Note
Go to the end to download the full example code.
21a. Assisted specification¶
Example of the estimation of several versions of the model using assisted specification algorithm. The catalog of specifications is defined in 21b. Specification of a catalog of models. All specifications are estimated. Have a look at plot_b22a_multiple_models for an example where the number of specifications is too high to be enumerated.
Michel Bierlaire, EPFL Sat Jun 28 2025, 19:21:26
import biogeme.biogeme_logging as blog
from biogeme.assisted import AssistedSpecification
from biogeme.multiobjectives import loglikelihood_dimension
from biogeme.results_processing import compile_estimation_results
from plot_b21b_multiple_models_spec import PARETO_FILE_NAME, the_biogeme
logger = blog.get_screen_logger(blog.INFO)
logger.info('Example b21a_multiple_models')
income_segmentation=INCOME: [{0: 'inc-zero', 1: 'inc-under50', 2: 'inc-50-100', 3: 'inc-100+', 4: 'inc-unknown'}] ref: inc-zero
Example b21a_multiple_models
Creation of the object capturing the assisted specification algorithm. Its constructor takes three arguments:
the biogeme object containing the specifications and the database,
an object defining the objectives to minimize. Here, we use the opposite of the log likelihood and the number of estimated parameters.
the name of the file where the estimated are saved, and organized into a Pareto set.
assisted_specification = AssistedSpecification(
biogeme_object=the_biogeme,
multi_objectives=loglikelihood_dimension,
pareto_file_name=PARETO_FILE_NAME,
)
Unable to read file b21_multiple_models.pareto. Pareto set empty.
The algorithm is run.
non_dominated_models = assisted_specification.run()
Biogeme parameters read from biogeme.toml.
Model with 4 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000000
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost asc_car Function Relgrad Radius Rho
0 -0.92 -0.67 -0.88 -0.49 5.4e+03 0.041 10 1.1 ++
1 -0.73 -1.2 -1 -0.18 5.3e+03 0.0072 1e+02 1.1 ++
2 -0.7 -1.3 -1.1 -0.16 5.3e+03 0.00018 1e+03 1 ++
3 -0.7 -1.3 -1.1 -0.16 5.3e+03 1.1e-07 1e+03 1 ++
default_specification=asc:no_seg;b_cost:no_seg;train_tt:linear
We consider all possible combinations of the catalogs.
Model 0/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000001
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.44 -0.66 -0.9 2 -1 -0.11 -0.35 -0.42 -0.06 -0.43 -0.22 5.7e+03 0.095 1 0.68 +
1 0.56 -1.4 -1.6 1.1 -0.96 -0.51 -0.49 0.3 0.066 -0.52 0.77 5.3e+03 0.02 1 0.84 +
2 0.66 -1.2 -2.2 0.34 -1.6 -0.36 0.25 0.62 0.96 -0.14 0.38 5.1e+03 0.029 1 0.87 +
3 0.33 -1.3 -1.7 0.42 -1.5 -0.37 0.23 0.59 0.84 -0.3 0.32 5.1e+03 0.0026 10 0.96 ++
4 0.35 -1.3 -1.7 0.45 -1.6 -0.37 0.23 0.59 0.85 -0.3 0.32 5.1e+03 7.5e-05 1e+02 0.98 ++
5 0.35 -1.3 -1.7 0.45 -1.6 -0.37 0.23 0.59 0.85 -0.3 0.32 5.1e+03 9e-08 1e+02 1 ++
Model 1/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000002
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.43 -0.62 -0.89 1.8 -1 -0.45 -0.24 5.6e+03 0.083 1 0.72 +
1 0.39 -1.5 -1.6 0.85 -1 -0.65 0.58 5.2e+03 0.028 10 0.94 ++
2 0.48 -1.3 -1.9 0.42 -1.1 -0.21 0.3 5.1e+03 0.0096 1e+02 0.95 ++
3 0.36 -1.3 -1.7 0.45 -1.1 -0.29 0.3 5.1e+03 0.0004 1e+03 0.98 ++
4 0.36 -1.3 -1.7 0.45 -1.1 -0.29 0.3 5.1e+03 6.7e-07 1e+03 1 ++
Model 2/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000003
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.43 -0.62 -0.89 1.9 -1 -0.18 -0.44 -0.23 5.6e+03 0.084 1 0.72 +
1 0.39 -1.5 -1.6 0.86 -0.97 -0.42 -0.63 0.58 5.2e+03 0.028 10 0.94 ++
2 0.51 -1.3 -1.9 0.4 -1 -1 -0.14 0.3 5.1e+03 0.011 1e+02 0.93 ++
3 0.39 -1.3 -1.7 0.44 -1 -1.1 -0.23 0.31 5.1e+03 0.00049 1e+03 0.98 ++
4 0.39 -1.3 -1.7 0.44 -1 -1.1 -0.23 0.31 5.1e+03 1.9e-06 1e+03 1 ++
