processing_000000.html
Results saved in file b09post_processing_000000.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000001.iter
Cannot read file __b09post_processing_000001.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_TRAIN ASC_TRAIN_GA B_COST B_TIME cube_tt_coef mu_existing square_tt_coef Function Relgrad Radius Rho
0 -0.17 -0.55 -0.35 1 -0.77 -2.1 0.0002 1.6 -0.11 8.4e+03 11 0.5 -0.11 -
1 0.31 -0.54 -0.42 1.1 -0.34 -1.8 0.00022 2.1 -0.11 8.2e+03 0.44 0.5 0.44 +
2 0.13 -0.59 -0.5 0.98 -0.54 -1.7 0.00019 1.8 -0.1 8.2e+03 2.1 5 1 ++
3 0.16 -0.65 -0.51 1.1 -0.6 -1.8 0.00019 1.6 -0.1 8.2e+03 4.3 50 0.99 ++
4 0.16 -0.68 -0.51 1.1 -0.6 -1.8 0.00019 1.6 -0.1 8.2e+03 0.22 5e+02 0.99 ++
5 0.16 -0.68 -0.51 1.1 -0.6 -1.8 0.00019 1.6 -0.1 8.2e+03 0.0042 5e+03 1 ++
6 0.16 -0.68 -0.51 1.1 -0.6 -1.8 0.00019 1.6 -0.1 8.2e+03 2.1e-05 5e+03 1 ++
Results saved in file b09post_processing_000001.html
Results saved in file b09post_processing_000001.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000002.iter
Cannot read file __b09post_processing_000002.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_TRAIN B_COST B_TIME Function Relgrad Radius Rho
0 -0.022 -0.7 -0.78 -1.1 8.7e+03 0.022 1 0.83 +
1 0.014 -0.66 -0.79 -1.3 8.7e+03 0.0011 10 1 ++
2 0.014 -0.66 -0.79 -1.3 8.7e+03 2.9e-06 10 1 ++
Results saved in file b09post_processing_000002.html
Results saved in file b09post_processing_000002.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000003.iter
Cannot read file __b09post_processing_000003.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_TRAIN ASC_TRAIN_GA B_COST B_TIME B_TIME_1st_clas Function Relgrad Radius Rho
0 -0.046 -1 -1.3 1.5 -0.77 -0.69 -0.5 8.3e+03 0.025 1 0.79 +
1 0.002 -1.2 -1.2 1.5 -0.78 -0.86 -0.61 8.3e+03 0.0015 10 1 ++
2 0.002 -1.2 -1.2 1.5 -0.78 -0.86 -0.61 8.3e+03 9.2e-06 10 1 ++
Results saved in file b09post_processing_000003.html
Results saved in file b09post_processing_000003.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000004.iter
Cannot read file __b09post_processing_000004.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_TRAIN ASC_TRAIN_GA B_COST_CAR B_COST_SM B_COST_TRAIN B_TIME B_TIME_commuter cube_tt_coef square_tt_coef Function Relgrad Radius Rho
0 -0.17 -1.1 -0.42 1.2 -0.35 -0.75 -1.2 -2.1 -1.1 0.00021 -0.11 8.1e+03 13 10 0.91 ++
1 -0.17 -1.1 -0.55 1.3 -0.36 -0.76 -1.1 -2.1 -1.1 0.0002 -0.11 8.1e+03 0.3 1e+02 1 ++
2 -0.18 -1.1 -0.56 1.3 -0.36 -0.76 -1.1 -2.1 -1.1 0.00021 -0.11 8.1e+03 0.0031 1e+03 1 ++
3 -0.18 -1.1 -0.56 1.3 -0.36 -0.76 -1.1 -2.1 -1.1 0.00021 -0.11 8.1e+03 7e-06 1e+03 1 ++
Results saved in file b09post_processing_000004.html
Results saved in file b09post_processing_000004.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000005.iter
Cannot read file __b09post_processing_000005.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. Function Relgrad Radius Rho
0 8.6e+03 23 0.5 0.068 -
1 8.2e+03 19 0.5 0.7 +
2 8.1e+03 4.6 5 0.94 ++
3 8.1e+03 0.76 50 1 ++
4 8.1e+03 0.017 5e+02 1 ++
5 8.1e+03 1.9e-05 5e+02 1 ++
Results saved in file b09post_processing_000005.html
Results saved in file b09post_processing_000005.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000006.iter
