Note
Go to the end to download the full example code.
Assisted specificationΒΆ
Example of the estimation of several versions of the model using assisted specification algorithm. The catalog of specifications is defined in Specification of a catalog of models . All specifications are estimated. Have a look at Assisted specification 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_b21multiple_models_spec import PARETO_FILE_NAME, the_biogeme
logger = blog.get_screen_logger(blog.INFO)
logger.info('Example b21multipleModels')
income_segmentation=INCOME: [{0: 'inc-zero', 1: 'inc-under50', 2: 'inc-50-100', 3: 'inc-100+', 4: 'inc-unknown'}] ref: inc-zero
Example b21multipleModels
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,
)
Biogeme parameters read from biogeme.toml.
Pareto set initialized from file with 36 elements [8 Pareto] and 0 invalid elements.
The algorithm is run.
non_dominated_models = assisted_specification.run()
Biogeme parameters read from biogeme.toml.
Model with 4 unknown parameters [max: 50]
*** Estimate b07everything_000125
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 8 unknown parameters [max: 50]
*** Estimate b07everything_000126
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 1/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000127
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 2/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000128
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 3/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000129
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 4/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000130
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 5/36
Biogeme parameters read from biogeme.toml.
Model with 13 unknown parameters [max: 50]
*** Estimate b07everything_000131
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 0.0001 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 5.2e-07 1.2e+02 1 ++
Model 6/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b07everything_000132
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 7/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000133
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 8/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b07everything_000134
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 9.3e-08 1e+02 1 ++
Model 9/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000135
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 10/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000136
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 11/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000137
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 12/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000138
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 13/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000139
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 14/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000140
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 15/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000141
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 16/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000142
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 17/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000143
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 18/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000144
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 19/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000145
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 20/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000146
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 21/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b07everything_000147
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 4.6e-10 1e+04 1 ++
Model 22/36
Biogeme parameters read from biogeme.toml.
Model with 4 unknown parameters [max: 50]
*** Estimate b07everything_000148
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 23/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000149
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 ++
Model 24/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b07everything_000150
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 25/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000151
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 26/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000152
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 27/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000153
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 28/36
Model 29/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000154
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 30/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000155
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 31/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000156
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 32/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000157
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 33/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000158
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 34/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000159
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 35/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000160
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 ++
Pareto file has been updated: b21multiple_models.pareto
Before the algorithm: 36 models, with 8 Pareto.
After the algorithm: 42 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 __b21multiple_models_000000.iter