Model 3/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000004
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.73 0.37 -1 1.6 -0.67 -0.082 -0.23 -0.28 -0.042 -0.43 -0.19 5.4e+03 0.039 1 0.86 +
1 -1.1 1.4 -1.3 0.83 -0.84 -0.21 -0.37 -0.12 -0.031 -0.19 -0.32 5.1e+03 0.023 10 1.1 ++
2 -0.93 2.1 -1.9 0.28 -1.6 -0.57 0.26 0.63 0.83 0.0088 -0.24 5e+03 0.0077 1e+02 0.91 ++
3 -1 2.1 -1.7 0.36 -1.6 -0.78 0.28 0.67 0.84 -0.065 -0.22 5e+03 0.00067 1e+03 1 ++
4 -1 2.1 -1.7 0.37 -1.6 -0.79 0.28 0.66 0.84 -0.068 -0.22 5e+03 9.8e-06 1e+04 1 ++
5 -1 2.1 -1.7 0.37 -1.6 -0.79 0.28 0.66 0.84 -0.068 -0.22 5e+03 5.8e-10 1e+04 1 ++
Model 4/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000005
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time lambda_time b_cost asc_car Function Relgrad Radius Rho
0 -0.71 -1 1.7 -0.82 -0.5 5.6e+03 0.058 1 0.77 +
1 -0.77 -1.7 0.69 -1.3 -0.35 5.4e+03 0.049 10 1 ++
2 -0.47 -1.7 0.53 -1 0.017 5.3e+03 0.002 1e+02 0.96 ++
3 -0.48 -1.7 0.51 -1.1 -0.0043 5.3e+03 1.3e-05 1e+03 1 ++
4 -0.48 -1.7 0.51 -1.1 -0.0043 5.3e+03 1.8e-09 1e+03 1 ++
Model 5/36
Biogeme parameters read from biogeme.toml.
Model with 13 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000006
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.48 -0.69 0.63 -0.93 2 -1 -0.11 -0.35 -0.42 -0.06 -0.43 -0.22 -0.25 5.6e+03 0.1 1 0.69 +
1 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 10 1.1 ++
2 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 5 -1.4e+03 -
3 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 2.5 -23 -
4 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 1.2 -1.8 -
5 -0.31 -0.96 2.1 -2 0.26 -1.3 -0.44 -0.44 -0.14 0.074 -0.44 0.53 -0.41 4.9e+03 0.022 1.2 0.69 +
6 -0.26 -1.1 2 -1.7 0.31 -1.5 -0.58 0.23 0.66 0.89 -0.45 0.44 -0.36 4.9e+03 0.0046 12 0.91 ++
7 -0.26 -1.1 2 -1.7 0.33 -1.6 -0.59 0.22 0.63 0.82 -0.45 0.45 -0.37 4.9e+03 9.9e-05 1.2e+02 1 ++
8 -0.26 -1.1 2 -1.7 0.33 -1.6 -0.59 0.22 0.63 0.82 -0.45 0.45 -0.37 4.9e+03 9.3e-08 1.2e+02 1 ++
Model 6/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000007
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.36 -0.78 -0.63 -1 0.12 -0.03 0.16 0.29 -0.56 0.012 5.3e+03 0.043 10 1.1 ++
1 0.017 -1.1 -1.2 -1.4 -0.28 0.17 0.49 0.72 -0.48 0.3 5.2e+03 0.0097 1e+02 1.1 ++
2 0.069 -1.2 -1.3 -1.5 -0.41 0.18 0.53 0.78 -0.47 0.33 5.2e+03 0.00037 1e+03 1 ++
3 0.069 -1.2 -1.3 -1.5 -0.41 0.18 0.53 0.78 -0.47 0.33 5.2e+03 5.1e-07 1e+03 1 ++
Model 7/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000008
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.78 0.18 -1 -0.34 -0.042 -0.13 -0.14 -0.021 -0.27 -0.11 5.4e+03 0.036 10 1 ++
1 -0.98 2.4 -1.6 -1.5 -0.066 0.41 0.65 0.77 -0.072 -0.068 5e+03 0.028 1e+02 0.94 ++
2 -1.1 2.1 -1.7 -1.6 -0.76 0.28 0.66 0.78 -0.07 -0.2 5e+03 0.00071 1e+03 1 ++
3 -1.1 2.1 -1.7 -1.6 -0.76 0.28 0.66 0.78 -0.07 -0.2 5e+03 5.1e-06 1e+03 1 ++
Model 8/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000009
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.37 -0.59 -1 -0.89 -0.15 -0.32 -0.12 5.3e+03 0.036 10 1 ++
1 0.41 -1.3 -1.7 -0.94 -0.88 -0.17 0.22 5.2e+03 0.0094 1e+02 1 ++
2 0.42 -1.3 -1.7 -0.96 -1 -0.18 0.25 5.2e+03 0.00022 1e+03 1 ++
3 0.42 -1.3 -1.7 -0.96 -1 -0.18 0.25 5.2e+03 2.3e-07 1e+03 1 ++
Model 9/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000010
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.51 -0.8 1 -0.6 -0.88 -0.46 -0.15 -0.21 5.1e+03 0.045 10 1.1 ++
1 -0.54 -0.96 1.7 -1.1 -1.1 -0.6 0.36 -0.37 5e+03 0.012 1e+02 1.1 ++
2 -0.53 -1.1 1.9 -1.2 -1.1 -0.61 0.41 -0.41 4.9e+03 0.0007 1e+03 1 ++
3 -0.53 -1.1 1.9 -1.2 -1.1 -0.61 0.41 -0.41 4.9e+03 4.3e-06 1e+03 1 ++
Model 10/36
Biogeme parameters read from biogeme.toml.