Cannot read file __b09post_processing_000006.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_TRAIN ASC_TRAIN_GA B_COST B_TIME cube_tt_coef square_tt_coef Function Relgrad Radius Rho
0 0.26 -1.1 -0.52 1.3 -0.78 -2.2 -7.9e-05 -0.048 8.3e+03 11 1 0.73 +
1 0.26 -1.1 -0.52 1.3 -0.78 -2.2 -7.9e-05 -0.048 8.3e+03 11 0.5 -6 -
2 0.26 -1.1 -0.52 1.3 -0.78 -2.2 -7.9e-05 -0.048 8.3e+03 11 0.25 -1.2 -
3 0.26 -1.1 -0.52 1.3 -0.78 -2.2 -7.9e-05 -0.048 8.3e+03 11 0.12 0.0099 -
4 0.24 -1.1 -0.65 1.3 -0.74 -2.3 0.00045 -0.13 8.3e+03 9.8 0.12 0.34 +
5 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.12 0.67 +
6 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.062 -0.69 -
7 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.031 -0.64 -
8 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.016 -0.64 -
9 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.0078 -0.48 -
10 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.0039 -0.47 -
11 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.002 -0.49 -
12 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.00098 -0.5 -
13 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.00049 -0.51 -
14 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.00024 -0.52 -
15 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00016 -0.11 8.2e+03 55 0.00012 -0.32 -
16 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00028 -0.11 8.2e+03 25 0.00012 0.18 +
17 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00028 -0.11 8.2e+03 25 6.1e-05 -0.46 -
18 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00022 -0.11 8.2e+03 4.7 6.1e-05 0.84 +
19 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00021 -0.11 8.2e+03 0.98 6.1e-05 0.88 +
20 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00021 -0.11 8.2e+03 0.031 0.00061 1 ++
21 0.21 -1.2 -0.77 1.4 -0.71 -2.3 0.00022 -0.11 8.2e+03 0.018 0.0061 1 ++
22 0.22 -1.2 -0.78 1.4 -0.71 -2.3 0.00022 -0.11 8.2e+03 0.069 0.061 1 ++
23 0.23 -1.2 -0.81 1.5 -0.73 -2.2 0.0002 -0.11 8.2e+03 1.1 0.61 0.99 ++
24 0.15 -1.2 -0.92 1.6 -0.72 -2.1 0.0002 -0.1 8.2e+03 0.21 6.1 1 ++
25 0.16 -1.3 -0.92 1.6 -0.72 -2.1 0.0002 -0.1 8.2e+03 0.00068 61 1 ++
26 0.16 -1.3 -0.92 1.6 -0.72 -2.1 0.0002 -0.1 8.2e+03 3.5e-05 61 1 ++
Results saved in file b09post_processing_000006.html
Results saved in file b09post_processing_000006.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000007.iter
Cannot read file __b09post_processing_000007.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_TRAIN ASC_TRAIN_GA B_COST B_TIME B_TIME_commuter cube_tt_coef mu_public square_tt_coef Function Relgrad Radius Rho
0 0.18 -1.3 -0.89 1.6 -0.71 -2 -1.1 0.0002 1 -0.11 8.2e+03 4.5 10 0.99 ++
1 0.17 -1.3 -0.91 1.6 -0.71 -2 -1.1 0.0002 1 -0.11 8.2e+03 0.14 1e+02 1 ++
2 0.17 -1.3 -0.9 1.6 -0.71 -2 -1.1 0.0002 1 -0.11 8.2e+03 0.39 1e+03 1 ++
3 0.17 -1.3 -0.9 1.6 -0.71 -2 -1.2 0.0002 1 -0.11 8.2e+03 0.092 1e+04 1 ++
4 0.17 -1.3 -0.9 1.6 -0.71 -2 -1.2 0.0002 1 -0.11 8.2e+03 7.4e-05 1e+04 1 ++
Results saved in file b09post_processing_000007.html
Results saved in file b09post_processing_000007.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000008.iter
Cannot read file __b09post_processing_000008.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_TRAIN B_COST B_TIME B_TIME_1st_clas Function Relgrad Radius Rho
0 0.0085 -0.71 -0.86 -0.91 -0.68 8.6e+03 0.00067 10 1 ++