Parameter values restored from __b21multiple_models_000000.iter
Starting values for the algorithm: {'asc_train_ref': -0.26118949275010445, 'asc_train_diff_male': -1.1195205183536523, 'asc_train_diff_GA': 1.9854139084913025, 'b_time': -1.7053348387931921, 'lambda_time': 0.3292434856239473, 'b_cost_ref': -1.575519605716697, 'b_cost_diff_inc-under50': -0.5878741661013013, 'b_cost_diff_inc-50-100': 0.21532146660967305, 'b_cost_diff_inc-100+': 0.6293032493669737, 'b_cost_diff_inc-unknown': 0.8175262402491592, 'asc_car_ref': -0.4531117907224833, 'asc_car_diff_male': 0.44856560098379494, 'asc_car_diff_GA': -0.37087421631981377}
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 -0.17 -1.2 2 -1.7 0.32 -1 1 -0.35 0.35 -1.1 4.9e+03 0.0067 1 0.84 +
1 -0.23 -1.2 2 -1.7 0.33 -1.1 2 -0.3 0.29 -1.7 4.9e+03 0.002 1 0.36 +
2 -0.23 -1.2 2 -1.7 0.33 -1.1 2 -0.3 0.29 -1.7 4.9e+03 0.002 0.5 -0.033 -
3 -0.23 -1.2 2 -1.7 0.33 -1.1 2 -0.3 0.29 -1.7 4.9e+03 0.002 0.25 -0.049 -
4 -0.23 -1.2 2 -1.7 0.33 -1.1 2 -0.3 0.29 -1.7 4.9e+03 0.002 0.12 -0.00017 -
5 -0.23 -1.2 2 -1.7 0.33 -1.1 2 -0.3 0.29 -1.7 4.9e+03 0.002 0.062 -0.051 -
6 -0.23 -1.1 1.9 -1.7 0.34 -1.1 2.1 -0.27 0.26 -1.8 4.9e+03 0.0013 0.062 0.13 +
7 -0.23 -1.1 1.9 -1.7 0.34 -1.1 2.1 -0.27 0.26 -1.8 4.9e+03 0.0013 0.031 -0.044 -
8 -0.23 -1.1 1.9 -1.7 0.34 -1.1 2.1 -0.27 0.26 -1.8 4.9e+03 0.0013 0.016 -0.12 -
9 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.25 -1.8 4.9e+03 0.0015 0.016 0.2 +
10 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.25 -1.8 4.9e+03 0.0015 0.0078 0.0082 -
11 -0.23 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.0078 0.23 +
12 -0.23 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.0039 -0.0066 -
13 -0.23 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.002 0.1 -
14 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.002 0.22 +
15 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.00098 0.0089 -
16 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.00049 0.014 -
17 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.00024 0.019 -
18 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 0.00012 0.03 -
19 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 6.1e-05 0.036 -
20 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 3.1e-05 0.04 -
21 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 1.5e-05 0.043 -
22 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 7.6e-06 0.045 -
23 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 3.8e-06 0.045 -
24 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 1.9e-06 0.046 -
25 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 9.5e-07 0.046 -
26 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 4.8e-07 0.046 -
27 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 2.4e-07 0.046 -
28 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 1.2e-07 0.046 -
29 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 6e-08 0.046 -
30 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 3e-08 0.046 -
31 -0.22 -1.1 2 -1.7 0.34 -1.1 2.1 -0.27 0.24 -1.8 4.9e+03 0.0014 1.5e-08 0.046 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 32
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:02.229331
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000000~01.html has been generated.
File b21multiple_models_000000~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000001.iter
Parameter values restored from __b21multiple_models_000001.iter
Starting values for the algorithm: {'asc_train': -3.5, 'b_time': -5.17702237179112, 'lambda_time': -0.3521469872880427, 'b_cost': -0.23692086340664398, 'asc_car': -0.52618542015524}
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 0 -5.2 -0.24 0 0 6.9e+03 1.2 0.5 -0.089 -
1 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.5 0.46 +
2 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.25 -0.48 -
3 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.12 -0.2 -
4 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.062 -0.16 -
5 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.031 -0.13 -
6 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.016 -0.12 -
7 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.0078 -0.12 -
8 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.0039 -0.11 -
9 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.002 -0.11 -
10 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.00098 -0.11 -
11 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.00049 -0.11 -
12 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.00024 -0.11 -
13 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 0.00012 -0.11 -
14 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 6.1e-05 -0.11 -
15 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 3.1e-05 -0.11 -
16 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 1.5e-05 -0.11 -
17 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 7.6e-06 -0.11 -
18 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 3.8e-06 -0.11 -
19 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 1.9e-06 -0.11 -
20 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 9.5e-07 -0.11 -
21 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 4.8e-07 -0.11 -
22 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 2.4e-07 -0.11 -
23 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 1.2e-07 -0.11 -
24 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 6e-08 -0.11 -
25 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 3e-08 -0.11 -
26 -0.5 0.065 -5.7 -0.37 -0.082 -0.5 6.4e+03 1 1.5e-08 -0.11 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 27
Proportion of Hessian calculation: 2/2 = 100.0%
Optimization time: 0:00:00.647344
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000001~01.html has been generated.