Model with 4 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000011
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost asc_car Function Relgrad Radius Rho
0 -0.74 -1 -0.39 -0.3 5.5e+03 0.044 10 1 ++
1 -0.54 -1.6 -0.93 -0.0041 5.3e+03 0.0052 1e+02 1.1 ++
2 -0.51 -1.7 -1 0.0019 5.3e+03 0.00015 1e+03 1 ++
3 -0.51 -1.7 -1 0.0019 5.3e+03 1.4e-07 1e+03 1 ++
Model 11/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000012
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.44 -0.6 0.47 -1 -0.69 -0.075 -0.25 -0.28 -0.042 -0.34 -0.16 -0.18 5.2e+03 0.036 10 1 ++
1 -0.24 -0.98 2 -1.6 -1.5 -0.3 0.23 0.6 0.76 -0.37 0.34 -0.28 4.9e+03 0.018 1e+02 1 ++
2 -0.25 -1.1 2 -1.7 -1.5 -0.59 0.21 0.63 0.78 -0.43 0.41 -0.34 4.9e+03 0.0011 1e+03 1 ++
3 -0.25 -1.2 2.1 -1.7 -1.6 -0.61 0.21 0.63 0.78 -0.43 0.42 -0.34 4.9e+03 9e-06 1e+04 1 ++
4 -0.25 -1.2 2.1 -1.7 -1.6 -0.61 0.21 0.63 0.78 -0.43 0.42 -0.34 4.9e+03 4.2e-08 1e+04 1 ++
Model 12/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000013
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.33 -0.81 -0.63 -0.89 -0.52 -0.039 5.3e+03 0.043 10 1.1 ++
1 0.038 -1.2 -1.2 -1 -0.47 0.28 5.2e+03 0.0093 1e+02 1.1 ++
2 0.089 -1.2 -1.2 -1.1 -0.46 0.31 5.2e+03 0.00033 1e+03 1 ++
3 0.089 -1.2 -1.2 -1.1 -0.46 0.31 5.2e+03 4.1e-07 1e+03 1 ++
Model 13/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000014
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost_ref b_cost_diff_GA asc_car Function Relgrad Radius Rho
0 -0.74 -1 -0.39 -0.095 -0.3 5.5e+03 0.043 10 1 ++
1 -0.52 -1.6 -0.88 -0.53 0.037 5.3e+03 0.0053 1e+02 1.1 ++
2 -0.48 -1.7 -0.95 -0.97 0.061 5.3e+03 0.00033 1e+03 1.1 ++
3 -0.48 -1.7 -0.95 -1.1 0.063 5.3e+03 1.1e-05 1e+04 1 ++
4 -0.48 -1.7 -0.95 -1.1 0.063 5.3e+03 1.7e-08 1e+04 1 ++
Model 14/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000015
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.51 -0.8 1 -0.6 -0.88 -0.0059 -0.46 -0.15 -0.19 5.1e+03 0.045 10 1.1 ++
1 -0.54 -0.97 1.7 -1.1 -1.1 0.93 -0.61 0.36 -0.93 4.9e+03 0.012 1e+02 1.1 ++
2 -0.54 -1.1 1.9 -1.2 -1.1 0.89 -0.62 0.41 -0.98 4.9e+03 0.0007 1e+03 1 ++
3 -0.54 -1.1 1.9 -1.2 -1.1 0.89 -0.62 0.41 -0.98 4.9e+03 4.4e-06 1e+03 1 ++
Model 15/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000016
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.46 -0.65 0.57 -0.92 1.9 -1 -0.17 -0.44 -0.24 -0.24 5.5e+03 0.088 1 0.73 +
1 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 10 1.2 ++
2 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 1.8 -14 -
3 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 0.88 -0.88 -
4 -0.56 -1.2 1.9 -1.6 0.36 -1.2 -0.16 -0.46 0.34 -0.35 4.9e+03 0.023 8.8 0.91 ++
5 -0.21 -1.1 1.9 -1.7 0.34 -1.1 1.6 -0.43 0.41 -1.3 4.9e+03 0.0036 8.8 0.82 +
6 -0.22 -1.2 2 -1.7 0.33 -1.1 1.2 -0.42 0.41 -1.2 4.9e+03 0.00065 88 1.2 ++
7 -0.22 -1.2 2 -1.7 0.33 -1.1 0.98 -0.42 0.41 -1.1 4.9e+03 0.00011 8.8e+02 1.1 ++
8 -0.22 -1.2 2 -1.7 0.33 -1.1 0.98 -0.42 0.41 -1.1 4.9e+03 5.3e-06 8.8e+02 1 ++
Model 16/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000017
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.46 -0.64 0.57 -0.92 1.9 -1 -0.45 -0.25 -0.24 5.5e+03 0.087 1 0.73 +
1 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 10 1.2 ++
2 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 1.6 -11 -
3 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 0.8 -0.46 -
4 -0.55 -1.2 1.9 -1.5 0.42 -1.1 -0.48 0.3 -0.4 4.9e+03 0.017 8 0.99 ++