1 0.0085 -0.71 -0.86 -0.91 -0.68 8.6e+03 2.7e-06 10 1 ++
Results saved in file b09post_processing_000008.html
Results saved in file b09post_processing_000008.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000009.iter
Cannot read file __b09post_processing_000009.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_CAR_GA ASC_CAR_one_lug ASC_CAR_several ASC_TRAIN ASC_TRAIN_GA ASC_TRAIN_one_l ASC_TRAIN_sever B_COST_CAR B_COST_SM B_COST_TRAIN B_TIME B_TIME_commuter cube_tt_coef square_tt_coef Function Relgrad Radius Rho
0 -0.14 -0.92 -0.082 -0.5 -0.88 1.2 0.49 0.44 -0.35 -0.75 -1 -2.1 -1.1 0.0002 -0.11 8.1e+03 2.5 10 1.1 ++
1 -0.13 -1 -0.083 -0.51 -0.92 1.2 0.54 0.51 -0.36 -0.76 -1.1 -2.1 -1.2 0.00021 -0.11 8.1e+03 0.25 1e+02 1 ++
2 -0.13 -1 -0.083 -0.51 -0.93 1.2 0.55 0.52 -0.36 -0.76 -1.1 -2.1 -1.2 0.00021 -0.11 8.1e+03 0.0021 1e+03 1 ++
3 -0.13 -1 -0.083 -0.51 -0.93 1.2 0.55 0.52 -0.36 -0.76 -1.1 -2.1 -1.2 0.00021 -0.11 8.1e+03 1.1e-05 1e+03 1 ++
Results saved in file b09post_processing_000009.html
Results saved in file b09post_processing_000009.pickle
Biogeme parameters provided by the user.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Recycling was requested, but no pickle file was found
*** Initial values of the parameters are obtained from the file __b09post_processing_000010.iter
Cannot read file __b09post_processing_000010.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR ASC_TRAIN B_COST_CAR B_COST_SM B_COST_TRAIN B_TIME Function Relgrad Radius Rho
0 -0.28 0.027 -0.35 -0.62 -1.4 -1.1 8.6e+03 0.053 1 0.67 +
1 -0.41 -0.079 -0.38 -0.81 -1.8 -1.2 8.5e+03 0.012 10 1.1 ++
2 -0.42 -0.049 -0.38 -0.82 -1.9 -1.3 8.4e+03 0.00078 1e+02 1 ++
3 -0.42 -0.049 -0.38 -0.82 -1.9 -1.3 8.4e+03 3.7e-06 1e+02 1 ++
Results saved in file b09post_processing_000010.html
Results saved in file b09post_processing_000010.pickle
We retrieve the first estimation results for illustration.
spec, results = next(iter(all_results.items()))
print(spec)
ASC:GA;B_COST_gen_altspec:altspec;B_TIME:COMMUTERS;B_TIME_gen_altspec:generic;model_catalog:nested existing;train_tt_catalog:power
print(results.short_summary())
Results for model b09post_processing_000000
Nbr of parameters: 12
Sample size: 10719
Excluded data: 9
Final log likelihood: -8091.615
Akaike Information Criterion: 16207.23
Bayesian Information Criterion: 16294.59
results.get_estimated_parameters()
The following plot illustrates all models that have been estimated. Each dot corresponds to a model. The x-coordinate corresponds to the Akaike Information Criterion (AIC). The y-coordinate corresponds to the Bayesian Information Criterion (BIC). Note that there is a third objective that does not appear on this picture: the number of parameters. If the shape of the dot is a circle, it means that it corresponds to a Pareto optimal model. If the shape is a cross, it means that the model has been Pareto optimal at some point during the algorithm and later removed as a new model dominating it has been found. If the shape is a start, it means that the model has been deemed invalid.
if can_plot:
_ = post_processing.plot(
label_x='Nbr of parameters',
label_y='Negative log likelihood',
objective_x=1,
objective_y=0,
)
Total running time of the script: (0 minutes 12.888 seconds)