File b21multiple_models_000001~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000002.iter
Parameter values restored from __b21multiple_models_000002.iter
Starting values for the algorithm: {'asc_train_ref': -0.5580850460270373, 'asc_train_diff_male': -0.874038274510957, 'asc_train_diff_GA': 0.875, 'b_time': -2.549909700411886, 'lambda_time': 0.8850585118642702, 'b_cost': -0.20353452565384322, 'asc_car_ref': -0.875, 'asc_car_diff_male': -0.875, 'asc_car_diff_GA': -0.4700120362966725}
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 0.26 -0.52 1.4 -1.5 -1.2 0.12 0.12 -0.43 5.6e+03 0.11 1 0.44 +
1 -0.0037 -0.85 1.5 -1.6 -2.2 0.4 0.55 -0.5 5.5e+03 0.24 1 0.22 +
2 -0.0037 -0.85 1.5 -1.6 -2.2 0.4 0.55 -0.5 5.5e+03 0.24 0.5 -0.21 -
3 -0.028 -1.2 1.8 -1.7 -2.7 0.16 1 -0.93 5.4e+03 0.25 0.5 0.32 +
4 0.23 -1.2 1.9 -1.6 -3.2 -0.26 1.5 -1.2 5.3e+03 0.13 0.5 0.2 +
5 0.099 -1.4 1.8 -1.9 -3.7 -0.68 1.6 -1.2 5.2e+03 0.075 0.5 0.4 +
6 0.099 -1.4 1.8 -1.9 -3.7 -0.68 1.6 -1.2 5.2e+03 0.075 0.25 -0.47 -
7 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 2.5 1.2 ++
8 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.91 -16 -
9 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.46 -5 -
10 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.23 -1.7 -
11 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.11 -1.1 -
12 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.057 -0.75 -
13 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.029 -0.59 -
14 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.014 -0.42 -
15 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.0071 -0.42 -
16 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.0036 -0.35 -
17 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.0018 -0.32 -
18 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.00089 -0.31 -
19 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.00045 -0.3 -
20 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.00022 -0.3 -
21 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 0.00011 -0.3 -
22 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 5.6e-05 -0.3 -
23 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 2.8e-05 -0.3 -
24 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 1.4e-05 -0.3 -
25 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 7e-06 -0.29 -
26 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 3.5e-06 -0.29 -
27 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 1.7e-06 -0.29 -
28 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 8.7e-07 -0.29 -
29 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 4.4e-07 -0.29 -
30 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 2.2e-07 -0.29 -
31 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 1.1e-07 -0.29 -
32 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 5.5e-08 -0.29 -
33 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 2.7e-08 -0.29 -
34 0.3 -1.3 1.9 -2 -4 -0.93 1.5 -1.3 5.1e+03 0.029 1.4e-08 -0.29 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.3630393080385081e-08
Number of iterations: 35
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:00.779081
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000002~01.html has been generated.
File b21multiple_models_000002~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000003.iter
Parameter values restored from __b21multiple_models_000003.iter
Starting values for the algorithm: {'asc_train_ref': 0.12501564761290923, 'asc_train_diff_male': -1.302939379720285, 'asc_train_diff_GA': 1.9430273190823513, 'b_time': -1.8819982158039121, 'b_cost': -1.8121332737470164, 'asc_car_ref': -0.8012014693839187, 'asc_car_diff_male': 0.8872036748436755, 'asc_car_diff_GA': -0.7764521690057898}
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 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.5 -0.046 -
1 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.25 -0.11 -
2 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.12 -0.098 -
3 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.062 -0.16 -
4 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.031 -0.15 -
5 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.016 -0.15 -
6 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.0078 -0.15 -
7 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.0039 -0.15 -
8 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.002 -0.15 -
9 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.00098 -0.14 -
10 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.00049 -0.14 -
11 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.00024 -0.14 -
12 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 0.00012 -0.14 -
13 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 6.1e-05 -0.14 -
14 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 3.1e-05 -0.14 -
15 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 1.5e-05 -0.14 -
16 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 7.6e-06 -0.14 -
17 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 3.8e-06 -0.14 -
18 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 1.9e-06 -0.14 -
19 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 9.5e-07 -0.14 -
20 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 4.8e-07 -0.14 -
21 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 2.4e-07 -0.14 -
22 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 1.2e-07 -0.14 -
23 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 6e-08 -0.14 -
24 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 3e-08 -0.14 -
25 0.13 -1.3 1.9 -1.9 1 -1.8 -0.8 0.89 -0.78 9.2e+03 0.19 1.5e-08 -0.14 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 26
Proportion of Hessian calculation: 1/1 = 100.0%
Optimization time: 0:00:02.255554
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000003~01.html has been generated.
File b21multiple_models_000003~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000004.iter
Parameter values restored from __b21multiple_models_000004.iter
Starting values for the algorithm: {'asc_train_ref': -1.0259779041009203, 'asc_train_diff_GA': 2.0417012426211842, 'b_time': -1.6680444783266624, 'lambda_time': 0.38240549309565697, 'b_cost': -1.0996092635678825, 'asc_car_ref': -0.06404634973454987, 'asc_car_diff_GA': -0.31338244218602307}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Optimization algorithm has converged.
Relative gradient: 5.030820226203682e-09
Cause of termination: Relative gradient = 5e-09 <= 6.1e-06
Number of function evaluations: 1
Number of gradient evaluations: 1
Number of hessian evaluations: 0
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 0
Optimization time: 0:00:00.701514
Calculate second derivatives and BHHH
File b21multiple_models_000004~01.html has been generated.