5 -0.21 -1.1 1.9 -1.7 0.33 -1.1 -0.42 0.41 -0.45 4.9e+03 0.00079 80 0.98 ++
6 -0.21 -1.1 1.9 -1.7 0.33 -1.1 -0.42 0.41 -0.45 4.9e+03 3.4e-06 80 1 ++
Model 17/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000018
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost_ref b_cost_diff_GA asc_car Function Relgrad Radius Rho
0 -0.92 -0.67 -0.9 0.097 -0.5 5.4e+03 0.041 10 1.1 ++
1 -0.71 -1.2 -0.98 -0.74 -0.13 5.3e+03 0.0075 1e+02 1.1 ++
2 -0.68 -1.3 -1 -1 -0.097 5.3e+03 0.0002 1e+03 1 ++
3 -0.68 -1.3 -1 -1 -0.097 5.3e+03 1.2e-06 1e+03 1 ++
Model 18/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000019
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time lambda_time b_cost_ref b_cost_diff_GA asc_car Function Relgrad Radius Rho
0 -0.71 -1 1.7 -0.82 -0.17 -0.5 5.6e+03 0.059 1 0.77 +
1 -0.78 -1.6 0.69 -1.3 -0.38 -0.33 5.4e+03 0.049 10 1 ++
2 -0.44 -1.7 0.53 -0.96 -1.2 0.085 5.3e+03 0.002 1e+02 0.96 ++
3 -0.46 -1.7 0.51 -1 -1.1 0.06 5.3e+03 1e-05 1e+03 1 ++
4 -0.46 -1.7 0.51 -1 -1.1 0.06 5.3e+03 7.2e-10 1e+03 1 ++
Model 19/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000020
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.33 -0.81 -0.63 -0.91 0.11 -0.52 -0.04 5.3e+03 0.043 10 1.1 ++
1 0.052 -1.1 -1.2 -0.98 -0.72 -0.42 0.29 5.2e+03 0.0097 1e+02 1.1 ++
2 0.11 -1.2 -1.3 -1 -1 -0.41 0.31 5.2e+03 0.00036 1e+03 1 ++
3 0.11 -1.2 -1.3 -1 -1 -0.41 0.31 5.2e+03 9.1e-07 1e+03 1 ++
Model 20/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000021
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car Function Relgrad Radius Rho
0 -0.92 -0.66 -1 0.026 -0.0026 0.2 0.21 -0.49 5.4e+03 0.041 10 1.1 ++
1 -0.74 -1.2 -1.4 -0.53 0.22 0.52 0.69 -0.17 5.3e+03 0.0075 1e+02 1.1 ++
2 -0.71 -1.3 -1.5 -0.66 0.24 0.56 0.75 -0.15 5.3e+03 0.0002 1e+03 1 ++
3 -0.71 -1.3 -1.5 -0.66 0.24 0.56 0.75 -0.15 5.3e+03 1.5e-07 1e+03 1 ++
Model 21/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000022
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.51 -0.82 1 -0.59 -0.69 -0.094 -0.32 -0.15 -0.041 -0.47 -0.15 -0.21 5.1e+03 0.045 10 1.1 ++
1 -0.57 -0.94 1.8 -1.1 -1.4 -0.37 0.15 0.51 0.71 -0.62 0.38 -0.29 4.9e+03 0.012 1e+02 1.1 ++
2 -0.58 -1.1 1.9 -1.2 -1.5 -0.6 0.17 0.56 0.75 -0.65 0.44 -0.33 4.9e+03 0.00078 1e+03 1 ++
3 -0.58 -1.1 1.9 -1.2 -1.5 -0.6 0.17 0.56 0.75 -0.65 0.44 -0.33 4.9e+03 4.5e-06 1e+03 1 ++
Model 22/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000023
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.37 -0.6 -1 -0.72 -0.082 -0.27 -0.28 -0.045 -0.32 -0.13 5.3e+03 0.036 10 1 ++
1 0.38 -1.3 -1.6 -1.4 -0.22 0.22 0.56 0.76 -0.22 0.24 5.2e+03 0.0092 1e+02 1 ++
2 0.38 -1.3 -1.7 -1.5 -0.36 0.23 0.6 0.81 -0.25 0.27 5.2e+03 0.00022 1e+03 1 ++
3 0.38 -1.3 -1.7 -1.5 -0.36 0.23 0.6 0.81 -0.25 0.27 5.2e+03 2.4e-07 1e+03 1 ++
Model 23/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000024
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.43 -0.59 0.47 -1 -0.76 -0.12 -0.34 -0.16 -0.18 5.2e+03 0.042 10 1 ++
1 -0.21 -1 2 -1.6 -1 0.89 -0.36 0.33 -0.91 4.9e+03 0.018 1e+02 1 ++
2 -0.2 -1.2 2 -1.7 -1.1 0.91 -0.39 0.37 -0.99 4.9e+03 0.0011 1e+03 1 ++
3 -0.2 -1.2 2 -1.7 -1.1 0.91 -0.39 0.38 -0.99 4.9e+03 8.4e-06 1e+04 1 ++
4 -0.2 -1.2 2 -1.7 -1.1 0.91 -0.39 0.38 -0.99 4.9e+03 5.4e-10 1e+04 1 ++
Model 24/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000025
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -1 0.85 -0.7 -0.75 -0.11 -0.31 -0.21 -0.052 -0.41 -0.23 5.2e+03 0.049 10 1.1 ++