File b21multiple_models_000004~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000005.iter
Parameter values restored from __b21multiple_models_000005.iter
Starting values for the algorithm: {'asc_train_ref': -0.20264549785499536, 'asc_train_diff_GA': 2.0271387620175396, 'b_time': -1.7020556248822927, 'b_cost': -1.0632584808816732, 'asc_car_ref': -0.38890294740129805, 'asc_car_diff_GA': -0.4153454921314874}
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 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 1 0.14 +
1 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.5 -1.7 -
2 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.25 -1.5 -
3 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.12 -1 -
4 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.062 -0.8 -
5 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.031 -0.71 -
6 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.016 -0.67 -
7 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.0078 -0.65 -
8 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.0039 -0.64 -
9 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.002 -0.64 -
10 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.00098 -0.64 -
11 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.00049 -0.64 -
12 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.00024 -0.63 -
13 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 0.00012 -0.63 -
14 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 6.1e-05 -0.63 -
15 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 3.1e-05 -0.63 -
16 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 1.5e-05 -0.63 -
17 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 7.6e-06 -0.63 -
18 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 3.8e-06 -0.63 -
19 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 1.9e-06 -0.63 -
20 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 9.5e-07 -0.63 -
21 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 4.8e-07 -0.63 -
22 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 2.4e-07 -0.63 -
23 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 1.2e-07 -0.63 -
24 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 6e-08 -0.63 -
25 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 3e-08 -0.63 -
26 -0.67 -1.8 -2.1 -0.14 5.7e+03 0.19 1.5e-08 -0.63 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 27
Proportion of Hessian calculation: 2/2 = 100.0%
Optimization time: 0:00:00.509600
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000005~01.html has been generated.
File b21multiple_models_000005~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000006.iter
Parameter values restored from __b21multiple_models_000006.iter
Starting values for the algorithm: {'asc_train_ref': -0.2204187987317722, 'asc_train_diff_male': -1.151262135247798, 'asc_train_diff_GA': 1.9592103270125723, 'b_time': -1.696198863769209, 'lambda_time': 0.3340292133468033, 'b_cost_ref': -1.1000273249513268, 'b_cost_diff_GA': 0.9150724693206711, 'asc_car_ref': -0.42185727184552724, 'asc_car_diff_male': 0.4127039445438218, 'asc_car_diff_GA': -1.026915244358154}
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 -0.22 -1.2 2 -1.7 0.33 -1.1 0 0 0 0 -0.42 0.41 -1 5.1e+03 0.054 0.5 -0.6 -
1 -0.22 -1.2 2 -1.7 0.33 -1.1 0 0 0 0 -0.42 0.41 -1 5.1e+03 0.054 0.25 -0.058 -
2 -0.21 -1.2 2 -1.8 0.36 -0.94 -0.01 -0.078 0.25 0.012 -0.58 0.31 -1 5.1e+03 0.056 0.25 0.2 +
3 -0.21 -1.2 2 -1.8 0.36 -0.94 -0.01 -0.078 0.25 0.012 -0.58 0.31 -1 5.1e+03 0.056 0.12 -0.013 -
4 -0.14 -1.1 2 -1.9 0.47 -0.81 -0.088 -0.2 0.38 0.089 -0.7 0.19 -1.2 5.1e+03 0.047 0.12 0.17 +
5 -0.11 -1.1 2 -1.9 0.44 -0.73 -0.096 -0.26 0.5 0.091 -0.83 0.076 -1.2 5e+03 0.046 0.12 0.15 +
6 -0.11 -1.1 2 -1.9 0.44 -0.73 -0.096 -0.26 0.5 0.091 -0.83 0.076 -1.2 5e+03 0.046 0.062 0.0044 -
7 -0.047 -1.1 2 -2 0.38 -0.67 -0.13 -0.32 0.56 0.092 -0.89 0.014 -1.2 5e+03 0.046 0.062 0.12 +
8 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.062 0.27 +
9 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.031 -0.016 -
10 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.016 0.0078 -
11 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.0078 0.041 -
12 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.0039 0.052 -
13 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.002 0.057 -
14 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.00098 0.06 -
15 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.00049 0.061 -
16 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.00024 0.061 -
17 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 0.00012 0.062 -
18 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 6.1e-05 0.062 -
19 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 3.1e-05 0.062 -
20 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 1.5e-05 0.062 -
21 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 7.6e-06 0.062 -
22 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 3.8e-06 0.062 -
23 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 1.9e-06 0.062 -
24 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 9.5e-07 0.062 -
25 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 4.8e-07 0.062 -
26 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 2.4e-07 0.062 -
27 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 1.2e-07 0.062 -
28 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 6e-08 0.062 -
29 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 3e-08 0.062 -
30 -0.062 -1.1 2 -2.1 0.37 -0.61 -0.14 -0.38 0.62 0.089 -0.95 -0.049 -1.2 5e+03 0.042 1.5e-08 0.062 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 31
Proportion of Hessian calculation: 6/6 = 100.0%
Optimization time: 0:00:02.363975
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000006~01.html has been generated.
File b21multiple_models_000006~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000007.iter
Parameter values restored from __b21multiple_models_000007.iter
Starting values for the algorithm: {'asc_train': -0.7011872849436401, 'b_time': -1.2778589565196719, 'b_cost': -1.0837900371207714, 'asc_car': -0.15463267198926273}
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 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.5 -0.7 -
1 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.25 -0.58 -
2 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.12 -0.71 -
3 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.062 -0.63 -
4 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.031 -0.6 -
5 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.016 -0.58 -
6 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.0078 -0.57 -
7 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.0039 -0.57 -
8 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.002 -0.56 -
9 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.00098 -0.56 -
10 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.00049 -0.56 -
11 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.00024 -0.56 -
12 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 0.00012 -0.56 -
13 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 6.1e-05 -0.56 -
14 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 3.1e-05 -0.56 -
15 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 1.5e-05 -0.56 -
16 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 7.6e-06 -0.56 -
17 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 3.8e-06 -0.56 -
18 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 1.9e-06 -0.56 -
19 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 9.5e-07 -0.56 -
20 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 4.8e-07 -0.56 -
21 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 2.4e-07 -0.56 -
22 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 1.2e-07 -0.56 -
23 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 6e-08 -0.56 -
24 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 3e-08 -0.56 -
25 -0.7 -1.3 1 -1.1 -0.15 7.1e+03 0.15 1.5e-08 -0.56 -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 26
Proportion of Hessian calculation: 1/1 = 100.0%
Optimization time: 0:00:01.816486
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000007~01.html has been generated.
File b21multiple_models_000007~01.yaml has been generated.
Pareto: 8
Considered: 36
Removed: 5
summary, description = compile_estimation_results(
non_dominated_models, use_short_names=True
)
print(summary)
Model_000000 ... Model_000007
Number of estimated parameters 10 ... 5
Sample size 6768 ... 6768
Final log likelihood -4893.717 ... -5331.252
Akaike Information Criterion 9807.434 ... 10672.5
Bayesian Information Criterion 9875.633 ... 10706.6
asc_train_ref (t-test) -0.225 (-2.45) ...
asc_train_diff_male (t-test) -1.14 (-13.2) ...
asc_train_diff_GA (t-test) 1.96 (21) ...
b_time (t-test) -1.7 (-21.3) ... -1.28 (-11.4)
lambda_time (t-test) 0.335 (4.6) ... 1 (6.72)
b_cost_ref (t-test) -1.09 (-15) ...
b_cost_diff_GA (t-test) 2.09 (7.05) ...
asc_car_ref (t-test) -0.268 (-2.88) ...
asc_car_diff_male (t-test) 0.238 (2.4) ...
asc_car_diff_GA (t-test) -1.79 (-5.26) ...
b_cost (t-test) ... -1.08 (-16)
asc_train (t-test) ... -0.701 (-9.28)
asc_car (t-test) ... -0.155 (-2.78)
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) ...
[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:MALE-GA;b_cost:GA;train_tt:boxcox AIC=9807.434
Model_000001: asc:GA;b_cost:no_seg;train_tt:log AIC=17391.1
Model_000002: asc:MALE-GA;b_cost:no_seg;train_tt:log AIC=12910.5
Model_000003: asc:MALE-GA;b_cost:no_seg;train_tt:boxcox AIC=10216.17
Model_000004: asc:GA;b_cost:no_seg;train_tt:boxcox AIC=10005.51
Model_000005: asc:no_seg;b_cost:no_seg;train_tt:linear AIC=11020.15
Model_000006: asc:MALE-GA;b_cost:INCOME;train_tt:boxcox AIC=11625.66
Model_000007: asc:no_seg;b_cost:no_seg;train_tt:boxcox AIC=10672.5
Total running time of the script: (1 minutes 23.782 seconds)