1 -1.2 1.9 -1.1 -1.5 -0.54 0.19 0.54 0.71 -0.28 -0.19 5e+03 0.012 1e+02 1.1 ++
2 -1.3 2 -1.2 -1.6 -0.78 0.23 0.59 0.78 -0.26 -0.21 5e+03 0.0006 1e+03 1 ++
3 -1.3 2 -1.2 -1.6 -0.78 0.23 0.59 0.78 -0.26 -0.21 5e+03 1.8e-06 1e+03 1 ++
Model 25/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000026
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.88 0.66 -0.79 -1 -0.36 -0.25 5.2e+03 0.047 10 1.1 ++
1 -1.2 1.9 -1.1 -1.1 -0.28 -0.28 5.1e+03 0.014 1e+02 1.1 ++
2 -1.3 2 -1.2 -1.1 -0.25 -0.3 5.1e+03 0.0007 1e+03 1 ++
3 -1.3 2 -1.2 -1.1 -0.25 -0.3 5.1e+03 2.4e-06 1e+03 1 ++
Model 26/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000027
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.44 -0.59 0.47 -1 -0.76 -0.34 -0.17 -0.18 5.2e+03 0.044 10 1 ++
1 -0.21 -1 2 -1.6 -1 -0.36 0.33 -0.35 4.9e+03 0.018 1e+02 1 ++
2 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.37 -0.42 4.9e+03 0.0011 1e+03 1 ++
3 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.38 -0.42 4.9e+03 8.5e-06 1e+04 1 ++
4 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.38 -0.42 4.9e+03 5.5e-10 1e+04 1 ++
Model 27/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000028
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.73 0.39 -1 1.6 -0.73 -0.45 -0.21 5.5e+03 0.049 1 0.83 +
1 -1.1 1.4 -1.3 0.9 -1.1 -0.2 -0.35 5.1e+03 0.022 10 1.1 ++
2 -0.87 2 -1.9 0.26 -1.1 0.037 -0.36 5e+03 0.012 10 0.82 +
3 -1 2 -1.7 0.36 -1.1 -0.061 -0.31 5e+03 0.0012 1e+02 1 ++
4 -1 2 -1.7 0.38 -1.1 -0.064 -0.31 5e+03 3.1e-05 1e+03 1 ++
5 -1 2 -1.7 0.38 -1.1 -0.064 -0.31 5e+03 3.6e-09 1e+03 1 ++
Model 28/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000029
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.76 0.19 -1 -0.36 -0.089 -0.27 -0.12 5.4e+03 0.044 10 1 ++
1 -0.98 2.4 -1.6 -0.98 0.71 -0.08 -0.61 5e+03 0.027 1e+02 0.93 ++
2 -1.1 2.1 -1.7 -1.1 0.92 -0.071 -0.87 5e+03 0.00067 1e+03 1 ++
3 -1.1 2.1 -1.7 -1.1 0.92 -0.071 -0.87 5e+03 2e-06 1e+03 1 ++
Model 29/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000030
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car Function Relgrad Radius Rho
0 -0.72 -1 1.6 -0.74 -0.092 -0.26 -0.31 -0.047 -0.48 5.6e+03 0.044 1 0.81 +
1 -0.64 -1.6 0.65 -0.91 -0.36 -0.47 0.12 -0.013 -0.22 5.3e+03 0.038 10 1 ++
2 -0.49 -1.7 0.51 -1.5 -0.59 0.27 0.6 0.8 0.012 5.3e+03 0.00074 1e+02 1 ++
3 -0.49 -1.7 0.5 -1.6 -0.65 0.28 0.62 0.81 0.0042 5.3e+03 7e-06 1e+03 1 ++
4 -0.49 -1.7 0.5 -1.6 -0.65 0.28 0.62 0.81 0.0042 5.3e+03 1.3e-09 1e+03 1 ++
Model 30/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000031
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho
0 -0.37 -0.59 -1 -0.89 -0.33 -0.13 5.3e+03 0.036 10 1 ++
1 0.4 -1.3 -1.6 -1 -0.22 0.22 5.2e+03 0.0091 1e+02 1 ++
2 0.4 -1.3 -1.7 -1 -0.24 0.25 5.2e+03 0.00022 1e+03 1 ++
3 0.4 -1.3 -1.7 -1 -0.24 0.25 5.2e+03 2.4e-07 1e+03 1 ++
Model 31/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000032
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -1 0.9 -0.7 -0.93 -0.072 -0.43 -0.22 5.2e+03 0.046 10 1.1 ++
1 -1.2 1.9 -1.1 -1.1 0.98 -0.28 -0.87 5.1e+03 0.011 1e+02 1.1 ++
2 -1.3 2 -1.2 -1.1 0.89 -0.25 -0.87 5e+03 0.00055 1e+03 1 ++
3 -1.3 2 -1.2 -1.1 0.89 -0.25 -0.87 5e+03 1.5e-06 1e+03 1 ++
Model 32/36
Model 33/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000033
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.73 0.39 -1 1.6 -0.73 -0.15 -0.45 -0.2 5.5e+03 0.05 1 0.83 +
1 -1.1 1.4 -1.3 0.91 -1.1 -0.2 -0.19 -0.33 5.1e+03 0.021 10 1.1 ++
2 -0.87 2 -1.9 0.26 -1.1 1.3 0.034 -1.1 5e+03 0.013 10 0.81 +
3 -1 2 -1.7 0.36 -1.1 1 -0.066 -0.95 5e+03 0.0012 1e+02 1 ++
4 -1 2 -1.7 0.38 -1.1 0.92 -0.068 -0.89 5e+03 3.3e-05 1e+03 1 ++
5 -1 2 -1.7 0.38 -1.1 0.92 -0.068 -0.89 5e+03 8.2e-08 1e+03 1 ++
Model 34/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000034
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car Function Relgrad Radius Rho
0 -0.75 -1 -0.36 -0.045 -0.13 -0.14 -0.023 -0.29 5.5e+03 0.035 10 1 ++
1 -0.54 -1.6 -1.4 -0.17 0.37 0.6 0.73 0.0049 5.3e+03 0.0064 1e+02 1.1 ++
2 -0.51 -1.7 -1.5 -0.64 0.28 0.63 0.75 0.011 5.3e+03 0.00037 1e+03 1 ++
3 -0.51 -1.7 -1.5 -0.64 0.28 0.63 0.75 0.011 5.3e+03 2.2e-06 1e+03 1 ++
Model 35/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b21_multiple_models_000035
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.76 0.19 -1 -0.37 -0.27 -0.12 5.4e+03 0.044 10 1 ++
1 -0.97 2.4 -1.6 -0.96 -0.072 -0.11 5e+03 0.027 1e+02 0.94 ++
2 -1 2.1 -1.7 -1.1 -0.067 -0.29 5e+03 0.00066 1e+03 1 ++
3 -1 2.1 -1.7 -1.1 -0.067 -0.29 5e+03 2.1e-06 1e+03 1 ++
Pareto file has been updated: b21_multiple_models.pareto
Before the algorithm: 1 models, with 1 Pareto.
After the algorithm: 36 models, with 8 Pareto.
VNS algorithm completed. Postprocessing of the Pareto optimal solutions
Pareto set initialized from file with 36 elements [8 Pareto] and 0 invalid elements.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000000.iter
Cannot read file __b21_multiple_models_000000.iter. Statement is ignored.
Starting values for the algorithm: {}
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time b_cost asc_car Function Relgrad Radius Rho
0 -0.92 -0.67 -0.88 -0.49 5.4e+03 0.041 10 1.1 ++
1 -0.73 -1.2 -1 -0.18 5.3e+03 0.0072 1e+02 1.1 ++
2 -0.7 -1.3 -1.1 -0.16 5.3e+03 0.00018 1e+03 1 ++
3 -0.7 -1.3 -1.1 -0.16 5.3e+03 1.1e-07 1e+03 1 ++
Optimization algorithm has converged.
Relative gradient: 1.059559503933971e-07
Cause of termination: Relative gradient = 1.1e-07 <= 6.1e-06
Number of function evaluations: 13
Number of gradient evaluations: 9
Number of hessian evaluations: 4
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 4
Proportion of Hessian calculation: 4/4 = 100.0%
Optimization time: 0:00:00.293176
Calculate second derivatives and BHHH
File b21_multiple_models_000000.html has been generated.
File b21_multiple_models_000000.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000001.iter
Cannot read file __b21_multiple_models_000001.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.73 0.39 -1 1.6 -0.73 -0.45 -0.21 5.5e+03 0.049 1 0.83 +
1 -1.1 1.4 -1.3 0.9 -1.1 -0.2 -0.35 5.1e+03 0.022 10 1.1 ++
2 -0.87 2 -1.9 0.26 -1.1 0.037 -0.36 5e+03 0.012 10 0.82 +
3 -1 2 -1.7 0.36 -1.1 -0.061 -0.31 5e+03 0.0012 1e+02 1 ++
4 -1 2 -1.7 0.38 -1.1 -0.064 -0.31 5e+03 3.1e-05 1e+03 1 ++
5 -1 2 -1.7 0.38 -1.1 -0.064 -0.31 5e+03 3.6e-09 1e+03 1 ++
Optimization algorithm has converged.
Relative gradient: 3.608609121164929e-09
Cause of termination: Relative gradient = 3.6e-09 <= 6.1e-06
Number of function evaluations: 19
Number of gradient evaluations: 13
Number of hessian evaluations: 6
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 6
Proportion of Hessian calculation: 6/6 = 100.0%
Optimization time: 0:00:00.986043
Calculate second derivatives and BHHH
File b21_multiple_models_000001.html has been generated.
File b21_multiple_models_000001.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000002.iter
Cannot read file __b21_multiple_models_000002.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.44 -0.59 0.47 -1 -0.76 -0.34 -0.17 -0.18 5.2e+03 0.044 10 1 ++
1 -0.21 -1 2 -1.6 -1 -0.36 0.33 -0.35 4.9e+03 0.018 1e+02 1 ++
2 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.37 -0.42 4.9e+03 0.0011 1e+03 1 ++
3 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.38 -0.42 4.9e+03 8.5e-06 1e+04 1 ++
4 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.38 -0.42 4.9e+03 5.5e-10 1e+04 1 ++
Optimization algorithm has converged.
Relative gradient: 5.482789752269039e-10
Cause of termination: Relative gradient = 5.5e-10 <= 6.1e-06
Number of function evaluations: 16
Number of gradient evaluations: 11
Number of hessian evaluations: 5
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 5
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:00.429961
Calculate second derivatives and BHHH
File b21_multiple_models_000002.html has been generated.
File b21_multiple_models_000002.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000003.iter
Cannot read file __b21_multiple_models_000003.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho
0 -0.76 0.19 -1 -0.37 -0.27 -0.12 5.4e+03 0.044 10 1 ++
1 -0.97 2.4 -1.6 -0.96 -0.072 -0.11 5e+03 0.027 1e+02 0.94 ++
2 -1 2.1 -1.7 -1.1 -0.067 -0.29 5e+03 0.00066 1e+03 1 ++
3 -1 2.1 -1.7 -1.1 -0.067 -0.29 5e+03 2.1e-06 1e+03 1 ++
Optimization algorithm has converged.
Relative gradient: 2.0806244410800506e-06
Cause of termination: Relative gradient = 2.1e-06 <= 6.1e-06
Number of function evaluations: 13
Number of gradient evaluations: 9
Number of hessian evaluations: 4
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 4
Proportion of Hessian calculation: 4/4 = 100.0%
Optimization time: 0:00:00.360752
Calculate second derivatives and BHHH
File b21_multiple_models_000003.html has been generated.
File b21_multiple_models_000003.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000004.iter
Cannot read file __b21_multiple_models_000004.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.48 -0.69 0.63 -0.93 2 -1 -0.11 -0.35 -0.42 -0.06 -0.43 -0.22 -0.25 5.6e+03 0.1 1 0.69 +
1 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 10 1.1 ++
2 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 5 -1.4e+03 -
3 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 2.5 -23 -
4 -0.46 -1.1 1.6 -0.92 1.5 -0.7 -0.23 -0.38 0.05 -0.0044 -0.35 0.26 -0.33 5.1e+03 0.014 1.2 -1.8 -
5 -0.31 -0.96 2.1 -2 0.26 -1.3 -0.44 -0.44 -0.14 0.074 -0.44 0.53 -0.41 4.9e+03 0.022 1.2 0.69 +
6 -0.26 -1.1 2 -1.7 0.31 -1.5 -0.58 0.23 0.66 0.89 -0.45 0.44 -0.36 4.9e+03 0.0046 12 0.91 ++
7 -0.26 -1.1 2 -1.7 0.33 -1.6 -0.59 0.22 0.63 0.82 -0.45 0.45 -0.37 4.9e+03 9.9e-05 1.2e+02 1 ++
8 -0.26 -1.1 2 -1.7 0.33 -1.6 -0.59 0.22 0.63 0.82 -0.45 0.45 -0.37 4.9e+03 9.3e-08 1.2e+02 1 ++
Optimization algorithm has converged.
Relative gradient: 9.314421529692506e-08
Cause of termination: Relative gradient = 9.3e-08 <= 6.1e-06
Number of function evaluations: 22
Number of gradient evaluations: 13
Number of hessian evaluations: 6
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 9
Proportion of Hessian calculation: 6/6 = 100.0%
Optimization time: 0:00:01.265093
Calculate second derivatives and BHHH
File b21_multiple_models_000004.html has been generated.
File b21_multiple_models_000004.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000005.iter
Cannot read file __b21_multiple_models_000005.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train b_time lambda_time b_cost asc_car Function Relgrad Radius Rho
0 -0.71 -1 1.7 -0.82 -0.5 5.6e+03 0.058 1 0.77 +
1 -0.77 -1.7 0.69 -1.3 -0.35 5.4e+03 0.049 10 1 ++
2 -0.47 -1.7 0.53 -1 0.017 5.3e+03 0.002 1e+02 0.96 ++
3 -0.48 -1.7 0.51 -1.1 -0.0043 5.3e+03 1.3e-05 1e+03 1 ++
4 -0.48 -1.7 0.51 -1.1 -0.0043 5.3e+03 1.8e-09 1e+03 1 ++
Optimization algorithm has converged.
Relative gradient: 1.7992210209022422e-09
Cause of termination: Relative gradient = 1.8e-09 <= 6.1e-06
Number of function evaluations: 16
Number of gradient evaluations: 11
Number of hessian evaluations: 5
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 5
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:00.859131
Calculate second derivatives and BHHH
File b21_multiple_models_000005.html has been generated.
File b21_multiple_models_000005.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000006.iter
Cannot read file __b21_multiple_models_000006.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.46 -0.64 0.57 -0.92 1.9 -1 -0.45 -0.25 -0.24 5.5e+03 0.087 1 0.73 +
1 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 10 1.2 ++
2 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 1.6 -11 -
3 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 0.8 -0.46 -
4 -0.55 -1.2 1.9 -1.5 0.42 -1.1 -0.48 0.3 -0.4 4.9e+03 0.017 8 0.99 ++
5 -0.21 -1.1 1.9 -1.7 0.33 -1.1 -0.42 0.41 -0.45 4.9e+03 0.00079 80 0.98 ++
6 -0.21 -1.1 1.9 -1.7 0.33 -1.1 -0.42 0.41 -0.45 4.9e+03 3.4e-06 80 1 ++
Optimization algorithm has converged.
Relative gradient: 3.374132016569103e-06
Cause of termination: Relative gradient = 3.4e-06 <= 6.1e-06
Number of function evaluations: 18
Number of gradient evaluations: 11
Number of hessian evaluations: 5
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 7
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:01.353647
Calculate second derivatives and BHHH
File b21_multiple_models_000006.html has been generated.
File b21_multiple_models_000006.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000007.iter
Cannot read file __b21_multiple_models_000007.iter. Statement is ignored.
Starting values for the algorithm: {}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho
0 -0.46 -0.65 0.57 -0.92 1.9 -1 -0.17 -0.44 -0.24 -0.24 5.5e+03 0.088 1 0.73 +
1 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 10 1.2 ++
2 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 1.8 -14 -
3 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 0.88 -0.88 -
4 -0.56 -1.2 1.9 -1.6 0.36 -1.2 -0.16 -0.46 0.34 -0.35 4.9e+03 0.023 8.8 0.91 ++
5 -0.21 -1.1 1.9 -1.7 0.34 -1.1 1.6 -0.43 0.41 -1.3 4.9e+03 0.0036 8.8 0.82 +
6 -0.22 -1.2 2 -1.7 0.33 -1.1 1.2 -0.42 0.41 -1.2 4.9e+03 0.00065 88 1.2 ++
7 -0.22 -1.2 2 -1.7 0.33 -1.1 0.98 -0.42 0.41 -1.1 4.9e+03 0.00011 8.8e+02 1.1 ++
8 -0.22 -1.2 2 -1.7 0.33 -1.1 0.98 -0.42 0.41 -1.1 4.9e+03 5.3e-06 8.8e+02 1 ++
Optimization algorithm has converged.
Relative gradient: 5.317220515909392e-06
Cause of termination: Relative gradient = 5.3e-06 <= 6.1e-06
Number of function evaluations: 24
Number of gradient evaluations: 15
Number of hessian evaluations: 7
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 9
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:01.081416
Calculate second derivatives and BHHH
File b21_multiple_models_000007.html has been generated.
File b21_multiple_models_000007.yaml has been generated.
Pareto: 8
Considered: 36
Removed: 10
summary, description = compile_estimation_results(
non_dominated_models, use_short_names=True
)
print(summary)
Model_000000 ... Model_000007
Number of estimated parameters 4 ... 10
Sample size 6768 ... 6768
Final log likelihood -5331.252 ... -4879.461
Akaike Information Criterion 10670.5 ... 9778.922
Bayesian Information Criterion 10697.78 ... 9847.122
asc_train (t-test) -0.701 (-8.49) ...
b_time (t-test) -1.28 (-12.3) ... -1.7 (-21.3)
b_cost (t-test) -1.08 (-15.9) ...
asc_car (t-test) -0.155 (-2.66) ...
asc_train_ref (t-test) ... -0.22 (-2.44)
asc_train_diff_GA (t-test) ... 1.96 (21.2)
lambda_time (t-test) ... 0.334 (4.55)
asc_car_ref (t-test) ... -0.422 (-4.29)
asc_car_diff_GA (t-test) ... -1.03 (-2.57)
asc_train_diff_male (t-test) ... -1.15 (-13.4)
asc_car_diff_male (t-test) ... 0.413 (3.95)
b_cost_ref (t-test) ... -1.1 (-15.1)
b_cost_diff_inc-under50 (t-test) ...
b_cost_diff_inc-50-100 (t-test) ...
b_cost_diff_inc-100+ (t-test) ...
b_cost_diff_inc-unknown (t-test) ...
b_cost_diff_GA (t-test) ... 0.918 (1.87)
[22 rows x 8 columns]
Explanation of the short names of the model.
for k, v in description.items():
if k != v:
print(f'{k}: {v} AIC={summary.at["Akaike Information Criterion", k]}')
Model_000000: asc:no_seg;b_cost:no_seg;train_tt:linear AIC=10670.5
Model_000001: asc:GA;b_cost:no_seg;train_tt:boxcox AIC=10005.51
Model_000002: asc:MALE-GA;b_cost:no_seg;train_tt:log AIC=9817.767
Model_000003: asc:GA;b_cost:no_seg;train_tt:log AIC=10054.47
Model_000004: asc:MALE-GA;b_cost:INCOME;train_tt:boxcox AIC=9750.73
Model_000005: asc:no_seg;b_cost:no_seg;train_tt:boxcox AIC=10594.19
Model_000006: asc:MALE-GA;b_cost:no_seg;train_tt:boxcox AIC=9781.834
Model_000007: asc:MALE-GA;b_cost:GA;train_tt:boxcox AIC=9778.922
Total running time of the script: (0 minutes 44.363 seconds)